Download Teacher Edition

State Standards
Curriculum Companion
Teacher’s Edition
Ron Larson
Laurie Boswell
Timothy D. Kanold
Lee Stiff
Copyright © by Houghton Mifflin Harcourt Publishing Company
All rights reserved. No part of this work may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying or recording, or by any information storage
and retrieval system, without the prior written permission of the copyright owner unless such copying
is expressly permitted by federal copyright law. Requests for permission to make copies of any part
of the work should be addressed to Houghton Mifflin Harcourt Publishing Company, Attn: Contracts,
Copyrights, and Licensing, 9400 South Park Center Loop, Orlando, Florida 32819.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best
Practices and Council of Chief State School Officers. All rights reserved.
This product is not sponsored or endorsed by the Common Core State Standards Initiative of the
National Governors Association Center for Best Practices and the Council of Chief State School
Officers.
Printed in the U.S.A.
ISBN 978-0-547-61822-7
1 2 3 4 5 6 7 8 9 10 XXX 20 19 18 17 16 15 14 13 12 11
4500000000
ABCDEFG
If you have received these materials as examination copies free of charge, Houghton
Mifflin Harcourt Publishing Company retains title to the materials and they may not
be resold. Resale of examination copies is strictly prohibited.
Possession of this publication in print format does not entitle users to convert this
publication, or any portion of it, into electronic format.
Larson Algebra 1
Common Core State Standards
Curriculum Companion
Teacher’s Edition
Contents
Correlation to Common Core State Standards. . . . . . . . . . . . . . . . . . . . . . .2
4-Year Scope and Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Essential Course of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Pacing for 50-Minute Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Pacing for 90-Minute Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Chapter Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Course Planners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Skills Readiness Pre-Course Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Additional Content
Lesson 1.5A Use Precision and Significant Digits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC1
Extension 3.1A Use Real and Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC8
Extension 3.4A Apply Properties of Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC11
Graphing Calculator Activity 4.7A Solve Linear Equations by Graphing Each Side . . . . . . . .CC13
Extension 5.7A Assess the Fit of a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC15
Graphing Calculator Activity 7.4A Multiply and Then Add Equations . . . . . . . . . . . . . . . . .CC18
Lesson 10.7A Solve Systems with Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC21
Lesson 10.8A Model Relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC28
Graphing Calculator Activity 10.8B Average Rate of Change . . . . . . . . . . . . . . . . . . . . . .CC35
Investigating Algebra Activity 13.5A Investigating Samples . . . . . . . . . . . . . . . . . . . . . .CC36
Lesson 13.6A Analyze Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC37
Investigating Algebra Activity 13.7A Investigating Dot Plots. . . . . . . . . . . . . . . . . . . . . .CC42
Extension 13.8A Analyze Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CC44
Standards for Mathematical Content
Correlation for Holt McDougal Larson Algebra 1, Geometry, and Algebra 2
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
Standards for Mathematical Content
(1 5 advanced; * 5 also a Modeling Standard)
Number and Quantity
CC.9-12.N.RN.1
Explain how the definition of the
meaning of rational exponents follows
from extending the properties of integer
exponents to those values, allowing for a
notation for radicals in terms of rational
exponents. For example, we define 51/3
to be the cube root of 5 because we want
(51/3)3 5 5(1/3)3 to hold, so (51/3)3 must
equal 5.
SE: 509–510
CC.9-12.N.RN.2
Rewrite expressions involving radicals and
rational exponents using the properties of
exponents.
SE: 509–510
CC.9-12.N.RN.3
Explain why the sum or product of two
CCCC: CC8–CC9
rational numbers is rational; that the sum
of a rational number and an irrational
number is irrational; and that the product of
a nonzero rational number and an irrational
number is irrational.
CC.9-12.N.Q.1
Use units as a way to understand problems
and to guide the solution of multi-step
problems; choose and interpret units
consistently in formulas; choose and
interpret the scale and the origin in graphs
and data displays.*
SE 5 Student Edition
2
Found throughout the
text. See for example:
SE: 17–18, 19–20, 27,
37, 42, 44–45, 47,
48, 137, 140–141,
227–228, 230–232,
429, 432–433, 519,
609, 612–613, 614,
665, 667–668, 886,
887–892, 893, 894
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 414–419, 459, 466,
469, 833, 1015
SE: 139, 423, 451,
457–459
SE: 420–427, 467, 469,
474, 505, 1015
SE: 50–56, 63, 68, 74,
78, 97, 160, 197,
317, 529, 705, 722,
723–725, 731–735,
739–742, 745,
747–752, 755–761,
763, 767–768, 777,
778, 780, 782–784,
801, 803–809,
810–817, 818,
820–825, 827,
829–836, 839–845,
850–854, 855,
858–861, 863–865,
866–867, 878,
888–889, 897,
916–917
Found throughout the
text. See for example:
SE: 5, 7, 9, 20, 24, 27,
30–31, 32, 34–36,
42, 46–47, 63, 74,
100, 103–104, 134,
137, 239, 242–243,
264, 345, 356, 358,
610, 616, 618–619,
624–625, 631, 987,
991–993, 995
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.N.Q.2
Define appropriate quantities for the
purpose of descriptive modeling.*
SE: 230, 337, 342, 888,
891, 893
CC.9-12.N.Q.3
Choose a level of accuracy appropriate to
CCCC: CC1–CC6
limitations on measurement when reporting
quantities.*
CC.9-12.N.CN.1
Know there is a complex number i such
that i 2 5 21, and every complex number
has the form a 1 bi with a and b real.
SE: 275–276
CC.9-12.N.CN.2
Use the relation i 2 5 21 and the
commutative, associative, and distributive
properties to add, subtract, and multiply
complex numbers.
SE: 276–278, 279–281,
291, 320–321, 323,
335, 1013
CC.9-12.N.CN.3
(1) Find the conjugate of a complex
number; use conjugates to find moduli and
quotients of complex numbers.
SE: 278–280, 291, 321,
323, 1013
CC.9-12.N.CN.4
(1) Represent complex numbers on
the complex plane in rectangular and
polar form (including real and imaginary
numbers), and explain why the rectangular
and polar forms of a given complex number
represent the same number.
SE: 278–280
CC.9-12.N.CN.5
(1) Represent addition, subtraction,
multiplication, and conjugation of
complex numbers geometrically on
the complex plane; use properties of this
representation for computation.
}
For example,
(1 – Ï 3 i)3 5 8 because
}
(1 – Ï 3 i) has modulus 2 and argument 120°.
SE: 281, 282
CC.9-12.N.CN.6
(1) Calculate the distance between
numbers in the complex plane as the
modulus of the difference, and the midpoint
of a segment as the average of the
numbers at its endpoints.
SE: 281, 282
CC.9-12.N.CN.7
Solve quadratic equations with real
coefficients that have complex solutions.
SE: 275, 279, 291, 323,
327, 1013
SE 5 Student Edition
Geometry
Algebra 2
Found throughout the
text. See for example:
SE: 13, 19, 20, 29, 34,
35, 36, 42, 54, 63,
66, 100, 101, 134,
155, 162, 181, 239,
254, 261, 262, 356,
373, 389, 560, 829
SE: 482, 727–728, 763,
765–768
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
3
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.N.CN.8
(1) Extend polynomial identities to the
complex numbers. For example, rewrite
x2 1 4 as (x 1 2i )(x 2 2i ).
SE: 380–382, 384, 407
CC.9-12.N.CN.9
(1) Know the Fundamental Theorem of
Algebra; show that it is true for quadratic
polynomials.
SE: 379–385, 405, 407
CC.9-12.N.VM.1
(1) Recognize vector quantities as having
both magnitude and direction. Represent
vector quantities by directed line segments,
and use appropriate symbols for vectors
and their magnitudes (e.g., v, |v|, ||v||, v ).
SE: 574–577, 587, A5,
A8
SE: A7, A9–A11
Number and Quantity
CC.9-12.N.VM.2
(1) Find the components of a vector by
subtracting the coordinates of an initial
point from the coordinates of a terminal
point.
SE: A7, A9
SE: A8, A10–A11
CC.9-12.N.VM.3
(1) Solve problems involving velocity and
other quantities that can be represented by
vectors.
SE: A9
SE: A11
(1) Add and subtract vectors.
SE: A5–A9
SE: A8, A10–A11
CC.9-12.N.VM.4
a. Add vectors end-to-end,
component-wise, and by the
parallelogram rule. Understand that the
magnitude of a sum of two vectors is
typically not the sum of the magnitudes.
b. Given two vectors in magnitude and
direction form, determine the magnitude
and direction of their sum.
c. Understand vector subtraction v 2 w
as v 1 (2w ), where 2w is the additive
inverse of w, with the same magnitude
as w and pointing in the opposite
direction. Represent vector subtraction
graphically by connecting the tips in the
appropriate order, and perform vector
subtraction component-wise.
SE 5 Student Edition
4
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
<…
Standards
CC.9-12.N.VM.5
Correlation to Standards for Mathematical Content
Descriptors
Algebra 1
(1) Multiply a vector by a scalar.
Geometry
Algebra 2
SE: A7, A9
SE: A8, A10
a. Represent scalar multiplication
graphically by scaling vectors and
possibly reversing their direction;
perform scalar multiplication
component-wise, e.g., as c(vx, vy) 5
(cvx, cvy).
b. Compute the magnitude of a scalar
multiple cv using ||cv || 5 |c |v. Compute
the direction of cv knowing that when
|c |v Þ 0, the direction of cv is either
along v (for c . 0) or against v (for
c , 0).
CC.9-12.N.VM.6
(+) Use matrices to represent and
manipulate data, e.g., to represent payoffs
or incidence relationships in a network.
SE: 94
SE: 583, 586–587
SE: 189, 192, 193
CC.9-12.N.VM.7
(1) Multiply matrices by scalars to produce
new matrices, e.g., as when all of the
payoffs in a game are doubled.
SE: 95
SE: 627–631, 639, 913
SE: 188, 191, 194,
224–225, 1012
CC.9-12.N.VM.8
(1) Add, subtract, and multiply matrices of
appropriate dimensions.
SE: 95
SE: 581, 584–585, 587,
912
SE: 187–188, 190–191,
194, 195–202, 209,
224, 1012
CC.9-12.N.VM.9
(1) Understand that, unlike multiplication
of numbers, matrix multiplication for
square matrices is not a commutative
operation, but still satisfies the associative
and distributive properties.
SE: 582–583, 586, 587,
912
SE: 188
CC.9-12.N.VM.10
(1) Understand that the zero and identity
matrices play a role in matrix addition and
multiplication similar to the role of 0 and 1
in the real numbers. The determinant of a
square matrix is nonzero if and only if the
matrix has a multiplicative inverse.
CC.9-12.N.VM.11
(1) Multiply a vector (regarded as a matrix
with one column) by a matrix of suitable
dimensions to produce another vector.
Work with matrices as transformations of
vectors.
SE: 582, 592–594, 600,
603
SE: A11
CC.9-12.N.VM.12
(1) Work with 2 3 2 matrices as a
transformations of the plane, and interpret
the absolute value of the determinant in
terms of area.
SE: 592–594, 600, 603
SE: 202
SE 5 Student Edition
SE: 210–212, 214, 1012
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
5
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
Interpret expressions that represent a
quantity in terms of its context.*
Found throughout the text.
See for example:
Found throughout the text.
See, for example:
Found throughout the text.
See for example:
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
SE: 96, 97–98, 99, 115,
121, 126–127,
244–245, 247–249,
253, 255, 256
SE: 49–52, 52–56,
433–435, 437, 439,
659–660, 699–700,
720–722, 730–732,
737–739, 747, 749,
755–757, 763, 779,
803–806, 810–813,
820–822
SE: 10, 11, 12, 13, 36,
66, 90, 239, 254,
261, 262, 337, 347,
356, 373, 389, 431,
829
SE: 106, 713, 804–806,
810–813, 819–822,
829–831, 872, 873
SE: 12–13, 14, 16, 24,
62, 65, 252–253,
255–256, 259–260,
263–264, 265,
319–320, 323,
346–347, 353–355,
356–357
Algebra
CC.9-12.A.SSE.1
b. Interpret complicated expressions by
viewing one or more of their parts as a
single entity. For example, interpret
P(1 1 r )n as the product of P and a
factor not depending on P.
CC.9-12.A.SSE.2
Use the structure of an expression to
identify ways to rewrite it. For example, see
x4 2 y4 as (x2)2 2 (y2)2, thus recognizing
it as a difference of squares that can be
factored as (x2 2 y2)(x2 1 y2).
SE: 96–98, 99–101,
105, 106, 120,
123–124, 125,
555–556, 561,
562–563, 569–570,
582, 583–584,
586–588, 592,
593–594, 596–597,
600–601, 603–604,
606–608, 610
CC.9-12.A.SSE.3
Choose and produce an equivalent form
of an expression to reveal and explain
properties of the quantity represented by
the expression.
SE: 524, 536, 593, 594,
595, 597, 598, 601,
602, 603, 604, 607,
609, 612, 641–642,
647, 669–670
a. Factor a quadratic expression to reveal
the zeros of the function it defines.
b. Complete the square in a quadratic
expression to reveal the maximum
or minimum value of the function it
defines.
c. Use the properties of exponents to
transform expressions for exponential
functions. For example the expression
1.15t can be rewritten as (1.151/12)12t
ø 1.01212t to reveal the approximate
equivalent monthly interest rate if the
annual rate is 15%.
SE 5 Student Edition
6
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 245–246, 248, 249,
255–256, 261–262,
287, 289–290,
490–491, 496
CCCC: CC2–CC3
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.A.SSE.4
Derive the formula for the sum of a finite
geometric series (when the common ratio
is not 1), and use the formula to solve
problems. For example, calculate mortgage
payments.
SE: 812–813, 815–817,
818, 820, 839, 841,
843, 847, 848, 872,
1021
CC.9-12.A.APR.1
Understand that polynomials form a system SE: 554–556, 557–559,
analogous to the integers, namely, they are
561, 562–565,
closed under the operations of addition,
565–568, 569–571,
subtraction, and multiplication; add,
572–574, 580, 581,
subtract, and multiply polynomials.
SE: 346–348, 349–352,
368, 369, 403, 407,
427, 474
CC.9-12.A.APR.2
Know and apply the Remainder Theorem:
For a polynomial p(x) and a number a, the
remainder on division by x 2 a is p (a ), so
p (a ) 5 0 if and only if (x 2 a ) is a factor
of p (x ).
SE: 363–365, 366–367,
371–373, 374–375,
404, 407, 411, 451,
1014
CC.9-12.A.APR.3
Identify zeros of polynomials when suitable
factorizations are available, and use the
zeros to construct a rough graph of the
function defined by the polynomial.
SE: 607, 641–642
SE: 353–356, 356–359,
362–365, 366–368,
369, 370–373,
374–377, 380, 382,
384, 387, 390–391,
399, 401, 404–405,
407, 419, 451
CC.9-12.A.APR.4
Prove polynomial identities and use them
to describe numerical relationships.
For example, the polynomial identity
(x2 1 y2)2 5 (x2 2 y2)2 1 (2xy )2 can be
used to generate Pythagorean triples.
SE: 569–571, 572–574,
600–602, 603–605,
741
SE: 347–348, 349–350,
353–355, 356–359
CC.9-12.A.APR.5
(1) Know and apply the Binomial Theorem
for the expansion of (x 1 y )n in powers of
x and y for a positive integer n, where
x and y are any numbers, with coefficients
determined for example by Pascal’s
Triangle. (The Binomial Theorem can be
proved by mathematical induction or
by a combinatorial argument.)
589, 605, 615,
616–617, 621, 624
SE 5 Student Edition
Geometry
Algebra 2
CCCC: CC7–CC8
SE: 693–694, 695, 697,
723, 735, 737, 741,
1019
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
7
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.A.APR.6
Rewrite simple rational expressions in
different forms; write a(x )/b(x ) in the form
q(x ) 1 r (x )/b(x ), where a(x ), b(x ), q(x ),
and r (x ) are polynomials with the degree
of r (x ) less than the degree of b (x ), using
inspection, long division, or, for the more
complicated examples, a computer algebra
system.
SE: 783, 784–787,
788–791, 794–797,
797–800, 810–811,
832, 835, 839, 949
SE: 362–364, 366, 377,
404, 407, 474, 1014
CC.9-12.A.APR.7
(1) Understand that rational expressions
SE: 802–805, 806–809,
form a system analogous to the rational
812–815, 816–819,
numbers, closed under addition,
826, 829, 830,
subtraction, multiplication, and division by a
833–834, 835, 906,
nonzero rational expression; add, subtract,
949
multiply, and divide rational expressions.
SE: 573–577, 577–580,
581, 582–585,
586–588, 595, 602,
605, 607, 625, 678,
1017
CC.9-12.A.CED.1
Create equations and inequalities in one
variable and use them to solve problems.
Include equations arising from linear and
quadratic functions, and simple rational
and exponential functions.*
Found throughout the
text. See for example:
SE: 137, 138–140, 143,
145–146, 150,
152–153, 155,
158–159, 358,
360–361, 365,
367–368, 371,
372–374, 380–381,
383, 385–386
Found throughout the
text. See, for example
SE: 13, 16, 19, 26, 30,
36, 39, 41, 45, 64,
65, 69, 309, 311,
313, 325, 330, 332,
339, 345, 348,
689–691, 692–693
SE: 19–20, 23–24, 42,
44, 46–47, 54,
57–58, 59, 64, 269,
270–271, 290, 295,
306, 356, 373, 376,
516, 594–595, 600,
937
CC.9-12.A.CED.2
Create equations in two or more variables
to represent relationships between
quantities; graph equations on coordinate
axes with labels and scales.*
Found throughout the
text. See, for example:
SE: 37, 39–40, 218,
219–221, 226–228,
229–232, 245,
247–249, 254–255,
257–259, 263, 265,
267–268, 283–285,
286–289, 292–295,
296–299, 303–305,
306–308, 313,
315–316
SE: 173–174, 175–177,
180–183, 184–187
Found throughout the
text. See, for example:
SE: 89–92, 93–96,
98–101, 101–104,
105, 106, 107,
109–111, 115–117,
118–119, 124–125,
127, 153–155,
157–158, 162, 166,
174–175, 176, 181,
184–185, 206, 209,
213, 216, 239,
242–243
CCCC: CC5–CC6
CCCC: CC7–CC8
SE 5 Student Edition
8
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.A.CED.3
Represent constraints by equations or
Found throughout the
inequalities, and by systems of equations
text. See for example:
and/or inequalities, and interpret solutions
SE: 29, 32–33, 37,
as viable or nonviable options in a modeling
39–40, 81, 83–84,
context. For example, represent inequalities
90, 92–93, 98,
describing nutritional and cost constraints
100–101, 150,
on combinations of different foods.*
Geometry
Algebra 2
Found throughout the
text. See for example:
SE: 36, 38–39, 100,
101, 103–104, 105,
134, 139–138, 139,
162, 165–166,
174–175, 176, 181,
185, 186, 213, 239,
242–243
152–153, 285,
288–289, 408,
410–411, 437, 438,
440–441, 453,
456–457, 468,
471–472, 473
CC.9-12.A.CED.4
Rearrange formulas to highlight a quantity
SE: 184–186, 187–189,
of interest, using the same reasoning as in
190, 191, 196, 197,
solving equations. For example, rearrange
199, 212, 940
Ohm’s law V 5 IR to highlight resistance R.*
SE: 483, 486–487, 843,
877
SE: 26–29, 30–32, 40,
58, 63, 65, 69, 88,
1010
CC.9-12.A.REI.1
Explain each step in solving a simple
Found throughout the
equation as following from the equality of
text. See for example:
numbers asserted at the previous step,
SE: 134–137, 137–138,
starting from the assumption that the
141–143, 144,
original equation has a solution. Construct a
148–149, 150,
viable argument to justify a solution method.
Found throughout the
text. See for example:
SE: 104, 105–106,
108–109, 111, 119,
136, 138, 178, 212,
899
Found throughout the
text. See for example:
SE: 18–20, 26–29
154–156, 168–169,
176–178, 184–186,
191, 192–196
CCCC: CC11–CC12
CC.9-12.A.REI.2
Solve simple rational and radical equations SE: 729–731, 732–734,
in one variable, and give examples showing
735, 755, 757,
how extraneous solutions may arise.
758–759, 760–761,
772, 820–822,
823–826, 830, 834,
835, 906, 948–949
SE 5 Student Edition
SE: 452–455, 456–459,
460–461, 462–463,
464, 465, 468, 469,
473, 474, 498, 513,
557, 589–592,
592–595, 596–597,
598–599, 600, 601,
602, 606, 607, 619,
678
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
9
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.A.REI.3
Solve linear equations and inequalities
in one variable, including equations with
coefficients represented by letters.
SE: 132–133, 134–137,
137–140, 141–143,
144–146, 148–150,
150–153, 154–156,
157–159, 160, 161,
163–164, 165–167,
173, 177–178,
179–181, 184–186,
187–189, 190, 191,
192–194, 196, 197,
354, 356–358,
359–361, 362,
363–365, 366–368,
369–371, 372–374,
377–378, 380–383,
384–387, 388,
390–392, 393–395
Found throughout the
text. See for example:
SE: 16, 26, 29, 37, 44,
54, 84, 89, 91, 155,
158, 161, 186, 229,
266, 268, 303, 311,
323, 330, 339, 357,
358, 363, 385
SE: 18–21, 21–24, 25,
26–29, 30–32, 33,
34–36, 37–40,
41–44, 44–47,
51–55, 55–58, 59,
62–64, 65, 66–67,
68–69
CC.9-12.A.REI.4
Solve quadratic equations in one variable.
SE: 585, 586, 589,
595–596, 597, 599,
602, 603, 605, 613,
618–619, 621,
622–623, 652–655,
655–658, 659, 661,
664–665, 666–668,
671–673, 674–676,
677, 678–680,
681–683, 695,
698–699, 701,
702–703, 707, 727
SE: 499, 882–883
SE: 252–255, 255–258,
259–262, 263–265,
266–269, 269–271,
272–273, 274, 282,
284–286, 288–291,
292–295, 296–299,
315, 319–321, 323
a. Use the method of completing the
square to transform any quadratic
equation in x into an equation of the
form (x 2 p)2 5 q that has the same
solutions. Derive the quadratic formula
from this form.
b. Solve quadratic equations by inspection
(e.g., for x2 5 49), taking square roots,
completing the square, the quadratic
formula and factoring, as appropriate
to the initial form of the equation.
Recognize when the quadratic formula
gives complex solutions and write them
as a 6 bi for real numbers a and b.
CC.9-12.A.REI.5
SE 5 Student Edition
10
Prove that, given a system of two equations CCCC: CC18–CC19
in two variables, replacing one equation by
the sum of that equation and a multiple of
the other produces a system with the same
solutions.
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.A.REI.6
Solve systems of linear equations exactly
and approximately (e.g., with graphs),
focusing on pairs of linear equations in two
variables.
SE: 426, 427–430,
430–433, 434,
435–438, 439–441,
442, 443, 444–447,
447–450, 451–454,
454–457, 458,
459–462, 462–465,
472, 473, 474,
475–478, 479,
480–481, 482–483,
485, 508
SE: 183, 186, 880
SE: 152, 153–155,
156–158, 159,
160–163, 164–167,
177, 178–181,
182–185, 186, 193,
202, 203–207,
207–209, 210–213,
214–217, 218–219,
220, 221, 222–224,
226, 227
CC.9-12.A.REI.7
Solve a simple system consisting of a linear CCCC: CC21–CC27
equation and a quadratic equation in two
variables algebraically and graphically. For
example, find the points of intersection
between the line y 5 23x and the circle
x 2 1 y 2 5 3.
SE: 658–661, 661–664,
667, 672, 673,
674–675, 677, 1018
CC.9-12.A.REI.8
(1) Represent a system of linear equations
as a single matrix equation in a vector
variable.
SE: 212–213, 214–217,
219, 226, 227, 1012
CC.9-12.A.REI.9
(1) Find the inverse of a matrix if it exists
and use it to solve systems of linear
equations (using technology for matrices of
dimension 3 3 3 or greater).
SE: 210–213, 214–217,
218–219, 226, 227,
1012
CC.9-12.A.REI.10
Understand that the graph of an equation
SE: 215
in two variables is the set of all its solutions
plotted in the coordinate plane, often
forming a curve (which could be a line).
SE: 74
CC.9-12.A.REI.11
Explain why the x-coordinates of the points
where the graphs of the equations y 5 f(x)
and y 5 g(x) intersect are the solutions of
the equation f(x) 5 g(x); find the solutions
approximately, e.g., using technology
to graph the functions, make tables of
values, or find successive approximations.
Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.*
SE 5 Student Edition
SE: 251–252, 643–646,
647–649, 651, 654,
713
CCCC: CC13–CC14
SE: 272–273, 360–361,
372, 374–375,
382–383, 387, 455,
460–461, 518,
523–525, 526–257,
931, 934, 938–939
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
11
Standards
Descriptors
Algebra 1
CC.9-12.A.REI.12
Graph the solutions to a linear inequality in SE: 404, 405–408,
two variables as a half-plane (excluding the
409–412, 413, 418,
boundary in the case of a strict inequality),
419, 422–423, 465,
and graph the solution set to a system of
466–468, 469–472,
linear inequalities in two variables as the
473, 474, 478, 479,
intersection of the corresponding half494, 559, 568, 580
planes.
Geometry
Algebra 2
SE: 207, 881
SE: 132–135, 135–138,
139, 140, 144, 145,
148, 150, 167,
168–170, 171–173,
174–175, 176, 186,
193, 209, 217, 221,
223, 227, 230, 232,
291, 299
Functions
CC.9-12.F.IF.1
Understand that a function from one set
(called the domain) to another set (called
the range) assigns to each element of the
domain exactly one element of the range.
If f is a function and x is an element of its
domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f
is the graph of the equation y = f(x).
SE: 35–36, 38, 43–45,
48, 49–50, 52, 56,
57, 167, 263, 264,
266–268
SE: 73–74, 77–78, 96,
141, 145, 148, 232,
1011
CC.9-12.F.IF.2
Use function notation, evaluate functions
for inputs in their domains, and interpret
statements that use function notation in
terms of a context.
SE: 262–265, 265–268,
269, 274, 275, 279,
330, 396–397, 941
SE: 75–76, 78, 81, 120,
127, 130–131,
141, 145, 149, 209,
258, 265, 291, 307,
379–383, 383–385,
388–389, 390–391,
393, 397, 399, 419,
428–431, 432–434,
435, 437, 439–441,
443, 445
CC.9-12.F.IF.3
Recognize that sequences are functions,
SE: 309–310, 539–540,
some-times defined recursively, whose
A3–A4, A5
domain is a subset of the integers. For
example, the Fibonacci sequence is defined
recursively by f(0) 5 f(1) 5 1, f(n 1 1) 5
f(n) 1 f(n 2 1) for n $ 1.
SE 5 Student Edition
12
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 78
SE: 794, 826, 827–830,
830–833, 835, 838,
839, 842, 843, 844,
846–847, 848, 1021
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.F.IF.4
For a function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms of
the quantities, and sketch graphs showing
key features given a verbal description
of the relationship. Key features include:
intercepts; intervals where the function
is increasing, decreasing, positive,
or negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.*
SE: 227–228, 230–232,
233, 238, 241–242,
267, 313, 315,
335–337, 339–341,
631, 633–634, 637,
639–640, 646,
648–649
CCCC: CC28–CC34
Geometry
Algebra 2
Found throughout the
text. See, for example:
SE: 91, 94–95, 106,
119, 125, 128–129,
130–131, 239,
241–243, 246–247,
250–251, 308,
311, 314, 336, 339,
387–389, 390–392,
396, 398, 908–911,
912–914
CCCC: CC2–CC3,
CC9–CC16
CC.9-12.F.IF.5
Relate the domain of a function to its graph SE: 44–45, 46, 51, 56,
and, where applicable, to the quantitative
57, 217–218,
relationship it describes. For example, if the
219–221, 228, 232,
function h(n) gives the number of person233, 263, 267 313,
hours it takes to assemble n engines in a
315, 526, 631, 633,
factory, then the positive integers would be
781
an appropriate domain for the function.*
SE: 72, 76, 78–79, 94,
96, 233, 251, 344,
391, 446–449,
49–451, 479, 482,
484, 487–488, 489,
491, 493–494, 496,
498, 503, 504,
559–561, 561–563,
565, 911
CC.9-12.F.IF.6
Calculate and interpret the average
rate of change of a function (presented
symbolically or as a table) over a specified
interval. Estimate the rate of change from
a graph.*
SE: 237–238, 240–242,
269, 294–295, 299,
301, 304–305, 307,
326, 327–330
SE: 85, 86–88, 104,
106, 115, 117,
118–119, 139, 143,
145, 146–147, 148
CCCC: CC35
CCCC: CC9–CC16
SE 5 Student Edition
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
13
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.F.IF.7
Graph functions expressed symbolically
and show key features of the graph, by
hand in simple cases and using technology
for more complicated cases.*
SE: 216–218, 219–220,
222, 225–228,
229–231, 244–246,
247–250, 251–252,
254, 257, 259,
262–265, 265–268,
269, 272–274, 275,
303, 306, 313, 315,
396–397, 521,
524–525, 532–533,
535–536, 560,
628–631, 632–634,
35–636, 638,
641–642, 643–646,
647, 650–651,
669–670, 692–693,
710–713, 714–716,
717, 766–767, 771,
773–774, 775–778,
779–781, 786–787,
792–793, A1–A2
SE: 182, 185–186, 499,
882–883
SE: 75–76, 77–78,
89–92, 93–96, 97,
121–122, 123–126,
127–129, 130–131,
236–239, 240–243,
245—248,
249–251, 336,
339–341, 342–344,
345, 387–389,
390–392, 446–449,
449–451, 478–480,
482–484, 486–488,
489–491, 493–494,
496–497, 502–503,
504–505, 558–561,
561–563564,
565–567, 568–571,
908–912, 912–914,
915–919, 919–922
a. Graph linear and quadratic functions
and show intercepts, maxima, and
minima.
b. Graph square root, cube root, and
piecewise-defined functions, including
step functions and absolute value
functions.
c. Graph polynomial functions, identifying
zeros when suitable factorizations are
available, and showing end behavior.
d. (1) Graph rational functions, identifying
zeros and asymptotes when suitable
factorizations are available, and
showing end behavior.
e. Graph exponential and logarithmic
functions, showing intercepts and end
behavior, and trigonometric functions,
showing period, midline, and amplitude.
CC.9-12.F.IF.8
Write a function defined by an expression in SE: 225–228, 229–230,
different but equivalent forms to reveal and
244–246, 247–250,
explain different properties of the function.
a. Use the process of factoring and
completing the square in a quadratic
function to show zeros, extreme values,
and symmetry of the graph, and
interpret these in terms of a context.
b. Use the properties of exponents to
interpret expressions for exponential
functions. For example, identify percent
rate of change in functions such as
y 5 (1.02)t, y 5 (0.97)t, y 5 (1.01)12t,
y 5 (1.2)t/10, and classify them as
representing exponential growth or decay.
CC.9-12.F.IF.9
SE 5 Student Edition
14
Compare properties of two functions
each represented in a different way
(algebraically, graphically, numerically
in tables, or by verbal descriptions). For
example, given a graph of one quadratic
function and an algebraic expression
for another, say which has the larger
maximum.
283–285, 286–289,
292–295, 296–299,
302–305, 305–308,
311–313, 314–316,
344, 522, 523, 534,
535, 635–636,
638–640, 641–642,
669–670
SE: 396–397, 521, 532,
628–630, 776
CCCC: CC28–CC34
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 236–239, 240–243,
244, 245–248,
249–251, 265,
478–481, 482–483,
486, 489
CCCC: CC2–CC3
CCCC: CC9–CC16
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.F.BF.1
Write a function that describes a
relationship between two quantities.*
SE: 285, 288–289,
294–295, 298–299,
304–305, 307–308,
313, 315–316,
326–327, 327–330,
331–332, 334,
335–338, 338–341,
342, 343, 348, 349,
352, 353, 520,
522–523, 524–525,
530, 531, 533, 535,
537, 686–687,
701, 778, 781, 787,
789–790, 799, 805,
808–809, 815,
817–819
SE: 112, 115–117,
117–120, 143, 145,
146, 148, 308, 311,
314, 316, 322, 323,
327, 393–396,
397–399, 400, 406,
407, 410–411,
428–431, 432–434,
435, 528, 529–533,
533–536, 542, 543,
547, 774, 775–777,
778–780, 781, 782,
786, 787, 791, 826,
827–830, 830–833,
941–943, 944–947
SE: 309–310, 539–540,
A3–A4, A5
SE: 798, 802–804,
806–808, 810–812,
814–816, 826,
827–830, 830–833,
838, 839, 841–842,
843, 844–845, 846
a. Determine an explicit expression, a
recursive process, or steps for calculation
from a context.
b. Combine standard function types using
arithmetic operations. For example, build a
function that models the temperature of a
cooling body by adding a constant function
to a decaying exponential, and relate these
functions to the model.
c. (+) Compose functions. For example, if
T(y ) is the temperature in the atmosphere
as a function of height, and h(t ) is the
height of a weather balloon as a function
of time, then T(h(t )) is the temperature at
the location of the weather balloon as a
function of time.
CC.9-12.F.BF.2
Write arithmetic and geometric sequences
both recursively and with an explicit
formula, use them to model situations, and
translate between the two forms.*
CC.9-12.F.BF.3
Identify the effect on the graph of replacing
f(x ) by f(x ) 1 k, kf(x ), f (kx ), and f (x 1 k)
for specific values of k (both positive
and negative); find the value of k given
the graphs. Experiment with cases and
illustrate an explanation of the effects
on the graph using technology. Include
recognizing even and odd functions from
their graphs and algebraic expressions for
them.
Geometry
Algebra 2
CCCC: CC44–CC45
SE: 263–265, 265–268,
269, 274, 290–291,
396–397, 521, 524,
532, 535–536,
669–670, 710–712,
713–714, 773–774,
775–777, 779
SE: 121–122, 123–126,
127–129, 139, 144,
145, 236–237, 240,
245, 249, 446–448,
449–450, 479, 482,
487, 489, 493, 496,
503, 504, 58–559,
561–562, 909–912,
913, 915–919,
919–922, 941–943,
944–947
CCCC: CC2–CC3,
CC9–CC16
SE 5 Student Edition
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
15
Standards
CC.9-12.F.BF.4
Descriptors
Algebra 1
Find inverse functions.
a. Solve an equation of the form f(x ) 5 c
for a simple function f that has an
inverse and write an expression for the
inverse. For example, f(x ) 5 2x 3 for
x . 0 or f (x ) 5 (x 1 1)/(x 2 1) for x Þ 1.
b. (1) Verify by composition that one
function is the inverse of another.
Geometry
Algebra 2
SE: 483, 485, 486–488
SE: 437, 438–442,
442–445, 453, 458,
474, 499, 501–502,
506, 516, 519, 522,
874, 875–877,
878–880, 931–934,
935–937
c. (1) Read values of an inverse function
from a graph or a table, given that the
function has an inverse.
d. (1) Produce an invertible function from
a non-invertible function by restricting
the domain.
CC.9-12.F.BF.5
(1) Understand the inverse relationship
between exponents and logarithms and use
this relationship to solve problems involving
logarithms and exponents.
CC.9-12.F.LE.1
Distinguish between situations that can
be modeled with linear functions and with
exponential functions.*
a. Prove that linear functions grow by
equal differences over equal intervals,
and that exponential functions grow by
equal factors over equal intervals.
SE: 499–502, 503–505,
506, 511, 513,
516–519, 520–522,
530–532, 538,
541–542, 543, 545,
546, 678, 1016
SE: 520–523, 523–527,
531, 535, 539–540,
684–687, 688–691,
692–693
CCCC: CC28–CC34
b. Recognize situations in which one
quantity changes at a constant rate per
unit interval relative to another.
c. Recognize situations in which a quantity
grows or decays by a constant percent
rate per unit interval relative to another.
SE 5 Student Edition
16
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 393–394, 774,
775–777, 778–780,
809
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.F.LE.2
Construct linear and exponential functions,
including arithmetic and geometric
sequences, given a graph, a description
of a relationship, or two input-output pairs
(include reading these from a table).*
SE: 44–45, 46–47,
283–285, 286–289,
292–295, 296–299,
302–305, 305–308,
309–310, 311–313,
314–316, 317, 318,
320, 321–322, 326,
327–330, 35–338,
338–341, 342,
520–523, 523–527,
530, 531–534,
535–538, 539–540,
A3–A4, A5
CC.9-12.F.LE.3
Observe using graphs and tables that a
CCCC: CC28–CC34
quantity increasing exponentially eventually
exceeds a quantity increasing linearly,
quadratically, or (more generally) as a
polynomial function.*
SE: 547
CC.9-12.F.LE.4
For exponential models, express as a
logarithm the solution to abct 5 d where
a, c, and d are numbers and the base b is
2, 10, or e; evaluate the logarithm using
technology.*
SE: 516, 520–522, 531,
536, 537, 538, 542,
543
CC.9-12.F.LE.5.
Interpret the parameters in a linear or
exponential function in terms of a context.*
CC.9-12.F.TF.1
Understand radian measure of an angle
as the length of the arc on the unit circle
subtended by the angle.
SE: 860–862, 863–865
CC.9-12.F.TF.2
Explain how the unit circle in the
coordinate plane enables the extension of
trigonometric functions to all real numbers,
interpreted as radian measures of angles
traversed counterclockwise around the unit
circle.
SE: 859–861, 866–870,
870–872, 899
SE 5 Student Edition
SE: 285, 294–295, 299,
304, 327, 329–330,
522–523, 527,
533–534, 537
Geometry
Algebra 2
SE: 98–101, 101–104,
105, 106, 108, 109,
112, 115–117,
118–119, 480–481,
483–485, 488,
489–491, 495,
496–497, 528,
529–530, 533–535,
798, 802–804,
806–808, 810–812,
814–816, 826,
827–830, 830–833,
838, 839, 841–842,
843, 844–845, 846
CCCC: CC9–CC16
SE: 91, 94, 106,
480–481, 482,
486, 489, 494
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
17
Standards
Descriptors
Algebra 1
Geometry
CC.9-12.F.TF.3
(1) Use special triangles to determine
geometrically the values of sine, cosine,
tangent for π/3, π/4 and π/6, and use the
unit circle to express the values of sine,
cosines, and tangent for x, p + x, and
2π – x in terms of their values for x, where
x is any real number.
SE: 853–854, 868, 874
CC.9-12.F.TF.4
(1) Use the unit circle to explain symmetry
(odd and even) and periodicity of
trigonometric functions.
The opportunity to
address this standard
can be found on the
following pages:
SE: 866–870, 908–912,
924
CC.9-12.F.TF.5
Choose trigonometric functions to model
periodic phenomena with specified
amplitude, frequency, and midline.*
SE: 910–911, 913–914,
916, 921–922, 940,
941–943, 944–947,
948, 963, 967, 969,
972
CC.9-12.F.TF.6
(1) Understand that restricting a
trigonometric function to a domain on
which it is always increasing or always
decreasing allows its inverse to be
constructed.
SE: 875, 897, 899
CC.9-12.F.TF.7
(1) Use inverse functions to solve
trigonometric equations that arise in
modeling contexts; evaluate the solutions
using technology, and interpret them in
terms of the context.*
SE: 931–934, 935–937,
938–939, 940, 947,
954, 964, 967, 969,
973, 1023
CC.9-12.F.TF.8
Prove the Pythagorean identity sin2(u) 1
cos2(u) 5 1 and use it to calculate
trigonometric ratios.
CC.9-12.F.TF.9
(1) Prove the addition and subtraction
formulas for sine, cosine, and tangent and
use them to solve problems.
SE: Ex. 32, p. 478
Algebra 2
SE: 924–927, 928–929,
934, 947, 954, 958,
966, 969, 973, 1023
SE: 949–951, 952–954,
962, 964, 968, 969,
973, 1023
Geometry
CC.9-12.G.CO.1
SE 5 Student Edition
18
Know precise definitions of angle, circle,
perpendicular line, parallel line, and line
segment, based on the undefined notions
of point, line, distance along a line, and
distance around a circular arc.
SE: 246, 247, 318–319,
321
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 2–3, 24–25, 81, 82,
147, 651, 746–747,
749
SE: 84, 859, 861
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.G.CO.2
Represent transformations in the plane
using, e.g., transparencies and geometry
software; describe transformations as
functions that take points in the plane as
inputs and give other points as outputs.
Compare transformations that preserve
distance and angle to those that do not
(e.g., translation versus horizontal stretch).
SE: 213–214
SE: 271, 273–275,
276–279, 285,
286, 289, 291, 408,
409–411, 412–415,
416, 421, 422, 427,
572–574, 576–579,
581, 585, 588,
589–590, 592,
593–594, 596, 597,
599–600, 602–603,
605, 606, 607,
608–609, 612–613,
615, 628, 630–631,
633
SE: 121–122, 123–126,
127–129, 988–989
CCCC: CC1–CC2,
CC3–CC8
CC.9-12.G.CO.3
Given a rectangle, parallelogram, trapezoid,
or regular polygon, describe the rotations
and reflections that carry it onto itself.
CC.9-12.G.CO.4
Develop definitions of rotations, reflections,
and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line
segments.
CC.9-12.G.CO.5
Given a geometric figure and a rotation,
reflection, or translation, draw the
transformed figure using, e.g., graph
paper, tracing paper, or geometry software.
Specify a sequence of transformations that
will carry a given figure onto another.
SE 5 Student Edition
SE: 214
SE: 619–621, 621–624,
639, 640, A10–A11
SE: 572–574, 576–579,
588, 589–592,
593–596, 598–601,
602–605, 607,
608–611, 611–615
SE: 213–214, 920–921
SE: 271, 273–275, 276,
278, 279, 280, 285,
286, 291, 572, 574,
576–578, 587, 588,
589–590, 593–594,
597, 598–599,
602–603, 606, 607,
608–611, 611–614,
616–618
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
19
Standards
Descriptors
CC.9-12.G.CO.6
Use geometric descriptions of rigid motions
to transform figures and to predict the
effect of a given rigid motion on a given
figure; given two figures, use the definition
of congruence in terms of rigid motions to
decide if they are congruent.
Algebra 1
Geometry
SE: 272–275, 276–279,
280, 285, 286, 289,
290–291, 572–575,
576–579, 581,
584–585, 587, 588,
589–592, 593–596,
597, 598–601,
602–605, 606, 607,
608–611, 611–615,
616–618, 634, 635,
636–638, 640
CCCC: CC1–CC2,
CC3–CC8
CC.9-12.G.CO.7
Use the definition of congruence in terms of
rigid motions to show that two triangles are
congruent if and only if corresponding pairs
of sides and corresponding pairs of angles
are congruent.
CCCC: CC1–CC2,
CC3–CC8
CC.9-12.G.CO.8
Explain how the criteria for triangle
congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms
of rigid motions.
CCCC: CC10–CC11
CC.9-12.G.CO.9
Prove geometric theorems about lines and
angles. Theorems include: vertical angles
are congruent; when a transversal crosses
parallel lines, alternate interior angles
are congruent and corresponding angles
are congruent; points on a perpendicular
bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
SE: 113–114, 118,
124–126, 129–130,
137, 153, 155–156,
159–160, 162–163,
168, 177, 190–192,
196, 303, 308
CC.9-12.G.CO.10
Prove theorems about triangles. Theorems
include: measures of interior angles of
a triangle sum to 180°; base angles of
isosceles triangles are congruent; the
segment joining midpoints of two sides of a
triangle is parallel to the third side and half
the length; the medians of a triangle meet
at a point.
SE: 216, 218–219, 224,
264–265, 269, 294,
295, 297, 300–301,
303–305, 308, 310,
312, 315–316, 318,
319–321, 323–324,
326–327, 328–329,
30, 334, 335, 338,
340–341, 932–936
SE 5 Student Edition
20
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
Algebra 2
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
Geometry
CC.9-12.G.CO.11
Prove theorems about parallelograms.
Theorems include: opposite sides are
congruent, the diagonals of a parallelogram
bisect each other, and conversely,
rectangles are parallelograms with
congruent diagonals.
SE: 514 515–517,
518–521, 522–525,
526–529, 530–531,
533–536, 537–540,
552–553, 554–557,
559, 561–563, 564
CC.9-12.G.CO.12
Make formal geometric constructions with
a variety of tools and methods (compass
and straightedge, string, reflective devices,
paper folding, dynamic geometry software,
etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle;
constructing perpendicular lines, including
the perpendicular bisector of a line
segment; and constructing a line parallel to
a given line through a point not on the line.
SE: 33–34, 169,
198–199, 235, 258,
261–262, 305, 307,
312, 314, 323, 401,
408, 527, 625, 629,
665, 671, 767
CC.9-12.G.CO.13
Construct an equilateral triangle, a square,
and a regular hexagon inscribed in a circle.
SE: 767
Algebra 2
CCCC: CC24–CC25
CC.9-12.G.SRT.1
Verify experimentally the properties of
dilations given by a center and a scale
factor:
SE: 408, 414, 625, 631,
633
a. A dilation takes a line not passing
through the center of the dilation to a
parallel line, and leaves a line passing
through the center unchanged.
CCCC: CC12,
CC13–CC19
b. The dilation of a line segment is longer
or shorter in the ratio given by the scale
factor.
CC.9-12.G.SRT.2
Given two figures, use the definition
of similarity in terms of similarity
transformations to decide if they
are similar; explain using similarity
transformations the meaning of
similarity for triangles as the equality
of all corresponding angles and the
proportionality of all corresponding pairs
of sides.
CCCC: CC13–CC19
CC.9-12.G.SRT.3
Use the properties of similarity
transformations to establish the AA criterion
for two triangles to be similar.
CCCC: CC20
SE 5 Student Edition
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
21
Standards
Descriptors
CC.9-12.G.SRT.4
Prove theorems about triangles. Theorems
include: a line parallel to one side of a
triangle divides the other two proportionally,
and conversely; the Pythagorean Theorem
proved using triangle similarity.
CC.9-12.G.SRT.5
Use congruence and similarity criteria
for triangles to solve problems and prove
relationships in geometric figures.
CC.9-12.G.SRT.6
Understand that by similarity, side ratios in
right triangles are properties of the angles
in the triangle, leading to definitions of
trigonometric ratios for acute angles.
SE: 466–467, 469, 473,
477
SE: 852–853
CC.9-12.G.SRT.7
Explain and use the relationship between
the sine and cosine of complementary
angles.
SE: 480
SE: 924, 927–928, 966
CC.9-12.G.SRT.8
Use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applied problems.
SE: 434, 437–439, 443,
445–446, 465, 468,
471–472, 474–476,
479–480, 482,
484–485, 487–488,
492, 496, 498, 500,
503
SE: 855, 857–858, 865,
877, 879–880, 896,
899, 901, 902–903,
914
CC.9-12.G.SRT.9
(1) Derive the formula A 5 }1 ab sin(C)
2
for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to
the opposite side.
SE: 479
SE: 885, 887
SE 5 Student Edition
22
Algebra 1
Geometry
Algebra 2
SE: 388–390, 394–395,
396, 397–398,
402–403, 448, 449,
452, 455–456, 457,
459, 463
SE: 174–175
SE: 738–739, 741–742,
746, 752, 757, 760
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 225–228, 228–231,
234–236, 236–239,
240–242, 243–246,
248, 249–252,
252–255, 256–258,
259–263, 283–284,
286, 290–291, 300,
372–375, 376–379,
381–383, 384–387,
388–391, 391–395,
397–399, 400–403,
405, 416, 420–421,
422, 424, 426,
449–452, 453–456,
457–460, 461–464
<…
Standards
Descriptors
CC.9-12.G.SRT.10
Correlation to Standards for Mathematical Content
Geometry
Algebra 2
(1) Prove the Laws of Sines and Cosines
and use them to solve problems.
SE: 490–491
SE: 881, 882–884,
886–888, 889–891,
892–894, 896, 897,
900, 901, 1022
CC.9-12.G.SRT.11
(1) Understand and apply the Law of
Sines and the Law of Cosines to find
unknown measurements in right and nonright triangles (e.g., surveying problems,
resultant forces).
SE: 490–491
SE: 881, 882–884,
886–888, 889–891,
892–894, 896, 897,
900, 901, 1022
CC.9-12.G.C.1
Prove that all circles are similar.
CCCC: CC13–CC19
CC.9-12.G.C.2
Identify and describe relationships among
inscribed angles, radii, and chords. Include
the relationship between central, inscribed,
and circumscribed angles; inscribed angles
on a diameter are right angles; the radius
of a circle is perpendicular to the tangent
where the radius intersects the circle.
SE: 650, 653–654,
656–658, 659–661,
661–663, 664–666,
667–670, 671,
672–675, 676–679,
705, 709–710, 712
CC.9-12.G.C.3
Construct the inscribed and circumscribed
circles of a triangle, and prove properties
of angles for a quadrilateral inscribed in a
circle.
SE: 306, 307, 312, 314,
675, 678
CC.9-12.G.C.4
(1) Construct a tangent line from a point
outside a given circle to the circle.
CCCC: CC24–CC25
CC.9-12.G.C.5
Derive using similarity the fact that the
length of the arc intercepted by an angle
is proportional to the radius, and define
the radian measure of the angle as the
constant of proportionality; derive the
formula for the area of a sector.
SE: 747, 749, 756, 758
CC.9-12.G.GPE.1
Derive the equation of a circle of given
center and radius using the Pythagorean
Theorem; complete the square to find the
center and radius of a circle given by an
equation.
SE: 699, 703
CC.9-12.G.GPE.2
Derive the equation of a parabola given a
focus and directrix.
SE: 620–622
CC.9-12.G.GPE.3
(1) Derive the equations of ellipses and
hyperbolas given foci and directrices.
SE: 638, 646
CC.9-12.G.GPE.4
Use coordinates to prove simple geometric
theorems algebraically. For example, prove
or disprove that a figure defined by four
given points in the coordinate plane is a
rectangle;
prove or disprove that the point
}
(1,Î3 ) lies on the circle centered at the
origin and containing the point (0, 2).
SE 5 Student Edition
Algebra 1
SE: 860–861
CCCC: CC27–CC28
SE: 294, 296–297,
298–301, 302, 309,
316, 320–321, 322,
344, 350–351, 17,
518–519, 525,
526–527, 531, 532,
538, 542, 546–547,
549, 555
SE: 626, 656, 664, 672,
673, 678, 1018
SE: 614, 617, 619
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
23
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.G.GPE.5.
Prove the slope criteria for parallel and
perpendicular lines and use them to solve
geometric problems (e.g., find the equation
of line parallel or perpendicular to a given
line that passes through a given point).
SE: 318–320, 321–323,
330, 343, 347, 349,
353
SE: 172–173, 175–176,
179, 180–181,
185–186, 193, 195,
197, 201, 204–205,
206, 209, 210–211
SE: 84–85, 86, 99,
102–103, 106, 145,
149
CC.9-12.G.GPE.6
Find the point on a directed line segment
between two given points that partitions
the segment in a given ratio.
CC.9-12.G.GPE.7
Use coordinates to compute perimeters
of polygons and areas of triangles and
rectangles, e.g., using the distance
formula.*
CC.9-12.G.GMD.1
Give an informal argument for the formulas
for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and
cone. Use dissection arguments, Cavalieri’s
principle, and informal limit arguments.
SE: 761, 769, 819–820,
828, 829
CC.9-12.G.GMD.2
(1) Give an informal argument using
Cavalieri’s principle for the formulas for the
volume of a sphere and other solid figures.
SE: 821–822, 824, 827,
832, 836, 859, 919
CC.9-12.G.GMD.3
Use volume formulas for cylinders,
pyramids, cones, and spheres to solve
problems.*
SE: 819–822, 822–825,
826–827, 829–831,
832–836, 837,
840–841, 843–845,
854, 855, 856,
859–860, 861,
862–863, 864–865,
866–867, 919
SE: 332, 334–335,
350–351, 356,
357–359, 360–361,
367, 369, 373, 386,
389, 392, 400, 407,
408, 410, 567,
569–571, 574,
579–580, 601, 610
CC.9-12.G.GMD.4
Identify the shapes of two-dimensional
cross-sections of three-dimensional
objects, and identify three-dimensional
objects generated by rotations of twodimensional objects.
SE: 797, 799–801, 818,
821, 825, 839, 864
SE: 649, 657, 667
SE 5 Student Edition
24
CCCC: CC22–CC23
SE: 750
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 22, 50–51, 53, 58,
63, 724, 732
CCCC: CC32–CC33
SE: 857
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
Geometry
CC.9-12.G.MG.1
Use geometric shapes, their measures, and
their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as
a cylinder).*
SE: 188–189, 494, 525,
791
Found throughout the
text. See, for example:
SE: 508, 510, 512, 517,
519–520, 523–524,
526, 528, 531, 532,
537, 539, 545, 657,
663, 665, 669, 674,
679, 682, 685, 717,
722, 725, 731, 735,
747, 751, 755, 760,
767, 796, 800, 805,
807–808, 813, 814
CC.9-12.G.MG.2
Apply concepts of density based on area
and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic
foot).*
SE: 30, 153, 183, 412,
516–517, 878
CCCC: CC30–CC31
CC.9-12.G.MG.3
Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost; working with typographic
grid systems based on ratios).*
Algebra 2
Found throughout the
text. See, for example:
SE: 7, 23, 31, 54, 58,
68, 107, 132, 151,
159, 170, 189, 213,
217, 223, 226, 230,
236, 238, 242, 269,
274, 278, 291, 295,
300, 317, 329, 342,
362, 390, 416, 455,
616–618, 677, 679,
722, 725, 738, 742
Statistics and Probability
CC.9-12.S.ID.1
Represent data with plots on the real
number line (dot plots, histograms, and box
plots).*
SE: 882–885, 886,
887–892, 893, 894,
900, 901, 904–905,
950
SE: 888–889
SE: 724–730, 731,
1008–1009
SE: 887
SE: 744–745, 749, 751,
787, 791
CCCC: CC42
CC.9-12.S.ID.2
Use statistics appropriate to the shape of
the data distribution to compare center
(median, mean) and spread (interquartile
range, standard deviation) of two or more
different data sets.*
SE: 874, 875–878,
879–880, 883, 885,
887, 891–892, 893,
901, 918
CCCC: CC44–CC45
SE 5 Student Edition
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
25
Standards
Descriptors
Algebra 1
CC.9-12.S.ID.3
Interpret differences in shape, center, and
spread in the context of the data sets,
accounting for possible effects of extreme
data points (outliers).*
SE: 878, 880, 885, 888,
891, 892, 893, 894,
901
CC.9-12.S.ID.4
Use the mean and standard deviation of
a data set to fit it to a normal distribution
and to estimate population percentages.
Recognize that there are data sets for
which such a procedure is not appropriate.
Use calculators, spreadsheets, and tables
to estimate areas under the normal curve.*
CC.9-12.S.ID.5
CC.9-12.SID.6
Algebra 2
SE: 746–748, 756
SE: 758–762, 785, 787,
1020
CCCC: CC31, CC33
Summarize categorical data for two
categories in two-way frequency tables.
Interpret relative frequencies in the context
of the data (including joint, marginal, and
conditional relative frequencies). Recognize
possible associations and trends in the
data.*
SE: 844, 847, 848, 870
Represent data on two quantitative
variables on a scatter plot, and describe
how the variables are related.*
SE: 26–330, 331–332,
335–341, 342–343,
348, 349, 352–353,
942
a. Fit a function to the data; use functions
fitted to data to solve problems in the
context of the data. Use given functions
or choose a function suggested by
the context. Emphasize linear and
exponential models.
Geometry
SE: 722, 1008
CCCC: CC37–CC41
SE: 115–117, 119,
120, 139, 143, 145,
148, 233, 271, 311,
314, 323, 327, 396,
398–399, 400, 530,
532–535, 537, 543,
547, 774, 775–780,
786, 787, 791, 943,
946, 947, 969,
1011, 1014, 1020
CCCC: CC15–CC16
b. Informally assess the fit of a function by
plotting and analyzing residuals.
c. Fit a linear function for a scatter plot
that suggests a linear association.
CC.9-12.S.ID.7
Interpret the slope (rate of change) and the
intercept (constant term) of a linear model
in the context of the data.*
SE: 237–238, 240–241,
245, 248–249,
304–305, 338, 340,
341
CC.9-12.S.ID.8
Compute (using technology) and interpret
the correlation coefficient of a linear fit.*
SE: 332, 333
SE: 114, 117–118
CC.9-12.S.ID.9
Distinguish between correlation and
causation.*
SE: 333
SE: 120
CC.9-12.S.IC.1
Understand statistics as a process for
making inferences about population
parameters based on a random sample
from that population.*
SE: 871, 874
SE 5 Student Edition
26
CCCC: CC36
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 173, 177–178, 182,
186
SE: 369
SE: 87, 91, 94
SE: 770–771
CCCC: CC34–CC35
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
CC.9-12.S.IC.2
Decide if a specified model is consistent
with results from a given data-generating
process, e.g., using simulation. For
example, a model says a spinning coin
falls heads up with probability 0.5. Would
a result of 5 tails in a row cause you to
question the model?*
SE: 849–850, 868–869
Recognize the purposes of and differences
among sample surveys, experiments,
and observational studies; explain how
randomization relates to each.*
SE: 871, 873–874
CC.9-12.S.IC.4
Use data from a sample survey to estimate
a population mean or proportion; develop
a margin of error through the use of
simulation models for random sampling.*
CCCC: CC36
CC.9-12.S.IC.5
Use data from a randomized experiment to
compare two treatments; use simulations
to decide if differences between
parameters are significant.*
SE: 850, 869, 874
Evaluate reports based on data.*
SE: 874
CC.9-12.S.IC.3
CC.9-12.S.IC.6
Geometry
Algebra 2
SE: 714, 722
CCCC: CC28–CC29
SE: 766–767, 769, 773,
782, 1020
CCCC: CC36–CC41
SE: 768–771, 780, 782,
787, 1020
CCCC: CC34–CC35
CCCC: CC42–CC43
CCCC: CC37–CC41
SE: 369, 770
SE: 771
CCCC: CC36–CC41
CC.9-12.S.CP.1
Describe events as subsets of a sample
space (the set of outcomes) using
characteristics (or categories) of the
outcomes, or as unions, intersections, or
complements of other events (“or,” “and,”
“not”).*
SE: 843, 846, 861,
865–867, 870,
930–931
CC.9-12.S.CP.2
Understand that two events A and B are
independent if the probability of A and B
occurring together is the product of their
probabilities, and use this characterization
to determine if they are independent.*
SE: 862–865, 898, 901,
907, 950
Understand the conditional probability of
A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that
the conditional probability of A given B is
the same as the probability of A, and the
conditional probability of B given A is the
same as the probability of B.*
SE: 863
CC.9-12.S.CP.3
SE 5 Student Edition
SE: 698, 706, 707–713,
716, 732, 1019
SE: 777, 893
SE: 717–723
CCCC: CC17–CC24
SE: 893
SE: 722
CCCC: CC17–CC24
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
27
Standards
Descriptors
CC.9-12.S.CP.4
Construct and interpret two-way frequency SE: 844, 847–848
tables of data when two categories
are associated with each object being
classified. Use the two-way table as
a sample space to decide if events
are independent and to approximate
conditional probabilities. For example,
collect data from a random sample of
students in your school on their favorite
subject among math, science, and English.
Estimate the probability that a randomly
selected student from your school will favor
science given that the student is in tenth
grade. Do the same for other subjects and
compare the results.*
SE: 19, 722
Recognize and explain the concepts of
conditional probability and independence in
everyday language and everyday situations.
For example, compare the chance of having
lung cancer if you are a smoker with the
chance of being a smoker if you have lung
cancer.*
SE: 717, 719–720, 722
CC.9-12.S.CP.5
Geometry
Algebra 2
CCCC: CC17–CC24
CCCC: CC17–CC24
Find the conditional probability of A given
B as the fraction of B’s outcomes that also
belong to A, and interpret the answer in
terms of the model.*
SE: 863, 865
CC.9-12.S.CP.7
Apply the Addition Rule, P(A or B ) 5 P (A )
1 P (B ) 2 P (A and B ), and interpret the
answer in terms of the model.*
SE: 862, 864, 865, 898
SE: 707–708, 710–711,
713, 736, 737
CC.9-12.S.CP.8
(1) Apply the general Multiplication Rule in
a uniform probability model, P(A and B)
5 P (A)P (B|A ) 5 P (B)P (A|B ), and interpret
the answer in terms of the model.*
SE: 862–864
SE: 718–722, 736, 737
CC.9-12.S.CP.9
(1) Use permutations and combinations to
compute probabilities of compound events
and solve problems.*
SE: 853, 855, 857, 859,
861–867
CC.9-12.S.MD.1
(1) Define a random variable for a quantity
of interest by assigning a numerical value
to each event in a sample space; graph the
corresponding probability distribution using
the same graphical displays as for data
distributions.*
CC.9-12.S.CP.6
SE 5 Student Edition
28
Algebra 1
SE: 719–721, 722–723
CCCC: CC17–CC24
CCCC: CC17–CC24
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
SE: 699, 702, 712
SE: 724–725, 727–728
<…
Correlation to Standards for Mathematical Content
Standards
Descriptors
Algebra 1
Geometry
Algebra 2
CC.9-12.S.MD.2
(1) Calculate the expected value of a
random variable; interpret it as the mean of
the probability distribution.*
SE: 750
CC.9-12.S.MD.3
(1) Develop a probability distribution for
a random variable defined for a sample
space in which theoretical probabilities can
be calculated; find the expected value. For
example, find the theoretical probability
distribution for the number of correct
answers obtained by guessing on all five
questions of a multiple-choice test where
each question has four choices, and find
the expected grade under various grading
schemes.*
SE: 724–726, 727–730,
731, 732, 736–737
CC.9-12.S.MD.4
(1) Develop a probability distribution for
a random variable defined for a sample
space in which probabilities are assigned
empirically; find the expected value. For
example, find a current data distribution on
the number of TV sets per household in the
United States, and calculate the expected
number of sets per household. How many
TV sets would you expect to find in 100
randomly selected households?*
SE: 726–729
CC.9-12.S.MD.5
(1) Weigh the possible outcomes of a
decision by assigning probabilities to payoff
values and finding expected values.*
SE: 750
a. Find the expected payoff for a game of
chance. For example, find the expected
winnings from a state lottery ticket or a
game at a fast-food restaurant.
b. Evaluate and compare strategies on the
basis of expected values. For example,
compare a high-deductible versus a
low-deductible automobile insurance
policy using various, but reasonable,
chances of having a minor or a major
accident.
CC.9-12.S.MD.6
(1) Use probabilities to make fair decisions
(e.g., drawing by lots, using a random
number generator).*
SE: 173, 872
SE: 766–767
CCCC: CC25–CC26
CC.9-12.S.MD.7
(1) Analyze decisions and strategies using
probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at
the end of a game).*
SE: 847
SE: 723
SE 5 Student Edition
CCCC: CC25–CC26
CCCC 5 Common Core Curriculum Companion
Correlation to Standards for Mathematical Content
29
4-Year Scope and Sequence
Holt McDougal Larson Algebra 1
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Problem Solving Strategies
R
R
R
R
Identify relationships
R
R
R
R
Choose an operation
R
R
R
R
Choose a method of computation
T
R
R
R
Make generalizations
R
R
R
R
Use a formula
T
R
R
R
Estimate or give an exact answer
R
R
R
R
Prioritize and sequence information
R
R
R
R
Identify too much or too little information
R
R
R
R
Write an equation
T
TR
R
R
Write the problem in your own words/Restate the question
R
R
R
R
Eliminate answer choices
R
R
R
R
Check that your answer is reasonable
R
R
R
R
Write algebraic expressions
R
R
R
R
Analyze units
R
R
R
R
Use a simulation
T
R
R
R
Interpret unfamiliar words/Understand the words in the problem
R
R
R
R
Identify important details in the problem
R
R
R
R
Choose a problem-solving strategy
R
R
R
R
Check that the question is answered
R
R
R
R
Break into simpler parts
R
R
R
R
Translate between words and math
R
R
R
R
Identify missing information
R
R
R
R
Make and test predictions
R
R
R
R
Explain and justify answers
R
R
R
R
Evaluate evidence and conclusions
T
R
R
R
Interpret charts, tables, and graphs
T
T
R
T
Classify and sort
R
R
R
R
Identify spatial relationships
R
R
R
R
Problem Solving
Skills
Reasoning
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
30
4-Year Scope and Sequence
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Use visual representations to solve problems
R
R
R
R
Solve nonroutine problems
R
R
R
R
Compare and contrast
R
R
R
R
Draw conclusions
R
R
R
R
Inductive and deductive reasoning
I
T
T
R
Evaluate exponents
R
R
R
R
Negative exponents
T
T
R
I
T
Number and Quantity
Read and write numbers
Evaluate rational exponents
Properties of Exponents
I
T
R
Scientific notation
T
R
R
Properties of Real Numbers
I
T
R
Integers
R
R
R
R
Square roots
T
R
R
R
Absolute value
T
R
R
R
I
T
R
R
IT
R
Quantities
Choose and interpret units
Precision and accuracy
Complex Numbers
Operations with complex numbers
IT
Complex numbers in the complex plane
IT
Ratio
Cross products
T
R
R
R
Indirect measurement
T
T
R
R
Solve proportions
T
R
R
R
Scale factor
T
R
R
R
Scale drawings
TR
R
R
Similar figures
TR
R
T
Percents greater than 100% and less than 1%
T
TR
Percent of a number
TR
TR
R
R
Percent one number is of another
T
TR
R
R
Percent change (increase and decrease)
T
TR
R
R
Proportion
R
Percent
R
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
31
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Find number when percent is known
T
TR
R
R
Circle graph
T
R
R
R
Simple interest
T
TR
Compound interest
IT
T
T
TR
R
R
Decimals
TR
R
R
R
Fractions
R
R
R
R
Mixed numbers
TR
R
R
R
Integers
TR
TR
R
R
Of exponential expressions
IT
TR
R
R
Decimal by a whole number
R
R
R
R
Decimal by a decimal
TR
R
R
R
Fraction by a whole number
R
R
R
R
Fraction by a fraction
TR
R
R
R
Mixed numbers
TR
R
R
R
Integers
TR
TR
R
R
Formulas
R
R
R
R
Variables
R
R
R
R
Write and evaluate algebraic expressions
R
R
R
R
Identify and combine like terms
R
R
R
R
Monomials: simplify, operations
IT
T
Polynomials
IT
T
Binomials and trinomials, definition
IT
T
R
IT
R
R
Operations
Order of operations
Order of operations
Addition and Subtraction
Multiplication and Division
Algebra and Functions
Equations and Expressions
Degree
R
R
Simplify polynomial expressions
IT
T
R
R
Add and subtract polynomials
IT
T
R
R
Multiply binomials
IT
T
R
R
FOIL method
IT
T
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
32
R
4-Year Scope and Sequence
R
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Difference of squares
IT
R
Perfect-square trinomial
IT
R
Multiply polynomials by monomials
IT
T
R
R
Divide polynomials by monomials
T
R
R
Divide polynomials by polynomials
IT
R
Properties of polynomial and rational expressions
IT
Factor binomials
IT
R
R
Factor trinomials
IT
R
R
Factor difference of squares
IT
R
Factor perfect-square trinomials
IT
R
Factor Theorem
IT
Binomial expansion
IT
Binomial Theorem
IT
Rational expressions: simplify, graph
IT
R
TR
Radical expressions: simplify, evaluate
IT
R
TR
Simplify expressions with complex numbers
Write linear equations
IT
T
TR
R
R
1-step equations
T
TR
R
R
2-step equations
T
TR
R
R
Multistep equations
T
TR
R
R
Equations with variables on both sides
T
TR
R
R
Relate graphs and equations
T
R
R
R
IT
R
R
Solve equations
Solve equations by factoring
Linear equations
T
T
R
R
Systems of equations
IT
T
R
TR
Absolute-value equations
IT
R
TR
Rational equations
IT
R
TR
T
R
TR
Quadratic equations
IT
Polynomial equations
Exponential equations
IT
IT
IT
TR
R
Logarithmic equations
Radical equations
TR
IT
IT
R
TR
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
33
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Compare numbers
R
R
R
R
Algebraic inequality
T
R
R
R
Write an inequality for a problem situation
T
R
R
R
1-step inequalities
T
TR
R
R
2-step inequalities
T
T
R
R
Graph inequalities
T
T
R
R
Graph compound inequalities
I
T
R
R
Graph inequalities in two variables
IT
R
R
Absolute-value inequalities
IT
Inequalities
Solve inequalities
TR
Rational inequalities
IT
Radical inequalities
IT
Coordinate plane
Ordered pairs
R
R
R
R
Origin
R
R
R
R
Axes
R
R
R
R
Graph in four quadrants
T
R
R
R
Find area by coordinates
R
Relations
R
R
Functions
T
TR
R
R
Transformations
T
TR
R
R
Linear equations
T
TR
R
R
Nonlinear equations
T
T
R
R
Systems of equations
T
T
R
R
Inequalities
T
T
R
R
IT
R
R
T
R
R
Systems of inequalities
Quadratic equations
T
Conics
Conic sections
Parabolas
T
Circles
T
T
R
TR
R
R
Ellipses
IT
Hyperbolas
IT
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
34
IT
4-Year Scope and Sequence
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Algebra 2
General equation for conics
IT
Identify conic from equation
IT
Transformations of conics
IT
Vectors
Magnitude, direction
I
I
Vector addition
I
I
Patterns
Arithmetic sequences
T
R
R
Arithmetic series
IT
Geometric sequences
I
T
Geometric series
IT
Infinite sequence
IT
Infinite geometric series
IT
Sigma notation
IT
Fibonacci sequence
IT
R
R
Pascal’s triangle
Fractals
R
T
IT
I
Binomial expansion
T
IT
Recursion
I
T
TR
R
Functions and relations
Evaluate functions
T
Operations with functions
T
Composite functions
IT
Relations
IT
T
Inverse of function or relation
Linear functions
IT
T
Rational functions
T
R
R
IT
T
Quadratic functions
IT
IT
T
Exponential functions
IT
T
T
Logarithmic functions
IT
Polynomial functions
IT
T
Radical functions
IT
T
Trigonometric functions
IT
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
35
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Modeling
Linear models
IT
R
Exponential models
IT
R
Quadratic models
I
TR
Matrices
Matrix operations
IT
IT
T
Determinants
IT
Identity and inverse matrices
IT
Solve systems of equations
IT
Transformation matrices
IT
Probability
Probability as ratio, proportion, decimal, percent
T
R
R
R
Making predictions
T
R
R
R
Tree diagrams
T
R
R
Combinations
T
T
R
Permutations
T
T
R
Fundamental Counting Principle
T
R
R
Factorial
IT
T
R
Mutually exclusive
T
T
R
R
Complementary events
T
T
R
R
Independent/dependent events
T
T
R
R
Finding outcomes
Theoretical probability
Conditional Probability
IT
TR
Experimental probability
Simulations
T
T
T
Random numbers
I
I
T
T
T
T
Frequency table/chart
R
R
Stem-and-leaf plot
T
R
R
IT
R
Odds
Odds
Data Analysis and Statistics
Organizing and Displaying Data
Two-way tables
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
36
4-Year Scope and Sequence
R
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Dot plot
IT
TR
R
R
Venn diagram
T
R
R
R
Histogram
T
R
R
R
Box-and-whisker plot
T
R
R
R
Scatter plot
R
R
R
R
Analyzing data
Surveys, experiments, and observational studies
I
TR
Identify correlation
T
T
R
Quartiles
T
T
Interquartile range
T
T
Line of best fit
T
T
R
Make predictions
R
R
R
Mean, median, mode
T
R
Determine best measure of central tendency
T
R
R
Standard deviation
I
T
Variance
I
T
R
R
Frequency distribution
IT
Normal distribution (bell curve)
IT
Binomial distribution
IT
Shape of distribution
I
TR
Standard normal curve
IT
Geometry
Points, lines, planes
R
R
Ray
R
R
Vertex
R
R
Classify
R
R
Vertical, adjacent, complementary, supplementary
R
R
Congruent
R
R
Relationships of angles formed by parallel lines and a transversal
IT
R
R
Angles
Angle relationship theorems
R
R
Sum of angle measures
R
R
Identify unknown angle measures
R
R
R
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
37
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Lines and line segments
Properties of intersecting lines and segments
T
Properties of parallel lines and segments
T
R
TR
Properties of perpendicular lines and segments
T
R
TR
TR
Triangles
Classify
T
Sum of the measures of the angles is 180 degrees
T
R
R
R
Right triangle relationships
T
R
R
R
Pythagorean Theorem
T
R
R
R
R
Prove triangles congruent
IT
Isosceles triangle properties and proofs
IT
Triangle inequality
IT
Similar triangles, identify
T
T
Exterior Angle Theorem
IT
Quadrilaterals
Classify
T
R
Angles
T
T
Sum of the measures of the angles is 360 degrees
T
R
Congruent quadrilaterals
Diagonals
R
T
T
T
Circles
Meaning of π
R
R
R
R
Radius
R
R
R
R
Diameter
R
R
R
R
Chord
IT
Arc
IT
R
Central angle
IT
R
Inscribed angles and arcs
IT
Chords, secants and tangents
IT
Area of sector
IT
R
Area
R
R
R
R
Circumference
R
R
R
R
IT
T
Equation of a circle
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
38
4-Year Scope and Sequence
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Other plane figures
Classify
R
Polygons
R
R
R
R
Similar figures
Similarity
R
R
R
Corresponding parts
T
R
R
R
R
R
R
Dilations
R
R
Isometry
IT
Transformations
Translations, reflections
T
Rotations
T
Transformation, definition
R
T
R
R
Mapping, image, preimage
IT
R
Transformation matrices
IT
Congruence and transformations
IT
Similarity and transformations
IT
Tessellation
T
Symmetry
T
R
R
R
R
Perimeter
Perimeter
R
R
Area
Regular polygons
T
Composite figures
T
Parallelograms and triangles
T
R
R
R
Squares
T
R
R
R
Trapezoids
T
R
R
R
Circles
T
R
R
R
T
Solid figures
Vertices, edges, faces
R
R
Hemisphere, great circle
T
Sphere
I
T
Pyramid, cube, prism
T
R
R
Cone, cylinder
T
R
R
Polyhedron
T
Solids of revolution
IT
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
39
Pre-Algebra
Algebra 1
Geometry
Algebra 2
Surface area
Prism
T
R
R
Pyramid
T
R
R
Cylinder
T
R
R
Cone
T
R
R
Sphere
I
T
R
Volume
Prism
T
R
R
R
Pyramid
T
R
R
R
Cylinder
T
R
R
R
Cone
T
R
R
R
Sphere
I
I
T
R
T
R
R
R
I
T
R
Coordinate geometry
Transformations in the coordinate plane
Distance in the coordinate plane
Coordinates in space
I
Reasoning and Proof
Logical reasoning in problem solving
IT
Theorem and postulate
IT
Inductive reasoning
I
T
T
Conjecturing
I
T
T
I
T
R
R
R
R
If-then statements
Venn diagrams
T
Truth tables
Deductive reasoning
I
T
T
Line segment proofs
IT
Angle relationship proofs
IT
Parallel lines proofs
IT
Triangle Sum Theorem proof
IT
Prove triangles congruent
IT
Isosceles triangle proofs
IT
Segments in triangles proofs
IT
Right triangle proofs
IT
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
R
IT
Proofs
40
R
R
<… 4-Year Scope and Sequence
Pre-Algebra
Algebra 1
Geometry
Parallelogram proofs
IT
Rhombus proofs
IT
Trapezoid proofs
IT
Similar triangle proofs
IT
Prove lines parallel
IT
Pythagorean Theorem proof
IT
Circle Theorem proofs
IT
Tangent proofs
IT
Algebra 2
Trigonometry
Trigonometric ratios
T
T
R
Inverse trigonometric ratios
I
T
R
Applications of right triangle trigonometry
IT
R
Law of sines
IT
IT
Law of cosines
IT
IT
Area of triangles
IT
T
Solving right triangles
IT
T
Special right triangles
IT
R
Unit circle
Radian measure
IT
IT
TR
Trigonometric functions, general angles
IT
Trigonometric functions, special angles
IT
Period
IT
Graphs of trigonometric functions
IT
Trigonometric equations
IT
I (Introduce) T (Teach and Test) R (Reinforce and Maintain)
4-Year Scope and Sequence
41
Essential Course of Study
Holt McDougal Larson Algebra 1
Chapter
Chapter 1 –
Expressions,
Equations, and
Functions
Chapter 3 –
Solving Linear
Equations
Pacing
(Days)
Lesson
1
1
1.1
Evaluate Expressions
1.2
Apply Order of Operations
1
2
1.3
Activity: Patterns and Expressions
1
1
1
1
1
1.3
Write Expressions
1.4
Write Equations and Inequalities
1.5
Use a Problem Solving Plan
1.6
Represent Functions as Rules and Tables
1
}
2
1.7
Activity: Scatter Plots and Functions
1
1.7
Represent Functions as Graphs
1
1.7
Extension: Determine Whether a Relation is a
Function
1
2.7
Find Square Roots and Compare Real Numbers
1
3.1A Extension: Use Real and Rational Numbers
3.1 Activity: Modeling One-Step Equations
CC.9-12.N.RN.3, CC.9-12.A.REI.1
CC.9-12.A.CED.1, CC.9-12.A.REI.1, CC.9-12.A.REI.3
1
1
2
1
3.1
Solve One-Step Equations
3.2
Solve Two-Step Equations
3.3
Solve Multi-Step Equations
3.4
Solve Equations with Variables on Both Sides
1
}
2
3.4
Activity: Solve Equations Using Tables
CC.9-12.A.CED.1, CC.9-12.A.REI.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.REI.3, CC.9-12.A.REI.11
CC.9-12.A.CED.1, CC.9-12.A.REI.3
1
1
1
1
3.4A Extension: Apply Properties of Equality
}
1
}
2
1.5A Use Precision and Measurement
3.5
Write Ratios and Proportions
3.6
Solve Proportions Using Cross Products
3.8
Rewrite Equations and Formulas
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
42
Content Standards
Essential Course of Study
CC.9-12.N.Q.1, CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1
CC.9-12.A.SSE.1, CC.9-12.A.CED.1, CC.9-12.N.Q.1
CC.9-12.A.CED.1
CC.9-12.A.CED.1
CC.9-12.N.Q.3
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.1
CC.9-12.S.ID.6, CC.9-12.F.IF.1
CC.9-12.F.IF.4, CC.9-12.F.IF.5, CC.9-12.F.IF.7a,
CC.9-12.F.LE.2
CC.9-12.F.IF.1
CC.9-12.N.Q.1, CC.9-12.N.Q.2
CC.9-12.A.REI.1
CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.REI.3
CC.9-12.N.Q.1, CC.9-12.A.CED.4, CC.9-12.A.REI.3
<…
Chapter
Chapter 4 –
Graphing Linear
Equations and
Functions
Pacing
(Days)
Lesson
1
2
4.1
Plot Points in a Coordinate Plane
4.2
Graph Linear Equations
1
2
1
}
2
4.2
Activity: Graphing Linear Equations
4.2
1
4.3
Extension: Identify Discrete and
Continuous Functions
Graph Using Intercepts
1
2
4.4
Activity: Slope and y-Intercept
2
4.4
Find Slope and Rate of Change
1
}
2
4.5
Activity: Slope and y-Intercept
1
4.5
Graph Using Slope-Intercept Form
1
2
4.5
1
4.6
Extension: Solve Linear Equations by
Graphing
Model Direct Variation
1
4.7
Graph Linear Functions
1
2
4.7A Activity: Solve Linear Equations by
Graphing Each Side
}
}
}
}
Essential Course of Study
Content Standards
CC.9-12.F.IF.5, CC.9-12.F.IF.7a
CC.9-12. A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.10, CC.9-12.F.IF.5, CC.9-12.F.IF.7a
CC.9-12.N.Q.1, CC.9-12.F.IF.7a
CC.9-12.F.IF.5
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.5, CC.9-12.F.IF.7a
CC.9-12.F.IF.4
CC.9-12.F.IF.4, CC.9-12.F.IF.6, CC.9-12.S.ID.7
CC.9-12.F.IF.4
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.5,
CC.9-12.F.IF.7a
CC.9-12.A.REI.3, CC.9-12.A.REI.11
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.6,
CC.9-12.F.IF.7a
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.1,
CC.9-12.F.IF.2, CC.9-12.F.IF.5, CC.9-12.F.IF.7a,
CC.9-12.F.BF.3
CC.9-12.A.REI.11
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
Essential Course of Study
43
Chapter
Chapter 5 –
Writing Linear
Equations
Pacing
(Days)
Lesson
1
2
5.1
Activity: Modeling Linear Relationships
CC.9-12.F.BF.1a, CC.9-12.F.LE.2
1
5.1
Write Linear Equations in Slope-Intercept Form
1
2
5.1
Activity: Investigate Families of Lines
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.BF.1a, CC.9-12.F.LE.2, CC.9-12.F.LE.5,
CC.9-12.S.ID.7
CC.9-12.F.BF.3
2
5.2
Use Linear Equations in Slope-Intercept Form
}
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.6, CC.9-12.F.BF.1a, CC.9-12.F.LE.2,
CC.9-12.F.LE.5, CC.9-12.S.ID.7
5.3 Write Linear Equations in Point-Slope Form
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.6, CC.9-12.F.IF.7a, CC.9-12.F.BF.1a,
CC.9-12.F.LE.2, CC.9-12.F.LE.5, CC.9-12.S.ID.7
5.3 Extension: Relate Arithmetic Sequences to Linear CC.9-12.F.IF.3, CC.9-12.F.BF.2
2
5.4
Functions
Write Linear Equations in Standard Form
1
5.5
Write Equations of Parallel and Perpendicular
Lines
1
5.6
Fit a Line to Data
1
2
1
}
2
1
}
2
5.6
Activity: Perform Linear Regression
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.6, CC.9-12.F.BF.1a, CC.9-12.F.LE.2,
CC.9-12.F.LE.5, CC.9-12.S.ID.6a, CC.9-12.S.ID.6c,
CC.9-12.S.ID.7
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c, CC.9-12.S.ID.8
5.6
Extension: Correlation and Causation
CC.9-12.S.ID.9
5.7
Activity: Collecting and Organizing Data
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c
1
5.7
Predict with Linear Models
1
2
1
}
2
5.7
Activity: Model Data from the Internet
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.BF.1a, CC.9-12.F.LE.2, CC.9-12.S.ID.6a,
CC.9-12.S.ID.6c, CC.9-12.S.ID.7
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c
}
}
2
1
2
}
}
5.7A Extension: Assess the Fit of a Model
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
44
Content Standards
Essential Course of Study
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.5, CC.9-12.F.LE.2
CC.9-12.F.LE.2, CC.9-12.G.GPE.5
CC.9-12.S.ID.6
<…
Chapter
Chapter 6 –
Solving and
Graphing Linear
Inequalities
Pacing
(Days)
Essential Course of Study
Lesson
1
6.1
1
2
6.2
1
6.2
1
6.3
6.3
Content Standards
CC.9-12.A.CED.1, CC.9-12.A.CED.3, CC.9-12.A.REI.3
6.4
Solve Inequalities Using Addition and
Subtraction
Solve Inequalities Using Multiplication
and Division
Activity: Inequalities with Negative
Coefficients
Solve Multi-Step Inequalities
Extension: Solve Linear Inequalities by
Graphing
Solve Compound Inequalities
2
6.4
Activity: Statements with And and Or
1
2
6.4
Activity: Solve Compound Inequalities
CC.9-12.A.REI.3
2
6.5
6.5
Solve Absolute Value Equations
Extension: Graph Absolute Value
Functions
Solve Absolute Value Inequalities
Activity: Linear Inequalities in Two
Variables
Graph Linear Inequalities in Two Variables
CC.9-12.A.CED.1, CC.9-12.A.CED.3, CC.9-12.F.IF.7b
CC.9-12.F.BF.3
}
1
}
2
1
}
2
}
1
}
2
1
1
}
2
2
6.6
6.7
6.7
CC.9-12.A.CED.1, CC.9-12.A.CED.3, CC.9-12.A.REI.3
CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.CED.3, CC.9-12.A.REI.3
CC.9-12.A.REI.10
CC.9-12.A.CED.1, CC.9-12.A.CED.3, CC.9-12.A.REI.3
CC.9-12.A.CED.1, CC.9-12.A.CED.3
CC.9-12.A.REI.12
CC.9-12.A.CED.3, CC.9-12.A.REI.12
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
Essential Course of Study
45
Chapter
Chapter 7 –
Systems of
Equations and
Inequalities
Pacing
(Days)
1
2
7.1
Activity: Solving Linear Systems Using Tables
CC.9-12.A.REI.6
1
7.1
Solve Linear Systems by Graphing
1
2
7.1
Activity: Solving Linear Systems by Graphing
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.6
CC.9-12.A.REI.6
2
7.2
Solve Linear Systems by Substitution
1
2
7.3
Activity: Linear Systems and Elimination
1
1
7.3
Solve Linear Systems by Adding or Subtracting
7.4
Solve Linear Systems by Multiplying First
1
2
7.4A Activity: Multiply and Then Add Equations
2
7.5
1
1
Additional Lesson A
Use Piecewise Functions
7.6 Solve Systems of Linear Inequalities
1
8.3
Define and Use Zero and Negative Exponents
CC.9-12.A.SSE.3c, CC.9-12.N.RN.1
1
}
2
8.3
Extension: Define and Use Fractional Exponents
CC.9-12.N.RN.1, CC.9-12.N.RN.2
2
8.5
Write and Graph Exponential Growth Functions
1
2
8.6
Activity: Exponential Models
CC.9-12.A.SSE.3c (in ex. 37), CC.9-12.A.CED.2,
CC.9-12.A.CED.3, CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7e, CC.9-12.F.IF.8b, CC.9-12.F.BF.1a,
CC.9-12.F.BF.3, CC.9-12.F.LE.1, CC.9-12.F.LE.2,
CC.9-12.F.LE.5
CC.9-12.F.LE.1c
1
8.6
Write and Graph Exponential Decay Functions
1
2
1
}
2
8.6
}
}
Exponents and
Exponential
Functions
}
}
Solve Special Types of Linear Systems
Extension: Relate Geometric Sequences to
Exponential Functions
Additional Lesson B
Define Sequences Recursively
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
46
Content Standards
}
}
Chapter 8 –
Lesson
Essential Course of Study
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.5,
CC.9-12.A.REI.6
CC.9-12.A.REI.6
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.6
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.5,
CC.9-12.A.REI.6
CC.9-12.A.REI.5
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.A.REI.5,
CC.9-12.A.REI.6
CC.9-12.F.IF.7b
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.12
CC.9-12.A.SSE.3c (in ex. 46), CC.9-12.A.CED.2,
CC.9-12.A.CED.3, CC.9-12.F.IF.7e, CC.9-12.F.IF.8b,
CC.9-12.F.BF.1a, CC.9-12.F.BF.3, CC.9-12.F.LE.2,
CC.9-12.F.LE.5
CC.9-12.F.IF.3, CC.9-12.F.BF.2, CC.9-12.F.LE.2
CC.9-12.F.IF.3, CC.9-12.F.BF.2
<…
Chapter
Chapter 9 –
Polynomials and
Factoring
Pacing
(Days)
Essential Course of Study
Lesson
Content Standards
1
9.1
Add and Subtract Polynomials
1
}
2
1
}
2
9.1
Activity: Graph Polynomial Functions
CC.9-12.A.APR.1, CC.9-12.F.IF.7c
CC.9-12.F.IF.7c
9.2
Activity: Multiplication with Algebra Tiles
CC.9-12.A.APR.1
1
1
2
9.2
9.3
Multiply Polynomials
Find Special Products of Polynomials
9.4
1
2
9.5
Solve Polynomial Equations in Factored
Form
Activity: Factorization with Algebra Tiles
CC.9-12.A.APR.1
CC.9-12.A.APR.1
CC.9-12.A.CED.1, CC.9-12.F.IF.8a
2
9.5
9.6
}
2
9.6
Factor x2 1 bx 1 c
Activity: More Factorization with Algebra
Tiles
Factor ax2 1 bx 1 c
1
9.7
Factor Special Products
1
9.8
Factor Polynomials Completely
1
}
2
CC.9-12.F.IF.8a
CC.9-12.A.CED.1, CC.9-12.A.REI.4b, CC.9-12.F.IF.8a
CC.9-12.F.IF.8a
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4b, CC.9-12.F.IF.8a
CC.9-12.A.SSE.3, CC.9-12.A.APR.4,
CC.9-12.A.CED.1, CC.9-12.A.REI.4b
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4b
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
Essential Course of Study
47
Chapter
Chapter 10 –
Pacing
(Days)
Lesson
2
10.1 Graph y 5 ax2 1 c
1
10.2 Graph y 5 ax2 1 bx 1 c
1
2
10.2 Extension: Graph Quadratic Functions in
Intercept Form
10.3 Solve Quadratic Equations by Graphing
Quadratic Equations
and Functions
}
2
1
2
}
2
1
2
}
10.5 Solve Quadratic Equations by Completing the
Square
1
10.5 Extension: Graph Quadratic Functions in Vertex
Form
1
10.6 Solve Quadratic Equations by the Quadratic
Formula
11.2 Extension: Derive the Quadratic Formula
1
2
1
1
10.7A Solve Systems with Quadratic Equations
10.8 Compare Linear, Exponential, and Quadratic
Models
1
2
10.8 Activity: Perform Regressions
1
10.8A Model Relationships
1
2
10.8B Activity: Average Rate of Change
}
}
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
48
Essential Course of Study
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.5, CC.9-12.F.IF.7a, CC.9-12.F.IF.7c,
CC.9-12.F.BF.3
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.7a,
CC.9-12.F.IF.7c, CC.9-12.F.BF.3
CC.9-12.A.APR.3
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.11, CC.9-12.F.IF.4, CC.9-12.F.IF.7a,
CC.9-12.F.IF.7c, CC.9-12.F.IF.8a
10.3 Activity: Find Minimum and Maximum Values and CC.9-12.N.Q.1, CC.9-12.A.REI.11, CC.9-12.F.IF.7a,
Zeros
CC.9-12.F.IF.7c
10.4 Use Square Roots to Solve Quadratic Equations
CC.9-12.A.CED.1, CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.4b, CC.9-12.A.REI.11
10.5 Activity: Completing the Square—Algebra Tiles
CC.9-12.A.SSE.3
2
}
Content Standards
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4a, CC.9-12.A.REI.4b
CC.9-12.A.SSE.3, CC.9-12.F.IF.7a, CC.9-12.F.IF.7c,
CC.9-12.F.IF.8a, CC.9-12.F.BF.3
CC.9-12.A.REI.4b
CC.9-12.A.REI.4a
CC.9-12.A.REI.11, CC.9-12.A.REI.7
CC.9-12.A.CED.2, CC.9-12.A.CED.3, CC.9-12.F.IF.4,
CC.9-12.F.IF.7a, CC.9-12.F.IF.7c, CC.9-12.F.IF.7e,
CC.9-12.F.BF.1a, CC.9-12.F.LE.1, CC.9-12.F.LE.5,
CC.9-12.S.ID.6a
CC.9-12.F.IF.7a, CC.9-12.F.IF.7e, CC.9-12.S.ID.6a
CC.9-12.F.IF.4, CC.9-12.F.IF.9, CC.9-12.F.LE.1,
CC.9-12.F.LE.3
CC.9-12.F.IF.6
<…
Chapter
Chapter 13 –
Probability and
Data Analysis
Pacing
(Days)
Essential Course of Study
Lesson
Content Standards
1
2
13.1 Activity: Find a Probability
1
13.1 Find Probabilities and Odds
2
1
1
}
2
13.2 Find Probabilities Using Permutations
13.3 Find Probabilities Using Combinations
13.3 Activity: Find Permutations and
Combinations
2
13.4 Find Probabilities of Compound Events
1
2
13.5A Activity: Investigating Samples
1
13.5 Analyze Surveys and Samples
CC.9-12.S.IC.1, CC.9-12.S.IC.3, CC.9-12.S.MD.6
1
13.6 Use Measures of Central Tendency and
Dispersion
13.6A Analyze Data
CC.9-12.S.ID.2, CC.9-12.S.ID.3
1
2
1
}
2
13.6 Extension: Calculate Variance and
Standard Deviation
13.7A Activity: Investigate Dot Plots
CC.9-12.S.ID.2, CC.9-12.S.ID.3
2
13.7 Interpret Stem-and-Leaf Plots and
Histograms
13.7 Activity: Draw Histograms
CC.9-12.S.ID.1, CC.9-12.S.ID.2, CC.9-12.S.ID.3
13.8 Interpret Box-and-Whisker Plots
13.8 Activity: Draw Box-and-Whisker Plots
CC.9-12.S.ID.1, CC.9-12.S.ID.2, CC.9-12.S.ID.3
CC.9-12.N.Q.1
13.8A Extension: Analyze Data
CC.9-12.S.ID.2
}
}
1
}
1
2
}
2
1
}
2
1
}
2
CC.9-12.S.ID.5, CC.9-12.S.CP.1, CC.9-12.S.CP.4,
CC.9-12.S.MD.7
CC.9-12.S.CP.9
CC.9-12.S.CP.1, CC.9-12.S.CP.2, CC.9-12.S.CP.3,
CC.9-12.S.CP.6, CC.9-12.S.CP.7, CC.9-12.S.CP.8,
CC.9-12.S.CP.9
CC.9-12.S.ID.5
CC.9-12.S.ID.1
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
Essential Course of Study
49
Pacing Guide for 50-Minute Classes
Holt McDougal Larson Algebra 1
This sequence was created as a guide to assist you in covering the Common Core State Standards for
Algebra 1. This 170-day schedule includes time for review and assessment. The schedule leaves room
for you to customize the pacing to your students’ needs.
Chapter 1
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 1.1
Lesson 1.2
Investigating Algebra
Activity 1.3
Lesson 1.3
Lesson 1.3 (cont.)
Lesson 1.4
Lesson 1.4 (cont.)
Mixed Review of
Problem Solving
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 1.6
Lesson 1.5A
Lesson 1.6
Investigating Algebra
Activity 1.7
Lesson 1.7
Lesson 1.7 (cont.)
Extension 1.7
DAY 11
DAY 12
DAY 13
DAY 14
Extension 1.7 (cont.)
Mixed Review of
Problem Solving
Chapter 1 Review
Chapter 1 Test
Standardized Test
Preparation
Standardized Test
Practice
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 2.7
Lesson 3.1A
Investigating Algebra
Activity 3.1
Lesson 3.1
Lesson 3.1 (cont.)
Lesson 3.2
Lesson 3.2 (cont.)
Lesson 3.3
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 3.3 (cont.)
Lesson 3.3 (cont.)
Lesson 3.4
Lesson 3.4 (cont.)
Spreadsheet Activity 3.4
Extension 3.4A
Mixed Review of
Problem Solving
Lesson 3.5
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 3.5 (cont.)
Lesson 3.6
Lesson 3.6 (cont.)
Lesson 3.8
Lesson 3.8 (cont.)
Mixed Review of
Problem Solving
Chapter 3 Review
Chapter 3 Test
DAY 16
DAY 17
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Chapter 3
50
Pacing Guide for 50-Minute Classes
<… Pacing Guide for 50-Minute Classes
Chapter 4
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 4.1
Lesson 4.2
Lesson 4.2 (cont.)
Graphing Calculator
Activity 4.2
Extension 4.2
Lesson 4.3
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Mixed Review of
Problem Solving
Investigating Algebra
Activity 4.4
Lesson 4.4
Lesson 4.4 (cont.)
Investigating Algebra
Activity 4.5
Lesson 4.5
Lesson 4.5 (cont.)
Extension 4.5
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 4.6
Lesson 4.7
Investigating Algebra
Activity 4.7A
Mixed Review of
Problem Solving
Chapter 4 Review
Chapter 4 Test
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algebra
Activity 5.1
Lesson 5.1
Lesson 5.1 (cont.)
Graphing Calculator
Activity 5.1
Lesson 5.2
Lesson 5.2 (cont.)
Lesson 5.3
DAY 17
Standardized Test
Preparation
Standardized Test
Practice
Chapter 5
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 5.3 (cont.)
Extension 5.3
Lesson 5.4
Lesson 5.4 (cont.)
Lesson 5.4 (cont.)
Mixed Review of
Problem Solving
Lesson 5.5
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 5.6
Graphing Calculator
Activity 5.6
Extension 5.6
Investigating Algebra
Activity 5.7
Lesson 5.7
Lesson 5.7 (cont.)
Internet
Activity 5.7
Extension 5.7A
Mixed Review of
Problem Solving
DAY 16
DAY 17
DAY 18
Chapter 5 Review
Chapter 5 Test
Standardized Test
Preparation
Standardized Test
Practice
Pacing Guide for 50-Minute Classes
51
Chapter 6
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 6.1
Investigating Algebra
Activity 6.2
Lesson 6.2
Lesson 6.2 (cont.)
Lesson 6.3
Lesson 6.3 (cont.)
Extension 6.3
Investigating Algebra
Activity 6.4
Lesson 6.4
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 6.4 (cont.)
Lesson 6.4 (cont.)
Graphing Calculator
Activity 6.4
Mixed Review of
Problem Solving
Lesson 6.5
Lesson 6.5 (cont.)
Lesson 6.5 (cont.)
Extension 6.5
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 6.6
Investigating Algebra
Activity 6.7
Lesson 6.7
Lesson 6.7 (cont.)
Lesson 6.7 (cont.)
Mixed Review of
Problem Solving
Chapter 6 Review
DAY 16
Day 17
Chapter 6 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 7
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algebra
Activity 7.1
Lesson 7.1
Lesson 7.1 (cont.)
Graphing Calculator
Activity 7.1
Lesson 7.2
Lesson 7.2 (cont.)
Investigating Algebra
Activity 7.3
Lesson 7.3
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 7.3 (cont.)
Lesson 7.4
Lesson 7.4 (cont.)
Graphing Calculator
Activity 7.4A
Mixed Review of
Problem Solving
Lesson 7.5
Lesson 7.5 (cont.)
Lesson 7.5 (cont.)
Additional Lesson A
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Additional Lesson A
(cont.)
Lesson 7.6
Lesson 7.6 (cont.)
Mixed Review of
Problem Solving
Chapter 7 Review
Chapter 7 Test
Standardized Test
Preparation
Standardized Test
Practice
DAY 16
Cumulative Review
52
Pacing Guide for 50-Minute Classes
<… Pacing Guide for 50-Minute Classes
Chapter 8
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 8.3
Extension 8.3
Mixed Review of
Problem Solving
Lesson 8.5
Lesson 8.5 (cont.)
Investigating Algebra
Activity 8.6
Lesson 8.6
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 8.6 (cont.)
Extension 8.6
Extension B
Mixed Review of
Problem Solving
Chapter 8 Review
Chapter 8 Test
Standardized Test
Preparation
Standardized Test
Practice
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 9.1
Graphing Calculator
Activity 9.1
Investigating Algebra
Activity 9.2
Lesson 9.2
Lesson 9.3
Lesson 9.4
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 9.4 (cont.)
Mixed Review of
Problem Solving
Investigating Algebra
Activity 9.5
Lesson 9.5
Lesson 9.5 (cont.)
Investigating Algebra
Activity 9.6
Lesson 9.6
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 9.6 (cont.)
Lesson 9.6 (cont.)
Lesson 9.7
Lesson 9.7 (cont.)
Lesson 9.8
Lesson 9.8 (cont.)
Mixed Review of
Problem Solving
Chapter 9 Review
DAY 16
DAY 17
Chapter 9 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 9
Pacing Guide for 50-Minute Classes
53
Chapter 10
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 10.1
Lesson 10.1 (cont.)
Lesson 10.2
Extension 10.2
Lesson 10.3
Lesson 10.3 (cont.)
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 10.3 (cont.)
Graphing Calculator
Activity 10.3
Lesson 10.4
Lesson 10.4 (cont.)
Mixed Review of
Problem Solving
Investigating Algebra
Activity 10.5
Lesson 10.5
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 10.5 (cont.)
Extension 10.5
Lesson 10.6
Lesson 10.6 (cont.)
Extension 11.2
Lesson 10.7A
DAY 16
DAY 17
DAY 18
DAY 19
DAY 20
Lesson 10.7A (cont.)
Lesson 10.8
Lesson 10.8 (cont.)
Graphing Calculator
Activity 10.8
Lesson 10.8A
Graphing Calculator
Activity 10.8B
Mixed Review of
Problem Solving
Chapter 10 Review
DAY 21
DAY 22
DAY 23
Chapter 10 Test
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
54
Pacing Guide for 50-Minute Classes
<… Pacing Guide for 50-Minute Classes
Chapter 13
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algebra
Activity 13.1
Lesson 13.1
Lesson 13.1 (cont.)
Lesson 13.2
Lesson 13.2 (cont.)
Lesson 13.2 (cont.)
Lesson 13.3
Lesson 13.3 (cont.)
Graphing Calculator
Activity 13.3
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 13.4
Lesson 13.4 (cont.)
Mixed Review of
Problem Solving
Investigating Algebra
Activity 13.5A
Lesson 13.5
Lesson 13.6
DAY 11
DAY 12
DAY 13
DAY 14
DAY 15
Lesson 13.6A
Extension 13.6
Investigating Algebra
Activity 13.7A
Lesson 13.7
Lesson 13.7 (cont.)
Graphing Calculator
Activity 13.7
Lesson 13.8
DAY 16
DAY 17
DAY 18
DAY 19
DAY 20
Lesson 13.8 (cont.)
Lesson 13.8 (cont.)
Graphing Calculator
Activity 13.8
Extension 13.8A
Mixed Review of
Problem Solving
Chapter 13 Review
Chapter 13 Test
DAY 21
DAY 22
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Pacing Guide for 50-Minute Classes
55
Pacing Guide for 90-Minute Classes
Holt McDougal Larson Algebra 1
This sequence was created as a guide to assist you in covering the Common Core State Standards for
Algebra 1. This 85-day schedule includes time for review and assessment. The schedule leaves room
for you to customize the pacing to your students’ needs.
Chapter 1
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 1.1
Lesson 1.2
Investigating Algebra
Activity 1.3
Lesson 1.3
Lesson 1.4
Lesson 1.4 (cont.)
Mixed Review of
Problem Solving
Lesson 1.5
Lesson 1.5A
Lesson 1.6
Investigating Algebra
Activity 1.7
Lesson 1.7
Extension 1.7
DAY 6
DAY 7
Mixed Review of
Problem Solving
Chapter 1 Review
Chapter 1 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 3
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 2.7
Lesson 3.1A
Investigating Algebra
Activity 3.1
Lesson 3.1
Lesson 3.2
Lesson 3.2 (cont.)
Lesson 3.3
Lesson 3.3 (cont.)
Lesson 3.4
Spreadsheet
Activity 3.4
Extension 3.4A
Mixed Review of
Problem Solving
Lesson 3.5
DAY 6
DAY 7
DAY 8
DAY 9
Lesson 3.5 (cont.)
Lesson 3.6
Lesson 3.8
Lesson 3.8 (cont.)
Mixed Review of
Problem Solving
Chapter 3 Review
Chapter 3 Test
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Chapter 4
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 4.1
Lesson 4.2
Lesson 4.2 (cont.)
Graphing Calculator
Activity 4.2
Extension 4.2
Lesson 4.3
Mixed Review of
Problem Solving
Investigating Algebra
Activity 4.4
Lesson 4.4
Investigating Algebra
Activity 4.5
Lesson 4.5
Extension 4.5
56
Pacing Guide for 90-Minute Classes
<… Pacing Guide for 90-Minute Classes
DAY 6
DAY 7
DAY 8
Lesson 4.6
Lesson 4.7
Graphing Calculator
Activity 4.7A
Mixed Review of
Problem Solving
Chapter 4 Review
Chapter 4 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 5
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algebra
Activity 5.1
Lesson 5.1
Graphing Calculator
Activity 5.1
Lesson 5.2
Lesson 5.3
Extension 5.3
Lesson 5.4
Lesson 5.4 (cont.)
Mixed Review of
Problem Solving
Lesson 5.5
DAY 6
DAY 7
DAY 8
DAY 9
Lesson 5.6
Graphing Calculator
Activity 5.6
Extension 5.6
Investigating Algebra
Activity 5.7
Lesson 5.7
Internet
Activity 5.7
Extension 5.7A
Mixed Review of
Problem Solving
Chapter 5 Review
Chapter 5 Test
Standardized Test
Preparation
Standardized Test
Practice
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 6.1
Investigating Algebra
Activity 6.2
Lesson 6.2
Lesson 6.2 (cont.)
Lesson 6.3
Extension 6.3
Investigating Algebra
Activity 6.4
Lesson 6.4
Lesson 6.4 (cont.)
Graphing Calculator
Activity 6.4
Mixed Review of
Problem Solving
Lesson 6.5
Lesson 6.5 (cont.)
Extension 6.5
DAY 6
DAY 7
DAY 8
Lesson 6.6
Investigating Algebra
Activity 6.7
Lesson 6.7
Mixed Review of
Problem Solving
Chapter 6 Review
Chapter 6 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 6
Pacing Guide for 90-Minute Classes
57
Chapter 7
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algbra
Activity 7.1
Lesson 7.1
Graphing Calculator
Activity 7.1
Lesson 7.2
Investigating Algebra
Activity 7.3
Lesson 7.3
Lesson 7.4
Lesson 7.4 (cont.)
Graphing Calculator
Activity 7.4A
Mixed Review of
Problem Solving
Lesson 7.5
Lesson 7.5 (cont.)
Extension A
DAY 6
DAY 7
DAY 8
DAY 9
Extension A (cont.)
Lesson 7.6
Mixed Review of
Problem Solving
Chapter 7 Review
Chapter 7 Test
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Chapter 8
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 8.3
Extension 8.3
Mixed Review of
Problem Solving
Lesson 8.5
Investigating Algebra
Activity 8.6
Lesson 8.6
Extension 8.6
Extension B
Mixed Review of
Problem Solving
Chapter 8 Review
Chapter 8 Test
Standardized Test
Preparation
Standardized Test
Practice
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 9.1
Graphing Calculator
Activity 9.1
Investigating Algebra
Activity 9.2
Lesson 9.2
Lesson 9.3
Lesson 9.4
Mixed Review of
Problem Solving
Investigating Algebra
Activity 9.5
Lesson 9.5
Lesson 9.5 (cont.)
Investigating Algebra
Activity 9.6
Lesson 9.6
DAY 6
DAY 7
DAY 8
Lesson 9.6 (cont.)
Lesson 9.7
Lesson 9.7 (cont.)
Lesson 9.8
Mixed Review of
Problem Solving
Chapter 9 Review
Chapter 9 Test
Standardized Test
Preparation
Standardized Test
Practice
Chapter 9
58
Pacing Guide for 90-Minute Classes
<… Pacing Guide for 90-Minute Classes
Chapter 10
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Lesson 10.1
Lesson 10.2
Extension 10.2
Lesson 10.3
Lesson 10.3 (cont.)
Graphing Calculator
Activity 10.3
Lesson 10.4
Mixed Review of
Problem Solving
Investigating Algebra
Activity 10.5
Lesson 10.5
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 10.5 (cont.)
Extension 10.5
Lesson 10.6
Extension 11.2
Lesson 10.7A
Lesson 10.8
Lesson 10.8 (cont.)
Graphing Calculator
Activity 10.8
Lesson 10.8A
Graphing Calculator
Activity 10.8B
Mixed Review of
Problem Solving
Chapter 10 Review
DAY 11
DAY 12
Chapter 10 Test
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Chapter 13
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
Investigating Algebra
Activity 13.1
Lesson 13.1
Lesson 13.2
Lesson 13.2 (cont.)
Lesson 13.3
Lesson 13.3 (cont.)
Graphing Calculator
Activity 13.3
Lesson 13.4
Lesson 13.4 (cont.)
Mixed Review of
Problem Solving
Investigating Algebra
Activity 13.5A
Lesson 13.5
Lesson 13.6
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
Lesson 13.6A
Extension 13.6
Investigating Algebra
Activity 13.7A
Lesson 13.7
Graphing Calculator
Activity 13.7
Lesson 13.8
Lesson 13.8 (cont.)
Graphing Calculator
Activity 13.8
Extension 13.8A
Mixed Review of
Problem Solving
Chapter 13 Review
DAY 11
DAY 12
Chapter 13 Test
Standardized Test
Preparation
Standardized Test
Practice
Cumulative Review
Pacing Guide for 90-Minute Classes
59
Chapter Prerequisites
Holt McDougal Larson Algebra 1
Content
Standards
Chapter
Key Skills and Concepts
Chapter 1
Write and evaluate expressions, equations,
and inequalities. Apply the order of
operations. Use a problem-solving plan
to solve real-world problems. Represent
functions as rules and as tables. Graph
functions given a rule or table of values.
CC.9-12.N.Q.1, CC.9-12.N.Q.2,
CC.9-12.N.Q.3, CC.9-12.A.SSE.1,
CC.9-12.A.CED.3, CC.9-12.F.IF.1,
CC.9-12.F.IF.5, CC.9-12.F.LE.2,
CC.9-12.S.ID.6
Classify real numbers. Compare and order
integers and rational numbers. Perform
basic operations. Find square roots.
Apply properties to evaluate and simplify
expressions. Use the distributive property to
write equivalent expressions. Use conditional
statements and logical reasoning to reason
with real numbers.
CC.9-12.7.NS.1,
CC.9-12.7.NS.2,
CC.9-12.7.NS.3,
CC.8.EE.2,
CC.8.EE.7
Lessons
Use properties of equality to solve one-step,
two-step, and multi-step equations in one
variable. Use properties of equality and the
distributive property to solve equations with
variables on both sides. Write ratios and
proportions. Solve proportions using cross
products. Solve percent problems, such as
finding the percent of a number, a base, and
part of a base. Rewrite equations in function
form. Solve formula and literal equations for
a given variable.
CC.9-12.N.RN.3,
CC.9-12.N.Q.1,
CC.9-12.N.Q.2,
CC.9-12.A.CED.1,
CC.9-12.A.CED.4,
CC.9-12.A.REI.1,
CC.9-12.A.REI.3,
CC.9-12.A.REI.11
Lesson
Plot points in a coordinate plane. Use tables,
x- and y-intercepts, and the slope and
y-intercept to graph linear equations and
functions. Interpret slope as a rate of change
in real-world situations and explore how
changing the slope and y-intercept changes
the graph. Use slope to identify parallel lines.
Write and graph direct variation equations
and use them to solve real-world problems.
Use function notation. Compare families of
graphs.
CC.9-12.N.Q.1, CC.9-12.A.CED.2,
CC.9-12.A.CED.3,
CC.9-12.A.REI.10,
CC.9-12.A.REI.11,
CC.9-12.A.REI.3, CC.9-12.F.IF.1,
CC.9-12.F.IF.2, CC.9-12.F.IF.4,
CC.9-12.F.IF.5, CC.9-12.F.IF.6,
CC.9-12.F.IF.7, CC.9-12.F.BF.3,
CC.9-12.S.ID.6, CC.9-12.S.ID.7
Lessons
Expressions, Equations, and
Functions
Chapter 2
Properties of Real Numbers
Chapter 3
Solving Linear Equations
Chapter 4
Graphing Linear Equations and
Functions
60
Chapter Prerequisites
Prerequisites
1.1, 1.2, 1.4
2.5
1.6, 1.7, 3.1,
3.2
<…
Chapter Prerequisites
Content
Standards
Chapter
Key Skills and Concepts
Chapter 5
Write equations of lines in slope-intercept
form given: the slope and y -intercept; the
slope and a point; or two points. Write and
graph equations using the slope and a point,
using a graph of the line, or using real-world
data. Write equations of lines in standard
form, and use these equations to solve realworld problems. Write and find equations of
lines parallel or perpendicular to a given line.
Make scatter plots of data. Use lines of fit
and the best-fitting line to model data and to
make predictions.
CC.9-12.A.CED.2,
CC.9-12.A.CED.3, CC.9-12.F.IF.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.6, CC.9-12.F.IF.7,
CC.9-12.F.BF.1, CC.9-12.F.BF.2,
CC.9-12.F.BF.3, CC.9-12.F.LE.2,
CC.9-12.F.LE.5, CC.9-12.G.GPE.5,
CC.9-12.S.ID.6, CC.9-12.S.ID.7,
CC.9-12.S.ID.8, CC.9-12.S.ID.9
Lessons
Write, solve, and graph one-step and multistep inequalities using addition, subtraction,
multiplication, and division. Reverse an
inequality sign when multiplying or dividing
by a negative number. Solve and graph
compound inequalities using and and or.
Solve absolute value equations using or.
Solve and graph absolute value inequalities
using and and or. Graph linear inequalities in
two variables.
CC.9-12.A.CED.1,
CC.9-12.A.CED.3,
CC.9-12.A.REI.3,
CC.9-12.A.REI.10,
CC.9-12.A.REI.12,
CC.9-12.F.IF.7,
CC.9-12.F.BF.3
Lessons
Use graphing, substitution, and elimination
to solve systems of linear equations. When
solving by the elimination method, either
add or subtract, or multiply first and then
add or subtract. Identify linear systems as
having one solution, no solution, or infinitely
many solutions. Solve systems of linear
inequalities.
CC.9-12.A.CED.2,
CC.9-12.A.CED.3,
CC.9-12.A.REI.5,
CC.9-12.A.REI.6,
CC.9-12.A.REI.12,
CC.9-12.F.IF.7
Lessons
Writing Linear Equations
Chapter 6
Solving and Graphing Linear
Inequalities
Chapter 7
Systems of Equations and
Inequalities
Prerequisites
4.5, 4.6
2.1, 3.1, 3.2,
4.2
3.3, 4.2, 4.3,
4.5, 6.1, 6.2,
6.3
Chapter Prerequisites
61
Content
Standards
Chapter
Key Skills and Concepts
Chapter 8
Use properties of exponents involving
products and quotients. Apply the product
of powers property, the power of a power
property, the power of a product property,
the quotient of powers property, and the
power of a quotient property. Use zero
and negative exponents. Read, write, and
compute with numbers in scientific notation.
Graph and write rules for exponential
functions, including exponential growth and
exponential decay functions.
CC.9-12.N.RN.1, CC.9-12.N.RN.2,
CC.9-12.A.SSE.3,
CC.9-12.A.CED.2,
CC.9-12.A.CED.3, CC.9-12.F.IF.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7, CC.9-12.F.IF.8,
CC.9-12.F.BF.1, CC.9-12.F.BF.2,
CC.9-12.F.BF.3, CC.9-12.F.LE.1,
CC.9-12.F.LE.2, CC.9-12.F.LE.5
Lessons
Identify, classify, add, subtract, and multiply
polynomials. Use vertical and horizontal
formats to find sums and differences. To find
products, use the distributive property, tables
of products, and patterns (including the FOIL
pattern, the square of a binomial pattern,
and the sum and difference patterns). Write
polynomials to describe and solve real-world
problems. Solve polynomial equations.
Factor polynomials and use factoring to solve
equations, to find the zeros of functions,
and to find the roots of equations. Factor
polynomials completely using a variety of
techniques.
CC.9-12.A.SSE.3,
CC.9-12.A.APR.1,
CC.9-12.A.APR.3,
CC.9-12.A.APR.4,
CC.9-12.A.CED.1,
CC.9-12.A.REI.4,
CC.9-12.F.IF.7,
CC.9-12.F.IF.8
Lessons
Graph quadratic functions and compare
them to the parent graph. Find the axis
of symmetry, the vertex, and minimum or
maximum values. Solve quadratic equations
by factoring, graphing, using square roots,
completing the square, and using the
quadratic formula. Use the discriminant to
determine the number and type of solutions
of a quadratic equation. Determine whether
a linear, exponential, or quadratic function
best models a set of data.
CC.9-12.N.Q.1, CC.9-12.A.SSE.3, Lessons
2.7, 4.1
CC.9-12.A.APR.3,
(Extension)
CC.9-12.A.CED.1,
CC.9-12.A.CED.2,
CC.9-12.A.CED.3,
CC.9-12.A.REI.4, CC.9-12.A.REI.7,
CC.9-12.A.REI.11, CC.9-12.F.IF.4,
CC.9-12.F.IF.5, CC.9-12.F.IF.6,
CC.9-12.F.IF.7, CC.9-12.F.IF.8,
CC.9-12.F.IF.9, CC.9-12.F.BF.1,
CC.9-12.F.BF.3, CC.9-12.F.LE.1,
CC.9-12.F.LE.3, CC.9-12.F.LE.5,
CC.9-12.S.ID.6a
Exponents and Exponential
Functions
Chapter 9
Polynomials and Factoring
Chapter 10
Quadratic Equations and
Functions
62
Chapter Prerequisites
Prerequisites
1.1, 1.7, 2.1
2.2, 2.3, 2.4,
2.5, 8.1
<…
Chapter Prerequisites
Content
Standards
Chapter
Key Skills and Concepts
Chapter 11
Graph square root functions. Simplify radical
expressions, including rationalizing the
denominator. Add, subtract, and multiply
radicals. Solve radical equations, including
equations and extraneous solutions. Apply
the Pythagorean theorem and its converse
as well as the distance and midpoint
formulas to solve problems.
CC.9-12.A.CED.2,
CC.9-12.A.CED.3,
CC.9-12.A.REI.2,
CC.9-12.A.REI.4,
CC.9-12.F.IF.5,
CC.9-12.F.IF.7,
CC.9-12.F.BF.3
Lessons
Model inverse variation by writing and
graphing inverse equations. Graph rational
equations and compare them to the parent
function. Divide polynomials and then use
this skill to graph rational functions. Simplify
rational expressions, stating any excluded
values. Multiply, divide, add, and subtract
rational expressions. Use these operations to
solve rational equations.
CC.9-12.A.APR.6,
CC.9-12.A.APR.7,
CC.9-12.A.CED.1,
CC.9-12.A.CED.2,
CC.9-12.A.CED.3,
CC.9-12.A.REI.2,
CC.9-12.F.IF.5,
CC.9-12.F.IF.7,
CC.9-12.F.BF.1,
CC.9-12.F.BF.3
Lessons
Calculate probabilities and odds of simple
events. Calculate probabilities of compound
events, identifying whether events are
mutually exclusive or overlapping, or
whether they are dependent or independent.
Identify potentially biased samples and
questions. Compare measures of central
tendency and measures of dispersion.
Analyze and display data.
CC.9-12.N.Q.1, CC.9-12.S.ID.1,
CC.9-12.S.ID.2, CC.9-12.S.ID.3,
CC.9-12.S.ID.5, CC.9-12.S.IC.1,
CC.9-12.S.IC.3, CC.9-12.S.CP.1,
CC.9-12.S.CP.2, CC.9-12.S.CP.3,
CC.9-12.S.CP.4, CC.9-12.S.CP.6,
CC.9-12.S.CP.7, CC.9-12.S.CP.8,
CC.9-12.S.CP.9, CC.9-12.S.MD.6,
CC.9-12.S.MD.7
Lessons
Radicals and Geometry
Connections
Chapter 12
Rational Equations and Functions
Chapter 13
Probability and Data Analysis
Prerequisites
1.1, 2.5, 2.7,
8.5, 9.5
3.5, 3.6, 9.5,
9.6, 9.7
2.6 and 6.6
(mean only)
Chapter Prerequisites
63
Course Planner for Differentiated Instruction
Chapter 1 – Expressions, Equations, and Functions
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
1.1
Evaluate
Expressions
(1 day)
CC.9-12.N.Q.1, CC.9-12.A.CED.1,
CC.9-12.A.REI.3
❏ Practice B 1.1, CR
❏ Notetaking Guide 1.1
❏ Key Questions to Ask, TE
❏ Study Guide 1.1, CR
❏ Inclusion Notes 1.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.1, CR
1.2
Apply Order of
Operations
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.REI.3
❏ Practice B 1.2, CR
❏ Notetaking Guide 1.2
❏ Key Questions to Ask, TE
❏ Study Guide 1.2, CR
❏ Inclusion Notes 1.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.2, CR
❏ Practice B 1.3, CR
❏ Notetaking Guide 1.3
❏ Key Questions to Ask, TE
❏ Study Guide 1.3, CR
❏ Inclusion Notes 1.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.3, CR
Assessment Options
❏ Quiz for 1.1 to 1.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 1.1 to 1.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
1.4
Write Equations CC.9-12.A.CED.1
and Inequalities
(1 day)
❏ Practice B 1.4, CR
❏ Notetaking Guide 1.4
❏ Key Questions to Ask, TE
❏ Study Guide 1.4, CR
❏ Inclusion Notes 1.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.4, CR
1.5
Use a Problem
Solving Plan
(1 day)
❏ Practice B 1.5, CR
❏ Notetaking Guide 1.5
❏ Key Questions to Ask, TE
❏ Study Guide 1.5, CR
❏ Inclusion Notes 1.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.5, CR
Activity: Patterns
and Expressions
(1/2 day)
CC.9-12.A.CED.1
1.3
CC.9-12.A.SSE.1, CC.9-12.A.CED.1,
CC.9-12.N.Q.1
Write
Expressions
(1 day)
CC.9-12.A.CED.1
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
64
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 1.1, CR
❏ Notetaking Guide 1.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.1, CR
❏ Practice C 1.1, CR
❏ Challenge 1.1, CR
❏ Pre-AP Best Practices 1.1, PAP
❏ Spanish Study Guide, 1.1
❏ Student Resources in Spanish, 1.1
❏ English Learner Notes 1.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 1.2, CR
❏ Notetaking Guide 1.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.2, CR
❏ Practice C 1.2, CR
❏ Challenge 1.2, CR
❏ Pre-AP Best Practices 1.2, PAP
❏ Spanish Study Guide, 1.2
❏ Student Resources in Spanish, 1.2
❏ English Learner Notes 1.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 1.3, CR
❏ Notetaking Guide 1.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.3, CR
❏ Practice C 1.3, CR
❏ Challenge 1.3, CR
❏ Pre-AP Best Practices 1.3, PAP
❏ Spanish Study Guide, 1.3
❏ Student Resources in Spanish, 1.3
❏ English Learner Notes 1.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 1.1 to 1.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 1.1 to 1.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 1.1 to 1.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 1.4, CR
❏ Notetaking Guide 1.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.4, CR
❏ Practice C 1.4, CR
❏ Challenge 1.4, CR
❏ Pre-AP Best Practices 1.4, PAP
❏ Spanish Study Guide, 1.4
❏ Student Resources in Spanish, 1.4
❏ English Learner Notes 1.4, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 1.5, CR
❏ Notetaking Guide 1.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.5, CR
❏ Practice C 1.5, CR
❏ Challenge 1.5, CR
❏ Pre-AP Best Practices 1.5, PAP
❏ Pre-AP Copymaster 1.5, PAP
❏ Spanish Study Guide, 1.5
❏ Student Resources in Spanish, 1.5
❏ English Learner Notes 1.5, DIR
❏ Multi-Language Visual Glossary
Course Planner
65
Course Planner for Differentiated Instruction
Chapter 1 – Expressions, Equations, and Functions
Lesson
1.5A Use Precision
and
Measurement
(CC) (1 day)
Content
Standards
CC.9-12.N.Q.3
Assessment Options
1.6
Represent
Functions as
Rules and
Tables
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.1
Activity: Scatter
Plots and Functions
(1/2 day)
CC.9-12.S.ID.6, CC.9-12.F.IF.1
1.7
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7a, CC.9-12.F.LE.2
Represent
Functions as
Graphs
(1 day)
Extension:
Determine Whether
a Relation is a
Function (1 day)
Assessment Options
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 1.5A, CR
❏ Key Questions to Ask, TE
❏ Study Guide 1.5A, CR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Quiz for 1.4 to 1.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 1.4 to 1.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Practice B 1.6, CR
❏ Notetaking Guide 1.6
❏ Key Questions to Ask, TE
❏ Study Guide 1.6, CR
❏ Inclusion Notes 1.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.6, CR
❏ Practice B 1.7, CR
❏ Notetaking Guide 1.7
❏ Key Questions to Ask, TE
❏ Study Guide 1.7, CR
❏ Inclusion Notes 1.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 1.7, CR
❏ Quiz for 1.6 to 1.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 1.6 to 1.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
CC.9-12.F.IF.1
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
66
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.5A, CR
❏ Challenge 1.5A, CR
❏ Pre-AP Best Practices 1.5A, PAP
❏ Multi-Language Visual Glossary
❏ Quiz for 1.4 to 1.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 1.4 to 1.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz 1.4 to 1.5, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
❏ Practice A 1.6, CR
❏ Notetaking Guide 1.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.6, CR
❏ Practice C 1.6, CR
❏ Challenge 1.6, CR
❏ Pre-AP Best Practices 1.6, PAP
❏ Pre-AP Copymaster 1.6, PAP
❏ Spanish Study Guide, 1.6
❏ Student Resources in Spanish, 1.6
❏ English Learner Notes 1.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 1.7, CR
❏ Notetaking Guide 1.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 1.7, CR
❏ Practice C 1.7, CR
❏ Challenge 1.7, CR
❏ Pre-AP Best Practices 1.7, PAP
❏ Pre-AP Copymaster 1.7, PAP
❏ Spanish Study Guide, 1.7
❏ Student Resources in Spanish, 1.7
❏ English Learner Notes 1.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 1.6 to 1.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 1.6 to 1.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 1.6 to 1.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
67
Course Planner for Differentiated Instruction
Chapter 2 – Properties of Real Numbers
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
2.1
Use Integers
and Rational
Numbers
❏ Practice B 2.1, CR
❏ Notetaking Guide 2.1
❏ Key Questions to Ask, TE
❏ Study Guide 2.1, CR
❏ Inclusion Notes 2.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.1, CR
2.2
Add Real
Numbers
❏ Practice B 2.2, CR
❏ Notetaking Guide 2.2
❏ Key Questions to Ask, TE
❏ Study Guide 2.2, CR
❏ Inclusion Notes 2.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.2, CR
2.3
Subtract Real
Numbers
❏ Practice B 2.3, CR
❏ Notetaking Guide 2.3
❏ Key Questions to Ask, TE
❏ Study Guide 2.3, CR
❏ Inclusion Notes 2.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.3, CR
Assessment Options
❏ Quiz for 2.1 to 2.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 2.1 to 2.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
2.4
Multiply Real
Numbers
❏ Practice B 2.4, CR
❏ Notetaking Guide 2.4
❏ Key Questions to Ask, TE
❏ Study Guide 2.4, CR
❏ Inclusion Notes 2.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.4, CR
2.5
Apply the
Distributive
Property
❏ Practice B 2.5, CR
❏ Notetaking Guide 2.5
❏ Key Questions to Ask, TE
❏ Study Guide 2.5, CR
❏ Inclusion Notes 2.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.5, CR
❏ Quiz for 2.4 to 2.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 2.4 to 2.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
68
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 2.1, CR
❏ Notetaking Guide 2.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.1, CR
❏ Practice C 2.1, CR
❏ Challenge 2.1, CR
❏ Pre-AP Best Practices 2.1, PAP
❏ Spanish Study Guide, 2.1
❏ Student Resources in Spanish, 2.1
❏ English Learner Notes 2.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 2.2, CR
❏ Notetaking Guide 2.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.2, CR
❏ Practice C 2.2, CR
❏ Challenge 2.2, CR
❏ Pre-AP Best Practices 2.2, PAP
❏ Spanish Study Guide, 2.2
❏ Student Resources in Spanish, 2.2
❏ English Learner Notes 2.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 2.3, CR
❏ Notetaking Guide 2.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.3, CR
❏ Practice C 2.3, CR
❏ Challenge 2.3, CR
❏ Pre-AP Best Practices 2.3, PAP
❏ Spanish Study Guide, 2.3
❏ Student Resources in Spanish, 2.3
❏ English Learner Notes 2.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 2.1 to 2.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 2.1 to 2.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 2.1 to 2.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 2.4, CR
❏ Notetaking Guide 2.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.4, CR
❏ Practice C 2.4, CR
❏ Challenge 2.4, CR
❏ Pre-AP Best Practices 2.4, PAP
❏ Spanish Study Guide, 2.4
❏ Student Resources in Spanish, 2.4
❏ English Learner Notes 2.4, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 2.5, CR
❏ Notetaking Guide 2.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.5, CR
❏ Practice C 2.5, CR
❏ Challenge 2.5, CR
❏ Pre-AP Best Practices 2.5, PAP
❏ Pre-AP Copymaster 2.5, PAP
❏ Spanish Study Guide, 2.5
❏ Student Resources in Spanish, 2.5
❏ English Learner Notes 2.5, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 2.4 to 2.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 2.4 to 2.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz 2.4 to 2.5, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
Course Planner
69
Course Planner for Differentiated Instruction
Chapter 2 – Properties of Real Numbers
Lesson
2.6
Divide Real
Numbers
2.7
Find Square
Roots and
Compare Real
Numbers
(1 day)
Assessment Options
Content
Standards
CC.9-12.N.Q.1, CC.9-12.N.Q.2
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 2.6, CR
❏ Notetaking Guide 2.6
❏ Key Questions to Ask, TE
❏ Study Guide 2.6, CR
❏ Inclusion Notes 2.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.6, CR
❏ Practice B 2.7, CR
❏ Notetaking Guide 2.7
❏ Key Questions to Ask, TE
❏ Study Guide 2.7, CR
❏ Inclusion Notes 2.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 2.7, CR
❏ Quiz for 2.6 to 2.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 2.6 to 2.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
70
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 2.6, CR
❏ Notetaking Guide 2.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.6, CR
❏ Practice C 2.6, CR
❏ Challenge 2.6, CR
❏ Pre-AP Best Practices 2.6, PAP
❏ Pre-AP Copymaster 2.6, PAP
❏ Spanish Study Guide, 2.6
❏ Student Resources in Spanish, 2.6
❏ English Learner Notes 2.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 2.7, CR
❏ Notetaking Guide 2.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 2.7, CR
❏ Practice C 2.7, CR
❏ Challenge 2.7, CR
❏ Pre-AP Best Practices 2.7, PAP
❏ Pre-AP Copymaster 2.7, PAP
❏ Spanish Study Guide, 2.7
❏ Student Resources in Spanish, 2.7
❏ English Learner Notes 2.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 2.6 to 2.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 2.6 to 2.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 2.6 to 2.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
71
Course Planner for Differentiated Instruction
Chapter 3 – Solving Linear Equations
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
Extension: Use
Real and Rational
Numbers (CC)
(1 day)
CC.9-12.N.RN.3, CC.9-12.A.REI.1
Activity: Modeling
One-Step Equations
(1/2 day)
CC.9-12.CED.1, CC.9-12.A.REI.1,
CC.9-12.A.REI.3
3.1
Solve One-Step
Equations
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.REI.1,
CC.9-12.A.REI.3
❏ Practice B 3.1, CR
❏ Notetaking Guide 3.1
❏ Key Questions to Ask, TE
❏ Study Guide 3.1, CR
❏ Inclusion Notes 3.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.1, CR
3.2
Solve Two-Step
Equations
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.REI.3
❏ Practice B 3.2, CR
❏ Notetaking Guide 3.2
❏ Key Questions to Ask, TE
❏ Study Guide 3.2, CR
❏ Inclusion Notes 3.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.2, CR
3.3
Solve MultiStep Equations
(2 days)
CC.9-12.A.CED.1, CC.9-12.A.REI.3
❏ Practice B 3.3, CR
❏ Notetaking Guide 3.3
❏ Key Questions to Ask, TE
❏ Study Guide 3.3, CR
❏ Inclusion Notes 3.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.3, CR
❏ Quiz for 3.1 to 3.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 3.1 to 3.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 3.4, CR
❏ Notetaking Guide 3.4
❏ Key Questions to Ask, TE
❏ Study Guide 3.4, CR
❏ Inclusion Notes 3.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.4, CR
Assessment Options
3.4
Solve
Equations with
Variables on
Both Sides
(1 day)
Activity: Solve
Equations Using
Tables
(1/2 day)
CC.9-12.A.CED.1, CC.9-12.A.REI.3,
CC.9-12.A.REI.11
CC.9-12.A.CED.1, CC.9-12.A.REI.3
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
72
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 3.1, CR
❏ Notetaking Guide 3.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.1, CR
❏ Practice C 3.1, CR
❏ Challenge 3.1, CR
❏ Pre-AP Best Practices 3.1, PAP
❏ Spanish Study Guide, 3.1
❏ Student Resources in Spanish, 3.1
❏ English Learner Notes 3.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 3.2, CR
❏ Notetaking Guide 3.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.2, CR
❏ Practice C 3.2, CR
❏ Challenge 3.2, CR
❏ Pre-AP Best Practices 3.2, PAP
❏ Spanish Study Guide, 3.2
❏ Student Resources in Spanish, 3.2
❏ English Learner Notes 3.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 3.3, CR
❏ Notetaking Guide 3.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.3, CR
❏ Practice C 3.3, CR
❏ Challenge 3.3, CR
❏ Pre-AP Best Practices 3.3, PAP
❏ Spanish Study Guide, 3.3
❏ Student Resources in Spanish, 3.3
❏ English Learner Notes 3.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 3.1 to 3.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 3.1 to 3.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 3.1 to 3.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 3.4, CR
❏ Notetaking Guide 3.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.4, CR
❏ Practice C 3.4, CR
❏ Challenge 3.4, CR
❏ Pre-AP Best Practices 3.4, PAP
❏ Spanish Study Guide, 3.4
❏ Student Resources in Spanish, 3.4
❏ English Learner Notes 3.4, DIR
❏ Multi-Language Visual Glossary
Course Planner
73
Course Planner for Differentiated Instruction
Chapter 3 – Solving Linear Equations
Lesson
Extension: Apply
Properties
of Equality (CC)
(1 day)
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
CC.9-12.A.REI.1
3.5
Write Ratios
CC.9-12.A.CED.1, CC.9-12.A.REI.3
and Proportions
(1 day)
❏ Practice B 3.5, CR
❏ Notetaking Guide 3.5
❏ Key Questions to Ask, TE
❏ Study Guide 3.5, CR
❏ Inclusion Notes 3.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.5, CR
3.6
Solve
Proportions
Using Cross
Products
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.REI.3
❏ Practice B 3.6, CR
❏ Notetaking Guide 3.6
❏ Key Questions to Ask, TE
❏ Study Guide 3.6, CR
❏ Inclusion Notes 3.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.6, CR
Assessment Options
❏ Quiz for 3.4 to 3.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 3.4 to 3.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
3.7
Solve Percent
Problems
❏ Practice B 3.7, CR
❏ Notetaking Guide 3.7
❏ Key Questions to Ask, TE
❏ Study Guide 3.7, CR
❏ Inclusion Notes 3.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.7, CR
3.8
Rewrite
Equations and
Formulas
(1 day)
❏ Practice B 3.8, CR
❏ Notetaking Guide 3.8
❏ Key Questions to Ask, TE
❏ Study Guide 3.8, CR
❏ Inclusion Notes 3.8, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 3.8, CR
❏ Quiz for 3.7 to 3.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 3.7 to 3.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Assessment Options
CC.9-12.N.Q.1, CC.9-12.A.CED.4,
CC.9-12.A.REI.3
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
74
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 3.5, CR
❏ Notetaking Guide 3.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.5, CR
❏ Practice C 3.5, CR
❏ Challenge 3.5, CR
❏ Pre-AP Best Practices 3.5, PAP
❏ Pre-AP Copymaster 3.5, PAP
❏ Spanish Study Guide, 3.5
❏ Student Resources in Spanish, 3.5
❏ English Learner Notes 3.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 3.6, CR
❏ Notetaking Guide 3.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.6, CR
❏ Practice C 3.6, CR
❏ Challenge 3.6, CR
❏ Pre-AP Best Practices 3.6, PAP
❏ Pre-AP Copymaster 3.6, PAP
❏ Spanish Study Guide, 3.6
❏ Student Resources in Spanish, 3.6
❏ English Learner Notes 3.6, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 3.4 to 3.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 3.4 to 3.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz 3.4 to 3.6, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
❏ Practice A 3.7, CR
❏ Notetaking Guide 3.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.7, CR
❏ Practice C 3.7, CR
❏ Challenge 3.7, CR
❏ Pre-AP Best Practices 3.7, PAP
❏ Pre-AP Copymaster 3.7, PAP
❏ Spanish Study Guide, 3.7
❏ Student Resources in Spanish, 3.7
❏ English Learner Notes 3.7, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 3.8, CR
❏ Notetaking Guide 3.8
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 3.8, CR
❏ Practice C 3.8, CR
❏ Challenge 3.8, CR
❏ Pre-AP Best Practices 3.8, PAP
❏ Pre-AP Copymaster 3.8, PAP
❏ Spanish Study Guide, 3.8
❏ Student Resources in Spanish, 3.8
❏ English Learner Notes 3.8, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 3.7 to 3.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 3.7 to 3.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 3.7 to 3.8, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
75
Course Planner for Differentiated Instruction
Chapter 4 – Graphing Linear Equations and Functions
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
4.1
Plot Points in
a Coordinate
Plane
(1 day)
CC.9-12.F.IF.5, CC.9-12.F.IF.7a
❏ Practice B 4.1, CR
❏ Notetaking Guide 4.1
❏ Key Questions to Ask, TE
❏ Study Guide 4.1, CR
❏ Inclusion Notes 4.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.1, CR
4.2
Graph Linear
Equations
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.10, CC.9-12.F.IF.5,
CC.9-12.F.IF.7a
❏ Practice B 4.2, CR
❏ Notetaking Guide 4.2
❏ Key Questions to Ask, TE
❏ Study Guide 4.2, CR
❏ Inclusion Notes 4.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.2, CR
❏ Practice B 4.3, CR
❏ Notetaking Guide 4.3
❏ Key Questions to Ask, TE
❏ Study Guide 4.3, CR
❏ Inclusion Notes 4.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.3, CR
❏ Quiz for 4.1 to 4.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 4.1 to 4.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 4.4, CR
❏ Notetaking Guide 4.4
❏ Key Questions to Ask, TE
❏ Study Guide 4.4, CR
❏ Inclusion Notes 4.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.4, CR
Activity: Graphing
Linear Equations
(1/2 day)
CC.9-12.N.Q.1, CC.9-12.F.IF.7a
Extension:
Identify Discrete
and Continuous
Functions (CC)
(1/2 day)
CC.9-12.F.IF.5
4.3
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7a
Graph Using
Intercepts
(1 day)
Assessment Options
Activity: Slopes
of Lines
(1/2 day)
CC.9-12.F.IF.4
4.4
CC.9-12.F.IF.4, CC.9-12.F.IF.6,
CC.9-12.S.ID.7
Find Slope and
Rate of Change
(2 days)
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
76
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 4.1, CR
❏ Notetaking Guide 4.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.1, CR
❏ Practice C 4.1, CR
❏ Challenge 4.1, CR
❏ Pre-AP Best Practices 4.1, PAP
❏ Spanish Study Guide, 4.1
❏ Student Resources in Spanish, 4.1
❏ English Learner Notes 4.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 4.2, CR
❏ Notetaking Guide 4.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.2, CR
❏ Practice C 4.2, CR
❏ Challenge 4.2, CR
❏ Pre-AP Best Practices 4.2, PAP
❏ Spanish Study Guide, 4.2
❏ Student Resources in Spanish, 4.2
❏ English Learner Notes 4.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 4.3, CR
❏ Notetaking Guide 4.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.3, CR
❏ Practice C 4.3, CR
❏ Challenge 4.3, CR
❏ Pre-AP Best Practices 4.3, PAP
❏ Spanish Study Guide, 4.3
❏ Student Resources in Spanish, 4.3
❏ English Learner Notes 4.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 4.1 to 4.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 4.1 to 4.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 4.1 to 4.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 4.4, CR
❏ Notetaking Guide 4.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.4, CR
❏ Practice C 4.4, CR
❏ Challenge 4.4, CR
❏ Pre-AP Best Practices 4.4, PAP
❏ Spanish Study Guide, 4.4
❏ Student Resources in Spanish, 4.4
❏ English Learner Notes 4.4, DIR
❏ Multi-Language Visual Glossary
Course Planner
77
Course Planner for Differentiated Instruction
Chapter 4 – Graphing Linear Equations and Functions
Lesson
Content
Standards
Activity: Slopes and
y-Intercept (1/2 day)
CC.9-12.F.IF.4
4.5
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.5, CC.9-12.F.IF.7a
Graph Using
Slope-Intercept
Form
(1 day)
Extension: Solve
Linear Equations by
Graphing (1/2 day)
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 4.5, CR
❏ Notetaking Guide 4.5
❏ Key Questions to Ask, TE
❏ Study Guide 4.5, CR
❏ Inclusion Notes 4.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.5, CR
❏ Quiz for 4.4 to 4.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 4.4 to 4.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
CC.9-12.A.REI.3, CC.9-12.A.REI.11
Assessment Options
4.6
Model Direct
Variation
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.6, CC.9-12.F.IF.7a
❏ Practice B 4.6, CR
❏ Notetaking Guide 4.6
❏ Key Questions to Ask, TE
❏ Study Guide 4.6, CR
❏ Inclusion Notes 4.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.6, CR
4.7
Graph Linear
Functions
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.1, CC.9-12.F.IF.2,
CC.9-12.F.IF.5, CC.9-12.F.IF.7a,
CC.9-12.F.BF.3
❏ Practice B 4.7, CR
❏ Notetaking Guide 4.7
❏ Key Questions to Ask, TE
❏ Study Guide 4.7, CR
❏ Inclusion Notes 4.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 4.7, CR
❏ Quiz for 4.6 to 4.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 4.6 to 4.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Activity: Solve
Linear Equations by
Graphing Each Side
(CC) (1/2 day)
Assessment Options
CC.9-12.A.REI.11
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
78
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 4.5, CR
❏ Notetaking Guide 4.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.5, CR
❏ Practice C 4.5, CR
❏ Challenge 4.5, CR
❏ Pre-AP Best Practices 4.5, PAP
❏ Pre-AP Copymaster 4.5, PAP
❏ Spanish Study Guide, 4.5
❏ Student Resources in Spanish, 4.5
❏ English Learner Notes 4.5, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 4.4 to 4.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 4.4 to 4.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz 4.4 to 4.5, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
❏ Practice A 4.6, CR
❏ Notetaking Guide 4.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.6, CR
❏ Practice C 4.6, CR
❏ Challenge 4.6, CR
❏ Pre-AP Best Practices 4.6, PAP
❏ Pre-AP Copymaster 4.6, PAP
❏ Spanish Study Guide, 4.6
❏ Student Resources in Spanish, 4.6
❏ English Learner Notes 4.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 4.7, CR
❏ Notetaking Guide 4.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 4.7, CR
❏ Practice C 4.7, CR
❏ Challenge 4.7, CR
❏ Pre-AP Best Practices 4.7, PAP
❏ Pre-AP Copymaster 4.7, PAP
❏ Spanish Study Guide, 4.7
❏ Student Resources in Spanish, 4.7
❏ English Learner Notes 4.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 4.6 to 4.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 4.6 to 4.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 4.6 to 4.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
79
Course Planner for Differentiated Instruction
Chapter 5 – Graphing Linear Equations and Functions
Lesson
Content
Standards
Activity: Modeling
Linear Relationships
(1/2 day)
CC.9-12.F.BF.1a, CC.9-12.F.LE.2
5.1
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.BF.1a,
CC.9-12.F.LE.2, CC.9-12.F.LE.5,
CC.9-12.S.ID.7
Write Linear
Equations
in SlopeIntercept Form
(1 day)
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 5.1, CR
❏ Notetaking Guide 5.1
❏ Key Questions to Ask, TE
❏ Study Guide 5.1, CR
❏ Inclusion Notes 5.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.1, CR
Activity: Investigate
Families of Lines
(1/2 day)
CC.9-12.F.BF.3
5.2
Use Linear
Equations
in SlopeIntercept Form
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.6,
CC.9-12.F.BF.1a, CC.9-12.F.LE.2,
CC.9-12.F.LE.5, CC.9-12.S.ID.7
❏ Practice B 5.2, CR
❏ Notetaking Guide 5.2
❏ Key Questions to Ask, TE
❏ Study Guide 5.2, CR
❏ Inclusion Notes 5.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.2, CR
5.3
Write Linear
Equations
in Point-Slope
Form
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.6,
CC.9-12.F.IF.7a, CC.9-12.F.BF.1a,
CC.9-12.F.LE.2, CC.9-12.F.LE.5,
CC.9-12.S.ID.7
❏ Practice B 5.3, CR
❏ Notetaking Guide 5.3
❏ Key Questions to Ask, TE
❏ Study Guide 5.3, CR
❏ Inclusion Notes 5.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.3, CR
❏ Practice B 5.4, CR
❏ Notetaking Guide 5.4
❏ Key Questions to Ask, TE
❏ Study Guide 5.4, CR
❏ Inclusion Notes 5.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.4, CR
❏ Quiz for 5.1 to 5.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 5.1 to 5.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
Extension:
Relate Arithmetic
Sequences to Linear
Functions (1/2 day)
CC.9-12.F.IF.3, CC.9-12.F.BF.2
5.4
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.LE.2
Write Linear
Equations in
Standard Form
(2 days)
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
80
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 5.1, CR
❏ Notetaking Guide 5.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.1, CR
❏ Practice C 5.1, CR
❏ Challenge 5.1, CR
❏ Pre-AP Best Practices 5.1, PAP
❏ Spanish Study Guide, 5.1
❏ Student Resources in Spanish, 5.1
❏ English Learner Notes 5.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 5.2, CR
❏ Notetaking Guide 5.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.2, CR
❏ Practice C 5.2, CR
❏ Challenge 5.2, CR
❏ Pre-AP Best Practices 5.2, PAP
❏ Spanish Study Guide, 5.2
❏ Student Resources in Spanish, 5.2
❏ English Learner Notes 5.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 5.3, CR
❏ Notetaking Guide 5.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.3, CR
❏ Practice C 5.3, CR
❏ Challenge 5.3, CR
❏ Pre-AP Best Practices 5.3, PAP
❏ Spanish Study Guide, 5.3
❏ Student Resources in Spanish, 5.3
❏ English Learner Notes 5.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 5.4, CR
❏ Notetaking Guide 5.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.4, CR
❏ Practice C 5.4, CR
❏ Challenge 5.4, CR
❏ Pre-AP Best Practices 5.4, PAP
❏ Spanish Study Guide, 5.4
❏ Student Resources in Spanish, 5.4
❏ English Learner Notes 5.4, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 5.1 to 5.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 5.1 to 5.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 5.1 to 5.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
Course Planner
81
Course Planner for Differentiated Instruction
Chapter 5 – Graphing Linear Equations and Functions
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
5.5
Write Equations
of Parallel and
Perpendicular
Lines
(1 day)
CC.9-12.F.LE.2, CC.9-12.G.GPE.5
❏ Practice B 5.5, CR
❏ Notetaking Guide 5.5
❏ Key Questions to Ask, TE
❏ Study Guide 5.5, CR
❏ Inclusion Notes 5.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.5, CR
5.6
Apply the
Distance
and Midpoint
Formulas
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.6,
CC.9-12.F.BF.1a, CC.9-12.F.LE.2,
CC.9-12.F.LE.5, CC.9-12.S.ID.6a,
CC.9-12.S.ID.6c, CC.9-12.S.ID.7
❏ Practice B 5.6, CR
❏ Notetaking Guide 5.6
❏ Key Questions to Ask, TE
❏ Study Guide 5.6, CR
❏ Inclusion Notes 5.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.6, CR
❏ Practice B 5.7, CR
❏ Notetaking Guide 5.7
❏ Key Questions to Ask, TE
❏ Study Guide 5.7, CR
❏ Inclusion Notes 5.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 5.7, CR
❏ Quiz for 5.5 to 5.7, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 5.5 to 5.7, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Activity: Perform
Linear Regression
(1/2 day)
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c,
CC.9-12.S.ID.8
Extension:
Correlation and
Causation (1/2 day)
CC.9-12.S.ID.9
Activity: Collecting
and Organizing Data
(1/2 day)
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c
5.7
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.BF.1a,
CC.9-12.F.LE.2, CC.9-12.S.ID.6a,
CC.9-12.S.ID.6c, CC.9-12.S.ID.7
Predict with
Linear Models
(1 day)
Activity: Model Data
from the Internet
(1/2 day)
CC.9-12.S.ID.6a, CC.9-12.S.ID.6c
Extension: Assess
the Fit of a Linear
Model (CC) (1/2 day)
CC.9-12.S.ID.6
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
82
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 5.5, CR
❏ Notetaking Guide 5.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.5, CR
❏ Practice C 5.5, CR
❏ Challenge 5.5, CR
❏ Pre-AP Best Practices 5.5, PAP
❏ Pre-AP Copymaster 5.5, PAP
❏ Spanish Study Guide, 5.5
❏ Student Resources in Spanish, 5.5
❏ English Learner Notes 5.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 5.6, CR
❏ Notetaking Guide 5.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.6, CR
❏ Practice C 5.6, CR
❏ Challenge 5.6, CR
❏ Pre-AP Best Practices 5.6, PAP
❏ Pre-AP Copymaster 5.6, PAP
❏ Spanish Study Guide, 5.6
❏ Student Resources in Spanish, 5.6
❏ English Learner Notes 5.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 5.7, CR
❏ Notetaking Guide 5.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 5.7, CR
❏ Practice C 5.7, CR
❏ Challenge 5.7, CR
❏ Pre-AP Best Practices 5.7, PAP
❏ Pre-AP Copymaster 5.7, PAP
❏ Spanish Study Guide, 5.7
❏ Student Resources in Spanish, 5.7
❏ English Learner Notes 5.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 5.5 to 5.7, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 5.5 to 5.7, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 5.5 to 5.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
83
Course Planner for Differentiated Instruction
Chapter 6 – Solving and Graphing Linear Inequalities
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
6.1
Solve
Inequalities
Using Addition
and Subtraction
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.CED.3,
CC.9-12.A.REI.3
❏ Practice B 6.1, CR
❏ Notetaking Guide 6.1
❏ Key Questions to Ask, TE
❏ Study Guide 6.1, CR
❏ Inclusion Notes 6.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.1, CR
6.2
Solve
Inequalities
Using
Multiplication
and Division
(1/2 day)
CC.9-12.A.CED.1, CC.9-12.A.CED.3,
CC.9-12.A.REI.3
❏ Practice B 6.2, CR
❏ Notetaking Guide 6.2
❏ Key Questions to Ask, TE
❏ Study Guide 6.2, CR
❏ Inclusion Notes 6.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.2, CR
❏ Quiz for 6.1 to 6.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 6.1 to 6.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 6.3, CR
❏ Notetaking Guide 6.3
❏ Key Questions to Ask, TE
❏ Study Guide 6.3, CR
❏ Inclusion Notes 6.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.3, CR
❏ Practice B 6.4, CR
❏ Notetaking Guide 6.4
❏ Key Questions to Ask, TE
❏ Study Guide 6.4, CR
❏ Inclusion Notes 6.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.4, CR
Activity: Inequalities
with Negative
Coefficients
(1 day)
CC.9-12.A.REI.3
Assessment Options
6.3
Solve
Multi-Step
Inequalities
(1 day)
CC.9-12.A.CED.1, CC.9-12.A.CED.3,
CC.9-12.A.REI.3
Extension: Solve
Linear Inequalities
by Graphing
(1/2 day)
CC.9-12.A.REI.10
6.4
CC.9-12.A.CED.1, CC.9-12.A.CED.3,
CC.9-12.A.REI.3
Solve
Compound
Inequalities
(2 days)
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
84
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 6.1, CR
❏ Notetaking Guide 6.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.1, CR
❏ Practice C 6.1, CR
❏ Challenge 6.1, CR
❏ Pre-AP Best Practices 6.1, PAP
❏ Spanish Study Guide, 6.1
❏ Student Resources in Spanish, 6.1
❏ English Learner Notes 6.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 6.2, CR
❏ Notetaking Guide 6.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.2, CR
❏ Practice C 6.2, CR
❏ Challenge 6.2, CR
❏ Pre-AP Best Practices 6.2, PAP
❏ Spanish Study Guide, 6.2
❏ Student Resources in Spanish, 6.2
❏ English Learner Notes 6.2, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 6.1 to 6.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 6.1 to 6.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 6.1 to 6.2, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 6.3, CR
❏ Notetaking Guide 6.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.3, CR
❏ Practice C 6.3, CR
❏ Challenge 6.3, CR
❏ Pre-AP Best Practices 6.3, PAP
❏ Spanish Study Guide, 6.3
❏ Student Resources in Spanish, 6.3
❏ English Learner Notes 6.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 6.4, CR
❏ Notetaking Guide 6.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.4, CR
❏ Practice C 6.4, CR
❏ Challenge 6.4, CR
❏ Pre-AP Best Practices 6.4, PAP
❏ Spanish Study Guide, 6.4
❏ Student Resources in Spanish, 6.4
❏ English Learner Notes 6.4, DIR
❏ Multi-Language Visual Glossary
Course Planner
85
Course Planner for Differentiated Instruction
Chapter 6 – Solving and Graphing Linear Inequalities
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Quiz for 6.3 to 6.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 6.3 to 6.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 6.5, CR
❏ Notetaking Guide 6.5
❏ Key Questions to Ask, TE
❏ Study Guide 6.5, CR
❏ Inclusion Notes 6.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.5, CR
❏ Practice B 6.6, CR
❏ Notetaking Guide 6.6
❏ Key Questions to Ask, TE
❏ Study Guide 6.6, CR
❏ Inclusion Notes 6.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.6, CR
❏ Practice B 6.7, CR
❏ Notetaking Guide 6.7
❏ Key Questions to Ask, TE
❏ Study Guide 6.7, CR
❏ Inclusion Notes 6.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 6.7, CR
❏ Quiz for 6.5 to 6.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 6.5 to 6.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Activity: Statements
with And and Or
(1/2 day)
Activity: Solve
Compound
Inequalities (1/2 day)
CC.9-12.A.REI.3
Assessment Options
6.5
Solve Absolute
Value Equations
(2 days)
CC.9-12.A.CED.1, CC.9-12.A.CED.3,
CC.9-12.F.IF.7b
Extension: Graph
Absolute Value
Functions (1/2 day)
CC.9-12.F.BF.3
6.6
CC.9-12.A.CED.1, CC.9-12.A.CED.3
Solve Absolute
Value
Inequalities
(1 day)
Activity: Linear
Inequalities in Two
Variables (1/2 day)
CC.9-12.A.REI.12
6.7
CC.9-12.A.CED.3, CC.9-12.A.REI.12
Graph Linear
Inequalities in
Two Variables
(2 days)
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
86
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Developing Learners
[RTI Tiers 1 and 2]
Advanced Learners
English Language Learners
❏ Quiz for 6.3 to 6.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 6.3 to 6.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 6.3 to 6.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 6.5, CR
❏ Notetaking Guide 6.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.5, CR
❏ Practice C 6.5, CR
❏ Challenge 6.5, CR
❏ Pre-AP Best Practices 6.5, PAP
❏ Pre-AP Copymaster 6.5, PAP
❏ Spanish Study Guide, 6.5
❏ Student Resources in Spanish, 6.5
❏ English Learner Notes 6.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 6.6, CR
❏ Notetaking Guide 6.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.6, CR
❏ Practice C 6.6, CR
❏ Challenge 6.6, CR
❏ Pre-AP Best Practices 6.6, PAP
❏ Pre-AP Copymaster 6.6, PAP
❏ Spanish Study Guide, 6.6
❏ Student Resources in Spanish, 6.6
❏ English Learner Notes 6.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 6.7, CR
❏ Notetaking Guide 6.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 6.7, CR
❏ Practice C 6.7, CR
❏ Challenge 6.7, CR
❏ Pre-AP Best Practices 6.7, PAP
❏ Pre-AP Copymaster 6.7, PAP
❏ Spanish Study Guide, 6.7
❏ Student Resources in Spanish, 6.7
❏ English Learner Notes 6.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 6.5 to 6.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 6.5 to 6.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 6.5 to 6.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
87
Course Planner for Differentiated Instruction
Chapter 7 – Systems of Equations and Inequalities
Lesson
Content
Standards
Activity: Solving
Linear Systems
Using Tables
(1/2 day)
CC.9-12.A.REI.6
7.1
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.6
Solve Linear
Systems by
Graphing
(1 day)
Activity: Solving
Linear Systems by
Graphing
(1/2 day)
CC.9-12.A.REI.6
7.2
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.5, CC.9-12.A.REI.6
Solve Linear
Systems by
Substitution
(2 days)
Assessment Options
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 7.1, CR
❏ Notetaking Guide 7.1
❏ Key Questions to Ask, TE
❏ Study Guide 7.1, CR
❏ Inclusion Notes 7.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.1, CR
❏ Practice B 7.2, CR
❏ Notetaking Guide 7.2
❏ Key Questions to Ask, TE
❏ Study Guide 7.2, CR
❏ Inclusion Notes 7.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.2, CR
❏ Quiz for 7.1 to 7.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 7.1 to 7.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
Activity: Linear
Systems and
Elimination
(1/2 day)
CC.9-12.A.REI.6
7.3
Solve Linear
Systems by
Adding and
Subtracting
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.6
❏ Practice B 7.3, CR
❏ Notetaking Guide 7.3
❏ Key Questions to Ask, TE
❏ Study Guide 7.3, CR
❏ Inclusion Notes 7.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.3, CR
7.4
Solve Linear
Systems by
Multiplying First
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.5, CC.9-12.A.REI.6
❏ Practice B 7.4, CR
❏ Notetaking Guide 7.4
❏ Key Questions to Ask, TE
❏ Study Guide 7.4, CR
❏ Inclusion Notes 7.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.4, CR
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
88
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 7.1, CR
❏ Notetaking Guide 7.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.1, CR
❏ Practice C 7.1, CR
❏ Challenge 7.1, CR
❏ Pre-AP Best Practices 7.1, PAP
❏ Spanish Study Guide, 7.1
❏ Student Resources in Spanish, 7.1
❏ English Learner Notes 7.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 7.2, CR
❏ Notetaking Guide 7.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.2, CR
❏ Practice C 7.2, CR
❏ Challenge 7.2, CR
❏ Pre-AP Best Practices 7.2, PAP
❏ Spanish Study Guide, 7.2
❏ Student Resources in Spanish, 7.2
❏ English Learner Notes 7.2, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 7.1 to 7.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 7.1 to 7.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 7.1 to 7.2, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 7.3, CR
❏ Notetaking Guide 7.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.3, CR
❏ Practice C 7.3, CR
❏ Challenge 7.3, CR
❏ Pre-AP Best Practices 7.3, PAP
❏ Spanish Study Guide, 7.3
❏ Student Resources in Spanish, 7.3
❏ English Learner Notes 7.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 7.4, CR
❏ Notetaking Guide 7.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.4, CR
❏ Practice C 7.4, CR
❏ Challenge 7.4, CR
❏ Pre-AP Best Practices 7.4, PAP
❏ Spanish Study Guide, 7.4
❏ Student Resources in Spanish, 7.4
❏ English Learner Notes 7.4, DIR
❏ Multi-Language Visual Glossary
Course Planner
89
Course Planner for Differentiated Instruction
Chapter 7 – Systems of Equations and Inequalities
Lesson
Activity: Multiply
and Then Add
Equations (CC)
(1/2 day)
Content
Standards
Special Needs Learners
[RTI Tier 2]
❏ Quiz for 7.3 to 7.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 7.3 to 7.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 7.5, CR
❏ Notetaking Guide 7.5
❏ Key Questions to Ask, TE
❏ Study Guide 7.5, CR
❏ Inclusion Notes 7.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.5, CR
❏ Practice B 7.6, CR
❏ Notetaking Guide 7.6
❏ Key Questions to Ask, TE
❏ Study Guide 7.6, CR
❏ Inclusion Notes 7.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 7.6, CR
❏ Quiz for 7.5 to 7.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 7.5 to 7.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
CC.9-12.A.REI.5
Assessment Options
7.5
Solve Special
Types of Linear
Systems
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.5, CC.9-12.A.REI.6
A
Extension:
Use Piecewise
Functions
(1 day)
CC.9-12.F.IF.7b
7.6
Solve Systems
of Linear
Inequalities
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.12
Assessment Options
On-Level Learners
[RTI Tier 1]
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
90
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Developing Learners
[RTI Tiers 1 and 2]
Advanced Learners
English Language Learners
❏ Quiz for 7.3 to 7.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 7.3 to 7.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 7.3 to 7.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 7.5, CR
❏ Notetaking Guide 7.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.5, CR
❏ Practice C 7.5, CR
❏ Challenge 7.5, CR
❏ Pre-AP Best Practices 7.5, PAP
❏ Pre-AP Copymaster 7.5, PAP
❏ Spanish Study Guide, 7.5
❏ Student Resources in Spanish, 7.5
❏ English Learner Notes 7.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 7.6, CR
❏ Notetaking Guide 7.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 7.6, CR
❏ Practice C 7.6, CR
❏ Challenge 7.6, CR
❏ Pre-AP Best Practices 7.6, PAP
❏ Pre-AP Copymaster 7.6, PAP
❏ Spanish Study Guide, 7.6
❏ Student Resources in Spanish, 7.6
❏ English Learner Notes 7.6, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 7.5 to 7.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 7.5 to 7.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 7.5 to 7.6, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
91
Course Planner for Differentiated Instruction
Chapter 8 – Exponents and Exponential Functions
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
8.1
Apply Exponent
Properties
Involving
Products
❏ Practice B 8.1, CR
❏ Notetaking Guide 8.1
❏ Key Questions to Ask, TE
❏ Study Guide 8.1, CR
❏ Inclusion Notes 8.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.1, CR
8.2
Apply Exponent
Properties
Involving
Quotients
❏ Practice B 8.2, CR
❏ Notetaking Guide 8.2
❏ Key Questions to Ask, TE
❏ Study Guide 8.2, CR
❏ Inclusion Notes 8.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.2, CR
❏ Quiz for 8.1 to 8.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 8.1 to 8.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 8.3, CR
❏ Notetaking Guide 8.3
❏ Key Questions to Ask, TE
❏ Study Guide 8.3, CR
❏ Inclusion Notes 8.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.3, CR
❏ Practice B 8.4, CR
❏ Notetaking Guide 8.4
❏ Key Questions to Ask, TE
❏ Study Guide 8.4, CR
❏ Inclusion Notes 8.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.4, CR
❏ Quiz for 8.3 to 8.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 8.3 to 8.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
Assessment Options
8.3
Define and
Use Zero
and Negative
Exponents
(1 day)
Extension: Define
and Use Fractional
Exponents
(1/2 day)
8.4
Use Scientific
Notation
(2 days)
Assessment Options
CC.9-12.A.SSE.3c, CC.9-12.N.RN.1
CC.9-12.N.RN.1, CC.9-12.N.RN.2
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
92
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 8.1, CR
❏ Notetaking Guide 8.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.1, CR
❏ Practice C 8.1, CR
❏ Challenge 8.1, CR
❏ Pre-AP Best Practices 8.1, PAP
❏ Spanish Study Guide, 8.1
❏ Student Resources in Spanish, 8.1
❏ English Learner Notes 8.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 8.2, CR
❏ Notetaking Guide 8.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.2, CR
❏ Practice C 8.2, CR
❏ Challenge 8.2, CR
❏ Pre-AP Best Practices 8.2, PAP
❏ Spanish Study Guide, 8.2
❏ Student Resources in Spanish, 8.2
❏ English Learner Notes 8.2, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 8.1 to 8.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 8.1 to 8.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 8.1 to 8.2, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 8.3, CR
❏ Notetaking Guide 8.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.3, CR
❏ Practice C 8.3, CR
❏ Challenge 8.3, CR
❏ Pre-AP Best Practices 8.3, PAP
❏ Spanish Study Guide, 8.3
❏ Student Resources in Spanish, 8.3
❏ English Learner Notes 8.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 8.4, CR
❏ Notetaking Guide 8.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.4, CR
❏ Practice C 8.4, CR
❏ Challenge 8.4, CR
❏ Pre-AP Best Practices 8.4, PAP
❏ Spanish Study Guide, 8.4
❏ Student Resources in Spanish, 8.4
❏ English Learner Notes 8.4, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 8.3 to 8.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 8.3 to 8.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 8.3 to 8.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
Course Planner
93
Course Planner for Differentiated Instruction
Chapter 8 – Exponents and Exponential Functions
Lesson
8.5
Write and
Graph
Exponential
Growth
Functions
(2 days)
Content
Standards
CC.9-12.A.SSE.3c (in ex. 37),
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7e, CC.9-12.F.IF.8b,
CC.9-12.F.BF.1a, CC.9-12.F.BF.3,
CC.9-12.F.LE.1, CC.9-12.F.LE.2,
CC.9-12.F.LE.5
Activity: Exponential
Models
(1/2 day)
CC.9-12.F.LE.1c
8.6
CC.9-12.A.SSE.3c (in ex. 46),
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.7e, CC.9-12.F.IF.8b,
CC.9-12.F.BF.1a, CC.9-12.F.BF.3,
CC.9-12.F.LE.2, CC.9-12.F.LE.5
Write and
Graph
Exponential
Decay
Functions
(1 day)
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 8.5, CR
❏ Notetaking Guide 8.5
❏ Key Questions to Ask, TE
❏ Study Guide 8.5, CR
❏ Inclusion Notes 8.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.5, CR
❏ Practice B 8.6, CR
❏ Notetaking Guide 8.6
❏ Key Questions to Ask, TE
❏ Study Guide 8.6, CR
❏ Inclusion Notes 8.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 8.6, CR
❏ Quiz for 8.5 to 8.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 8.5 to 8.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
CC.9-12.F.IF.3, CC.9-12.F.BF.2,
Extension: Relate
Geometric Sequences CC.9-12.F.LE.2
to Exponential
Functions (1/2 day)
B
Extension:
Define
Sequences
Recursively
(1/2 day)
Assessment Options
CC.9-12.F.IF.3, CC.9-12.F.BF.2
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
94
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 8.5, CR
❏ Notetaking Guide 8.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.5, CR
❏ Practice C 8.5, CR
❏ Challenge 8.5, CR
❏ Pre-AP Best Practices 8.5, PAP
❏ Pre-AP Copymaster 8.5, PAP
❏ Spanish Study Guide, 8.5
❏ Student Resources in Spanish, 8.5
❏ English Learner Notes 8.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 8.6, CR
❏ Notetaking Guide 8.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 8.6, CR
❏ Practice C 8.6, CR
❏ Challenge 8.6, CR
❏ Pre-AP Best Practices 8.6, PAP
❏ Pre-AP Copymaster 8.6, PAP
❏ Spanish Study Guide, 8.6
❏ Student Resources in Spanish, 8.6
❏ English Learner Notes 8.6, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 8.5 to 8.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 8.5 to 8.6, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 8.5 to 8.6, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
95
Course Planner for Differentiated Instruction
Chapter 9 – Polynomials and Factoring
Lesson
9.1
Add and
Subtract
Polynomials
(1 day)
Content
Standards
CC.9-12.A.APR.1, CC.9-12.F.IF.7c
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 9.1, CR
❏ Notetaking Guide 9.1
❏ Key Questions to Ask, TE
❏ Study Guide 9.1, CR
❏ Inclusion Notes 9.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.1, CR
Activity: Graph
Polynomial
Functions
(1/2 day)
CC.9-12.F.IF.7c
Activity:
Multiplication with
Algebra Tiles
(1/2 day)
CC.9-12.A.APR.1
9.2
Multiply
Polynomials
(1 day)
CC.9-12.A.APR.1
❏ Practice B 9.2, CR
❏ Notetaking Guide 9.2
❏ Key Questions to Ask, TE
❏ Study Guide 9.2, CR
❏ Inclusion Notes 9.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.2, CR
9.3
Find Special
Products of
Polynomials
(1 day)
CC.9-12.A.APR.1
❏ Practice B 9.3, CR
❏ Notetaking Guide 9.3
❏ Key Questions to Ask, TE
❏ Study Guide 9.3, CR
❏ Inclusion Notes 9.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.3, CR
❏ Quiz for 9.1 to 9.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 9.1 to 9.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 9.4, CR
❏ Notetaking Guide 9.4
❏ Key Questions to Ask, TE
❏ Study Guide 9.4, CR
❏ Inclusion Notes 9.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.4, CR
Assessment Options
9.4
Solve
Polynomial
Equations in
Factored Form
(2 days)
CC.9-12.A.CED.1, CC.9-12.F.IF.8a
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
96
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 9.1, CR
❏ Notetaking Guide 9.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.1, CR
❏ Practice C 9.1, CR
❏ Challenge 9.1, CR
❏ Pre-AP Best Practices 9.1, PAP
❏ Spanish Study Guide, 9.1
❏ Student Resources in Spanish, 9.1
❏ English Learner Notes 9.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 9.2, CR
❏ Notetaking Guide 9.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.2, CR
❏ Practice C 9.2, CR
❏ Challenge 9.2, CR
❏ Pre-AP Best Practices 9.2, PAP
❏ Spanish Study Guide, 9.2
❏ Student Resources in Spanish, 9.2
❏ English Learner Notes 9.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 9.3, CR
❏ Notetaking Guide 9.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.3, CR
❏ Practice C 9.3, CR
❏ Challenge 9.3, CR
❏ Pre-AP Best Practices 9.3, PAP
❏ Spanish Study Guide, 9.3
❏ Student Resources in Spanish, 9.3
❏ English Learner Notes 9.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 9.1 to 9.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 9.1 to 9.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 9.1 to 9.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 9.4, CR
❏ Notetaking Guide 9.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.4, CR
❏ Practice C 9.4, CR
❏ Challenge 9.4, CR
❏ Pre-AP Best Practices 9.4, PAP
❏ Spanish Study Guide, 9.4
❏ Student Resources in Spanish, 9.4
❏ English Learner Notes 9.4, DIR
❏ Multi-Language Visual Glossary
Course Planner
97
Course Planner for Differentiated Instruction
Chapter 9 – Polynomials and Factoring
Lesson
Content
Standards
Activity: Factorization
with Algebra Tiles
(1/2 day)
CC.9-12.F.IF.8a
9.5
CC.9-12.A.CED.1, CC.9-12.A.REI.4b,
CC.9-12.F.IF.8a
Factor
x² 1 bx 1 c
(2 days)
Activity: More
Factorization with
Algebra Tiles
(1/2 day)
CC.9-12.F.IF.8a
9.6
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4b, CC.9-12.F.IF.8a
Factor
ax² ⴙ bx 1 c
(2 days)
Assessment Options
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 9.5, CR
❏ Notetaking Guide 9.5
❏ Key Questions to Ask, TE
❏ Study Guide 9.5, CR
❏ Inclusion Notes 9.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.5, CR
❏ Practice B 9.6, CR
❏ Notetaking Guide 9.6
❏ Key Questions to Ask, TE
❏ Study Guide 9.6, CR
❏ Inclusion Notes 9.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.6, CR
❏ Quiz for 9.4 to 9.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 9.4 to 9.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
9.7
Factor Special
Products
(1 day)
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4b
❏ Practice B 9.7, CR
❏ Notetaking Guide 9.7
❏ Key Questions to Ask, TE
❏ Study Guide 9.7, CR
❏ Inclusion Notes 9.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.7, CR
9.8
Factor
Polynomials
Completely
(1 day)
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4b
❏ Practice B 9.8, CR
❏ Notetaking Guide 9.8
❏ Key Questions to Ask, TE
❏ Study Guide 9.8, CR
❏ Inclusion Notes 9.8, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 9.8, CR
❏ Quiz for 9.7 to 9.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 9.7 to 9.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
98
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 9.5, CR
❏ Notetaking Guide 9.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.5, CR
❏ Practice C 9.5, CR
❏ Challenge 9.5, CR
❏ Pre-AP Best Practices 9.5, PAP
❏ Pre-AP Copymaster 9.5, PAP
❏ Spanish Study Guide, 9.5
❏ Student Resources in Spanish, 9.5
❏ English Learner Notes 9.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 9.6, CR
❏ Notetaking Guide 9.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.6, CR
❏ Practice C 9.6, CR
❏ Challenge 9.6, CR
❏ Pre-AP Best Practices 9.6, PAP
❏ Pre-AP Copymaster 9.6, PAP
❏ Spanish Study Guide, 9.6
❏ Student Resources in Spanish, 9.6
❏ English Learner Notes 9.6, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 9.4 to 9.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 9.4 to 9.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz 9.4 to 9.6, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
❏ Practice A 9.7, CR
❏ Notetaking Guide 9.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.7, CR
❏ Practice C 9.7, CR
❏ Challenge 9.7, CR
❏ Pre-AP Best Practices 9.7, PAP
❏ Pre-AP Copymaster 9.7, PAP
❏ Spanish Study Guide, 9.7
❏ Student Resources in Spanish, 9.7
❏ English Learner Notes 9.7, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 9.8, CR
❏ Notetaking Guide 9.8
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 9.8, CR
❏ Practice C 9.8, CR
❏ Challenge 9.8, CR
❏ Pre-AP Best Practices 9.8, PAP
❏ Pre-AP Copymaster 9.8, PAP
❏ Spanish Study Guide, 9.8
❏ Student Resources in Spanish, 9.8
❏ English Learner Notes 9.8, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 9.7 to 9.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 9.7 to 9.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 9.7 to 9.8, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
99
Course Planner for Differentiated Instruction
Chapter 10 – Quadratic Equations and Functions
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
10.1 Graph
y 5 ax² 1 c
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.5,
CC.9-12.F.IF.7a, CC.9-12.F.IF.7c,
CC.9-12.F.BF.3
❏ Practice B 10.1, CR
❏ Notetaking Guide 10.1
❏ Key Questions to Ask, TE
❏ Study Guide 10.1, CR
❏ Inclusion Notes 10.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.1, CR
10.2 Graph
y 5 ax² 1 bx 1 c
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.7a, CC.9-12.F.IF.7c,
CC.9-12.F.BF.3
❏ Practice B 10.2, CR
❏ Notetaking Guide 10.2
❏ Key Questions to Ask, TE
❏ Study Guide 10.2, CR
❏ Inclusion Notes 10.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.2, CR
Extension: Graph
Quadratic Functions
in Intercept Form
(1/2 day)
CC.9-12.A.APR.3
10.3 Solve Quadratic
Equations by
Graphing
(2 days)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.A.REI.11, CC.9-12.F.IF.4,
CC.9-12.F.IF.7a, CC.9-12.F.IF.7c,
CC.9-12.F.IF.8a
❏ Practice B 10.3, CR
❏ Notetaking Guide 10.3
❏ Key Questions to Ask, TE
❏ Study Guide 10.3, CR
❏ Inclusion Notes 10.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.3, CR
Activity: Find
Minimum and
Maximum Values
and Zeros
(1/2 day)
CC.9-12.N.Q.1, CC.9-12.A.REI.11,
CC.9-12.F.IF.7a, CC.9-12.F.IF.7c
❏ Quiz for 10.1 to 10.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 10.1 to 10.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
100
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 10.1, CR
❏ Notetaking Guide 10.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.1, CR
❏ Practice C 10.1, CR
❏ Challenge 10.1, CR
❏ Pre-AP Best Practices 10.1, PAP
❏ Spanish Study Guide, 10.1
❏ Student Resources in Spanish, 10.1
❏ English Learner Notes 10.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 10.2, CR
❏ Notetaking Guide 10.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.2, CR
❏ Practice C 10.2, CR
❏ Challenge 10.2, CR
❏ Pre-AP Best Practices 10.2, PAP
❏ Spanish Study Guide, 10.2
❏ Student Resources in Spanish, 10.2
❏ English Learner Notes 10.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 10.3, CR
❏ Notetaking Guide 10.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.3, CR
❏ Practice C 10.3, CR
❏ Challenge 10.3, CR
❏ Pre-AP Best Practices 10.3, PAP
❏ Spanish Study Guide, 10.3
❏ Student Resources in Spanish, 10.3
❏ English Learner Notes 10.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 10.1 to 10.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 10.1 to 10.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 10.1 to 10.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
Course Planner
101
Course Planner for Differentiated Instruction
Chapter 10 – Quadratic Equations and Functions
Lesson
Content
Standards
10.4 Use Square
Roots to Solve
Quadratic
Equations
(2 days)
CC.9-12.A.CED.1, CC.9-12.A.CED.2,
CC.9-12.A.CED.3, CC.9-12.A.REI.4b,
CC.9-12.A.REI.11
Activity: Completing
the Square —
Algebra Tiles (1/2 day)
CC.9-12.A.SSE.3
10.5 Solve Quadratic
Equations by
Completing the
Square
(2 days)
CC.9-12.A.SSE.3, CC.9-12.A.CED.1,
CC.9-12.A.REI.4a, CC.9-12.A.REI.4b
Extension: Graph
Quadratic Functions
in Vertex Form
(1 day)
CC.9-12.A.SSE.3, CC.9-12.F.IF.7a,
CC.9-12.F.IF.7c, CC.9-12.F.IF.8a,
CC.9-12.F.BF.3
10.6 Solve Quadratic
Equations by
the Quadratic
Formula
(1 day)
CC.9-12.A.REI.4b
Assessment Options
10.7A Solve Systems
with Quadratic
Equations (CC)
(1 day)
CC.9-12.A.REI.11, CC.9-12.A.REI.7
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 10.4, CR
❏ Notetaking Guide 10.4
❏ Key Questions to Ask, TE
❏ Study Guide 10.4, CR
❏ Inclusion Notes 10.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.4, CR
❏ Practice B 10.5, CR
❏ Notetaking Guide 10.5
❏ Key Questions to Ask, TE
❏ Study Guide 10.5, CR
❏ Inclusion Notes 10.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.5, CR
❏ Practice B 10.6, CR
❏ Notetaking Guide 10.6
❏ Key Questions to Ask, TE
❏ Study Guide 10.6, CR
❏ Inclusion Notes 10.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.6, CR
❏ Quiz for 10.4 to 10.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 10.4 to 10.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Practice B 10.7A, CR
❏ Key Questions to Ask, TE
❏ Study Guide 10.7A, CR
❏ Differentiated Instruction, TE
❏ Remediation Book
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
102
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 10.4, CR
❏ Notetaking Guide 10.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.4, CR
❏ Practice C 10.4, CR
❏ Challenge 10.4, CR
❏ Pre-AP Best Practices 10.4, PAP
❏ Spanish Study Guide, 10.4
❏ Student Resources in Spanish, 10.4
❏ English Learner Notes 10.4, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 10.5, CR
❏ Notetaking Guide 10.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.5, CR
❏ Practice C 10.5, CR
❏ Challenge 10.5, CR
❏ Pre-AP Best Practices 10.5, PAP
❏ Pre-AP Copymaster 10.5, PAP
❏ Spanish Study Guide, 10.5
❏ Student Resources in Spanish, 10.5
❏ English Learner Notes 10.5, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 10.6, CR
❏ Notetaking Guide 10.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.6, CR
❏ Practice C 10.6, CR
❏ Challenge 10.6, CR
❏ Pre-AP Best Practices 10.6, PAP
❏ Pre-AP Copymaster 10.6, PAP
❏ Spanish Study Guide, 10.6
❏ Student Resources in Spanish, 10.6
❏ English Learner Notes 10.6, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 10.4 to 10.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 10.4 to 10.6, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Test and Practice Generator
❏ Quiz for 10.4 to 10.6, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, Spanish AR
❏ Test and Practice Generator
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.7A, CR
❏ Challenge 10.7A, CR
❏ Pre-AP Best Practices 10.7A, PAP
❏ Multi-Language Visual Glossary
Course Planner
103
Course Planner for Differentiated Instruction
Chapter 10 – Quadratic Equations and Functions
Lesson
Content
Standards
10.7 Interpret the
Discriminant
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 10.7, CR
❏ Notetaking Guide 10.7
❏ Key Questions to Ask, TE
❏ Study Guide 10.7, CR
❏ Inclusion Notes 10.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.7, CR
10.7A Solve
Systems with
Quadratic
Equations
(CC) (1 day)
CC.9-12.A.REI.7, CC.9-12.A.REI.11
❏ Practice B 10.7A, CR
❏ Key Questions to Ask, TE
❏ Study Guide 10.7A, CR
❏ Differentiated Instruction, TE
❏ Remediation Book
10.8 Compare
Linear,
Exponential,
and Quadratic
Models
(1 day)
CC.9-12.A.CED.2, CC.9-12.A.CED.3,
CC.9-12.F.IF.4, CC.9-12.F.IF.7a,
CC.9-12.F.IF.7c, CC.9-12.F.IF.7e,
CC.9-12.F.BF.1a, CC.9-12.F.LE.1,
CC.9-12.F.LE.5, CC.9-12.S.ID.6a
❏ Practice B 10.8, CR
❏ Notetaking Guide 10.8
❏ Key Questions to Ask, TE
❏ Study Guide 10.8, CR
❏ Inclusion Notes 10.8, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 10.8, CR
Activity: Perform
Regressions
(1/2 day)
CC.9-12.F.IF.7a, CC.9-12.F.IF.7e,
CC.9-12.S.ID.6a
10.8A Model
Relationships
(CC)
(1 day)
CC.9-12.F.IF.4, CC.9-12.F.IF.9,
CC.9-12.F.LE.1, CC.9-12.F.LE.3
❏ Practice B 10.8A, CR
❏ Key Questions to Ask, TE
❏ Study Guide 10.8A, CR
❏ Differentiated Instruction, TE
❏ Remediation Book
Activity: Average
Rate of Change (CC)
(1/2 day)
CC.9-12.F.IF.6
❏ Quiz for 10.7 to 10.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 10.7 to 10.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
104
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 10.7, CR
❏ Notetaking Guide 10.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.7, CR
❏ Practice C 10.7, CR
❏ Challenge 10.7, CR
❏ Pre-AP Best Practices 10.7, PAP
❏ Pre-AP Copymaster 10.7, PAP
❏ Spanish Study Guide, 10.7
❏ Student Resources in Spanish, 10.7
❏ English Learner Notes 10.7, DIR
❏ Multi-Language Visual Glossary
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.7A, CR
❏ Challenge 10.7A, CR
❏ Pre-AP Best Practices 10.7A, PAP
❏ Multi-Language Visual Glossary
❏ Practice A 10.8, CR
❏ Notetaking Guide 10.8
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.8, CR
❏ Practice C 10.8, CR
❏ Challenge 10.8, CR
❏ Pre-AP Best Practices 10.8, PAP
❏ Pre-AP Copymaster 10.8, PAP
❏ Spanish Study Guide, 10.8
❏ Student Resources in Spanish, 10.8
❏ English Learner Notes 10.8, DIR
❏ Multi-Language Visual Glossary
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 10.8A, CR
❏ Challenge 10.8A, CR
❏ Pre-AP Best Practices 10.8A, PAP
❏ Multi-Language Visual Glossary
❏ Quiz for 10.7 to 10.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 10.7 to 10.8, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 10.7 to 10.8, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
105
Course Planner for Differentiated Instruction
Chapter 11 – Radicals and Geometry Connections
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
11.1 Graph Square
Root Functions
❏ Practice B 11.1, CR
❏ Notetaking Guide 11.1
❏ Key Questions to Ask, TE
❏ Study Guide 11.1, CR
❏ Inclusion Notes 11.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 11.1, CR
11.2 Simplify Radical
Expressions
❏ Practice B 11.2, CR
❏ Notetaking Guide 11.2
❏ Key Questions to Ask, TE
❏ Study Guide 11.2, CR
❏ Inclusion Notes 11.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 11.2, CR
11.3 Solve Radical
Equations
❏ Practice B 11.3, CR
❏ Notetaking Guide 11.3
❏ Key Questions to Ask, TE
❏ Study Guide 11.3, CR
❏ Inclusion Notes 11.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 11.3, CR
Assessment Options
❏ Quiz for 11.1 to 11.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 11.1 to 11.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
11.4 Apply the
Pythagorean
Theorem and
Its Converse
❏ Practice B 11.4, CR
❏ Notetaking Guide 11.4
❏ Key Questions to Ask, TE
❏ Study Guide 11.4, CR
❏ Inclusion Notes 11.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 11.4, CR
11.5 Apply the
Distance
and Midpoint
Formulas
❏ Practice B 11.5, CR
❏ Notetaking Guide 11.5
❏ Key Questions to Ask, TE
❏ Study Guide 11.5, CR
❏ Inclusion Notes 11.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 11.5, CR
Assessment Options
❏ Quiz for 11.4 to 11.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 11.4 to 11.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Lesson
Extension: Derive
the Quadratic
Formula (1/2 day)
Content
Standards
CC.9-12.A.REI.4a
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
106
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 11.1, CR
❏ Notetaking Guide 11.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 11.1, CR
❏ Practice C 11.1, CR
❏ Challenge 11.1, CR
❏ Pre-AP Best Practices 11.1, PAP
❏ Spanish Study Guide, 11.1
❏ Student Resources in Spanish, 11.1
❏ English Learner Notes 11.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 11.2, CR
❏ Notetaking Guide 11.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 11.2, CR
❏ Practice C 11.2, CR
❏ Challenge 11.2, CR
❏ Pre-AP Best Practices 11.2, PAP
❏ Spanish Study Guide, 11.2
❏ Student Resources in Spanish, 11.2
❏ English Learner Notes 11.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 11.3, CR
❏ Notetaking Guide 11.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 11.3, CR
❏ Practice C 11.3, CR
❏ Challenge 11.3, CR
❏ Pre-AP Best Practices 11.3, PAP
❏ Spanish Study Guide, 11.3
❏ Student Resources in Spanish, 11.3
❏ English Learner Notes 11.3, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 11.1 to 11.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 11.1 to 11.3, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 11.1 to 11.3, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 11.4, CR
❏ Notetaking Guide 11.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 11.4, CR
❏ Practice C 11.4, CR
❏ Challenge 11.4, CR
❏ Pre-AP Best Practices 11.4, PAP
❏ Spanish Study Guide, 11.4
❏ Student Resources in Spanish, 11.4
❏ English Learner Notes 11.4, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 11.5, CR
❏ Notetaking Guide 11.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 11.5, CR
❏ Practice C 11.5, CR
❏ Challenge 11.5, CR
❏ Pre-AP Best Practices 11.5, PAP
❏ Pre-AP Copymaster 11.5, PAP
❏ Spanish Study Guide, 11.5
❏ Student Resources in Spanish, 11.5
❏ English Learner Notes 11.5, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 11.4 to 11.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 11.4 to 11.5, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 11.4 to 11.5, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
107
Course Planner for Differentiated Instruction
Chapter 12 – Rational Equations and Functions
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
12.1 Model Inverse
Variation
❏ Practice B 12.1, CR
❏ Notetaking Guide 12.1
❏ Key Questions to Ask, TE
❏ Study Guide 12.1, CR
❏ Inclusion Notes 12.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.1, CR
12.2 Graph Rational
Functions
❏ Practice B 12.2, CR
❏ Notetaking Guide 12.2
❏ Key Questions to Ask, TE
❏ Study Guide 12.2, CR
❏ Inclusion Notes 12.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.2, CR
Assessment Options
❏ Quiz for 12.1 to 12.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 12.1 to 12.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
12.3 Divide
Polynomial
❏ Practice B 12.3, CR
❏ Notetaking Guide 12.3
❏ Key Questions to Ask, TE
❏ Study Guide 12.3, CR
❏ Inclusion Notes 12.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.3, CR
12.4 Simplify
Rational
Expressions
❏ Practice B 12.4, CR
❏ Notetaking Guide 12.4
❏ Key Questions to Ask, TE
❏ Study Guide 12.4, CR
❏ Inclusion Notes 12.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.4, CR
Assessment Options
❏ Quiz for 12.3 to 12.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 12.3 to 12.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
12.5 Multiply and
Divide Rational
Expressions
❏ Practice B 12.5, CR
❏ Notetaking Guide 12.5
❏ Key Questions to Ask, TE
❏ Study Guide 12.5, CR
❏ Inclusion Notes 12.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.5, CR
Lesson
Content
Standards
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
108
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 12.1, CR
❏ Notetaking Guide 12.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.1, CR
❏ Practice C 12.1, CR
❏ Challenge 12.1, CR
❏ Pre-AP Best Practices 12.1, PAP
❏ Spanish Study Guide, 12.1
❏ Student Resources in Spanish, 12.1
❏ English Learner Notes 12.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 12.2, CR
❏ Notetaking Guide 12.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.2, CR
❏ Practice C 12.2, CR
❏ Challenge 12.2, CR
❏ Pre-AP Best Practices 12.2, PAP
❏ Spanish Study Guide, 12.2
❏ Student Resources in Spanish, 12.2
❏ English Learner Notes 12.2, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 12.1 to 12.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 12.1 to 12.2, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 12.1 to 12.2, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 12.3, CR
❏ Notetaking Guide 12.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.3, CR
❏ Practice C 12.3, CR
❏ Challenge 12.3, CR
❏ Pre-AP Best Practices 12.3, PAP
❏ Spanish Study Guide, 12.3
❏ Student Resources in Spanish, 12.3
❏ English Learner Notes 12.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 12.4, CR
❏ Notetaking Guide 12.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.4, CR
❏ Practice C 12.4, CR
❏ Challenge 12.4, CR
❏ Pre-AP Best Practices 12.4, PAP
❏ Spanish Study Guide, 12.4
❏ Student Resources in Spanish, 12.4
❏ English Learner Notes 12.4, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 12.3 to 12.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 12.3 to 12.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 12.3 to 12.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish AR
❏ Test and Practice Generator
❏ Practice A 12.5, CR
❏ Notetaking Guide 12.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.5, CR
❏ Practice C 12.5, CR
❏ Challenge 12.5, CR
❏ Pre-AP Best Practices 12.5, PAP
❏ Pre-AP Copymaster 12.5, PAP
❏ Spanish Study Guide, 12.5
❏ Student Resources in Spanish, 12.5
❏ English Learner Notes 12.5, DIR
❏ Multi-Language Visual Glossary
Course Planner
109
Course Planner for Differentiated Instruction
Chapter 12 – Rational Equations and Functions
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
12.6 Add and
Subtract
Rational
Expressions
❏ Practice B 12.6, CR
❏ Notetaking Guide 12.6
❏ Key Questions to Ask, TE
❏ Study Guide 12.6, CR
❏ Inclusion Notes 12.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.6, CR
12.7 Solve Rational
Equations
❏ Practice B 12.7, CR
❏ Notetaking Guide 12.7
❏ Key Questions to Ask, TE
❏ Study Guide 12.7, CR
❏ Inclusion Notes 12.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 12.7, CR
Assessment Options
❏ Quiz for 12.5 to 12.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 12.5 to 12.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Lesson
Content
Standards
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
110
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 12.6, CR
❏ Notetaking Guide 12.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.6, CR
❏ Practice C 12.6, CR
❏ Challenge 12.6, CR
❏ Pre-AP Best Practices 12.6, PAP
❏ Pre-AP Copymaster 12.6, PAP
❏ Spanish Study Guide, 12.6
❏ Student Resources in Spanish, 12.6
❏ English Learner Notes 12.6, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 12.7, CR
❏ Notetaking Guide 12.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 12.7, CR
❏ Practice C 12.7, CR
❏ Challenge 12.7, CR
❏ Pre-AP Best Practices 12.7, PAP
❏ Pre-AP Copymaster 12.7, PAP
❏ Spanish Study Guide, 12.7
❏ Student Resources in Spanish, 12.7
❏ English Learner Notes 12.7, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 12.5 to 12.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 12.5 to 12.7, SE
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 12.5 to 12.7, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 3, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
111
Course Planner for Differentiated Instruction
Chapter 13 – Probability and Data Analysis
Lesson
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
❏ Practice B 13.1, CR
❏ Notetaking Guide 13.1
❏ Key Questions to Ask, TE
❏ Study Guide 13.1, CR
❏ Inclusion Notes 13.1, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.1, CR
❏ Practice B 13.2, CR
❏ Notetaking Guide 13.2
❏ Key Questions to Ask, TE
❏ Study Guide 13.2, CR
❏ Inclusion Notes 13.2, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.2, CR
CC.9-12.S.CP.9
❏ Practice B 13.3, CR
❏ Notetaking Guide 13.3
❏ Key Questions to Ask, TE
❏ Study Guide 13.3, CR
❏ Inclusion Notes 13.3, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.3, CR
CC.9-12.S.CP.1, CC.9-12.S.CP.2,
CC.9-12.S.CP.3, CC.9-12.S.CP.6,
CC.9-12.S.CP.7, CC.9-12.S.CP.8,
CC.9-12.S.CP.9
❏ Practice B 13.4, CR
❏ Notetaking Guide 13.4
❏ Key Questions to Ask, TE
❏ Study Guide 13.4, CR
❏ Inclusion Notes 13.4, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.4, CR
❏ Quiz for 13.1 to 13.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 13.1 to 13.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Practice B 13.5, CR
❏ Notetaking Guide 13.5
❏ Key Questions to Ask, TE
❏ Study Guide 13.5, CR
❏ Inclusion Notes 13.5, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.5, CR
Activity: Find a
Probability (1/2 day)
13.1 Find Probability
and Odds
(1 day)
CC.9-12.S.ID.5, CC.9-12.S.CP.1,
CC.9-12.S.CP.4, CC.9-12.S.MD.7
13.2 Find
Probabilities
Using
Permutations
(2 days)
13.3 Find
Probabilities
Using
Combinations
(1 day)
Activity: Find
Permutations and
Combinations (1/2 day)
13.4 Find
Probabilities
of Compound
Events
(2 days)
Assessment Options
Activity: Investigating
Samples (CC) (1/2 day)
13.5 Analyze
Surveys and
Samples
(1 day)
CC.9-12.S.IC.1, CC.9-12.S.IC.3,
CC.9-12.S.MD.6
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
112
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 13.1, CR
❏ Notetaking Guide 13.1
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.1, CR
❏ Practice C 13.1, CR
❏ Challenge 13.1, CR
❏ Pre-AP Best Practices 13.1, PAP
❏ Spanish Study Guide, 13.1
❏ Student Resources in Spanish, 13.1
❏ English Learner Notes 13.1, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 13.2, CR
❏ Notetaking Guide 13.2
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.2, CR
❏ Practice C 13.2, CR
❏ Challenge 13.2, CR
❏ Pre-AP Best Practices 13.2, PAP
❏ Spanish Study Guide, 13.2
❏ Student Resources in Spanish, 13.2
❏ English Learner Notes 13.2, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 13.3, CR
❏ Notetaking Guide 13.3
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.3, CR
❏ Practice C 13.3, CR
❏ Challenge 13.3, CR
❏ Pre-AP Best Practices 13.3, PAP
❏ Spanish Study Guide, 13.3
❏ Student Resources in Spanish, 13.3
❏ English Learner Notes 13.3, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 13.4, CR
❏ Notetaking Guide 13.4
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.4, CR
❏ Practice C 13.4, CR
❏ Challenge 13.4, CR
❏ Pre-AP Best Practices 13.4, PAP
❏ Spanish Study Guide, 13.4
❏ Student Resources in Spanish, 13.4
❏ English Learner Notes 13.4, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 13.1 to 13.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz for 13.1 to 13.4, SE
❏ Online Quiz
❏ Quiz 1, AR
❏ Test and Practice Generator
❏ Quiz 13.1 to 13.4, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 1, Spanish A
❏ Test and Practice Generator
❏ Practice A 13.5, CR
❏ Notetaking Guide 13.5
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.5, CR
❏ Practice C 13.5, CR
❏ Challenge 13.5, CR
❏ Pre-AP Best Practices 13.5, PAP
❏ Pre-AP Copymaster 13.5, PAP
❏ Spanish Study Guide, 13.5
❏ Student Resources in Spanish, 13.5
❏ English Learner Notes 13.5, DIR
❏ Multi-Language Visual Glossary
Course Planner
113
Course Planner for Differentiated Instruction
Chapter 13 – Probability and Data Analysis
Content
Standards
On-Level Learners
[RTI Tier 1]
Special Needs Learners
[RTI Tier 2]
13.6 Use Measures
of Central
Tendency and
Dispersion
(1 day)
CC.9-12.S.ID.2, CC.9-12.S.ID.3
❏ Practice B 13.6, CR
❏ Notetaking Guide 13.6
❏ Key Questions to Ask, TE
❏ Study Guide 13.6, CR
❏ Inclusion Notes 13.6, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.6, CR
13.6A Analyze
Data (CC)
(1 day)
CC.9-12.S.ID.5
❏ Practice B 13.6A, CR
❏ Key Questions to Ask, TE
❏ Study Guide 13.6A, CR
❏ Differentiated Instruction, TE
❏ Remediation Book
Extension: Calculate
Variance and
Standard Deviation
(1/2 day)
CC.9-12.S.ID.2, CC.9-12.S.ID.3
Activity: Investigate
Dot Plots (CC) (1/2 day)
CC.9-12.S.ID.1
13.7 Interpret Stemand-Leaf Plots
and Histograms
(2 days)
CC.9-12.S.ID.1, CC.9-12.S.ID.2,
CC.9-12.S.ID.3
❏ Practice B 13.7, CR
❏ Notetaking Guide 13.7
❏ Key Questions to Ask, TE
❏ Study Guide 13.7, CR
❏ Inclusion Notes 13.7, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.7, CR
13.8 Interpret Boxand-Whiskers
Plots
(2 days)
CC.9-12.S.ID.1, CC.9-12.S.ID.2,
CC.9-12.S.ID.3
❏ Practice B 13.8, CR
❏ Notetaking Guide 13.8
❏ Key Questions to Ask, TE
❏ Study Guide 13.8, CR
❏ Inclusion Notes 13.8, DIR
❏ Differentiated Instruction, TE
❏ Remediation Book
❏ Practice A 13.8, CR
Activity: Draw Boxand-Whisker Plots
(1/2 day)
CC.9-12.N.Q.1
Extension: Analyze
Data (CC) (1/2 day)
CC.9-12.S.ID.2
❏ Quiz for 13.5 to 13.8, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test B, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz for 13.5 to 13.8, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
Lesson
Activity: Draw
Histograms (1/2 day)
Assessment Options
See pp. 2–29 for the full text of the Common Core Mathematics Content Standards for High School.
114
Course Planner
<…
K Red Type Minimum Course of Study
Chapter Resources
CR
E
Y
Assessment Resources
AR
Developing Learners
[RTI Tiers 1 and 2]
CC
DIR
SE
Course Planner
Curriculum Companion
Differentiated Instruction Resources
Student Edition
TE
PAP
Teacher’s Edition
Pre-AP Resources
Advanced Learners
English Language Learners
❏ Practice A 13.6, CR
❏ Notetaking Guide 13.6
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.6, CR
❏ Practice C 13.6, CR
❏ Challenge 13.6, CR
❏ Pre-AP Best Practices 13.6, PAP
❏ Pre-AP Copymaster 13.6, PAP
❏ Spanish Study Guide, 13.6
❏ Student Resources in Spanish, 13.6
❏ English Learner Notes 13.6, DIR
❏ Multi-Language Visual Glossary
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.6A, CR
❏ Challenge 13.6A, CR
❏ Pre-AP Best Practices 13.6A, PAP
❏ Multi-Language Visual Glossary
❏ Practice A 13.7, CR
❏ Notetaking Guide 13.7
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.7, CR
❏ Practice C 13.7, CR
❏ Challenge 13.7, CR
❏ Pre-AP Best Practices 13.7, PAP
❏ Pre-AP Copymaster 13.7, PAP
❏ Spanish Study Guide, 13.7
❏ Student Resources in Spanish, 13.7
❏ English Learner Notes 13.7, DIR
❏ Multi-Language Visual Glossary
❏ Practice A 13.8, CR
❏ Notetaking Guide 13.8
❏ Key Questions to Ask, TE
❏ Differentiated Instruction, DIR
❏ Study Guide 13.8, CR
❏ Practice C 13.8, CR
❏ Challenge 13.8, CR
❏ Pre-AP Best Practices 13.8, PAP
❏ Pre-AP Copymaster 13.8, PAP
❏ Spanish Study Guide, 13.8
❏ Student Resources in Spanish, 13.8
❏ English Learner Notes 13.8, DIR
❏ Multi-Language Visual Glossary
❏ Quiz for 13.5 to 13.8, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test A, AR
❏ Chapter Test, Benchmark Tests
❏ Test and Practice Generator
❏ Quiz for 13.5 to 13.8, SE
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, SE
❏ Chapter Test C, AR
❏ Standardized Test, AR
❏ SAT/ACT Test, AR
❏ Alternative Assessment, AR
❏ Test and Practice Generator
❏ Quiz 13.5 to 13.8, Student Resources in Spanish
❏ Online Quiz
❏ Quiz 2, AR
❏ Chapter Test, Student Resources in Spanish
❏ Chapter Test B, Spanish AR
❏ Standardized Test, Spanish AR
❏ SAT/ACT Test, Spanish AR
❏ Alternative Assessment, Spanish AR
❏ Test and Practice Generator
Course Planner
115
Skills Readiness
Pre-Course Test
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
9.
63
493
43
59.96
18.57
2.38
12.72
2.7
1.7
MULTIPLY AND DIVIDE INTEGERS
Solve.
Perform each indicated operation.
1. 548 - 485
2. 29 × 17
FRACTIONS, DECIMALS, AND PERCENTS
Add or subtract.
4. 34.26 + 25.7
5. 24.8 - 6.23
MULTIPLY DECIMALS
ORDER OF OPERATIONS
Multiply.
Evaluate each expression.
6. 3.4 × 0.7
Skills Readiness
20. 16 + 4 ÷ 4
7. 5.3 × 2.4
21. 5 + 4 × 32
DIVIDE DECIMALS
DISTRIBUTIVE PROPERTY
Divide.
Simplify each expression.
8. 18.9 ÷ 7
216
12
248
6
0.15, 15%
1.375, 137.5%
17
41
84 1 6t
8h 2 56
$5.50 per sandwich
14 photos per day
t 5 195 1 15w
T
Q
P
,
.
5
27
7
t 5 24
u 5 226
9c 2 2 23
3h 1 j
y59
w 5 15
r59
q 5 12
(22, 1), (21, 4), (0, 7), (1, 10),
(2, 13)
44. (22, 25), (21, 16), (0, 9), (1, 4),
(2, 1)
For each problem, write an equivalent decimal
and percent.
3
11
18. _
19. _
20
8
ADD AND SUBTRACT DECIMALS
4
__
11. 1
10
12. 1_12
13. _57
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
17. -42 ÷ (-7)
16. 16(-3)
3. 774 ÷ 18
10. _1
116
WHOLE NUMBER OPERATIONS
22. 6(14 + t)
9. 0.85 ÷ 0.5
23. (h - 7)8
MULTIPLY AND DIVIDE FRACTIONS
RATES AND UNIT RATES
Multiply or divide. Give your answer in
simplest form.
Find each unit rate.
4
3 ×_
10. _
25. 98 photos in 7 days
8
24. $33 for 6 sandwiches
7 ÷7
11. _
6
10
ADD AND SUBTRACT FRACTIONS
CONNECT WORDS AND ALGEBRA
Add or subtract. Give your answer in simplest
form.
7
3 5
4 +_
12. _
13. 1_ - _
7 7
5 10
26. Eloise has collected $195 for charity. Each
week she will collect an additional $15.
Write an equation representing the total
amount t (in dollars) that Eloise will have
collected after w weeks.
ADD AND SUBTRACT INTEGERS
Perform each indicated operation.
14. -63 + 47
15. -21 - (-33)
LAG1_MTNAESE476841_PT.indd TN68
y
45–46.
8/30/10 9:13:47 AM
47.
y
y
48.
D
1
E
1
1
1
x
1
x
21
x
<… Skills Readiness
GRAPH NUMBERS ON A NUMBER LINE
SOLVE PROPORTIONS
Identify each number on the number line.
Solve each proportion.
r
6
9
3 =_
41. _
42. _ = _
q
15
18
5
P
23
Q
22
R
S
0
21
T
1
2
Pre-Course Test
3
Skills Readiness
FUNCTION TABLES
27. 3
28. -1.5
Generate ordered pairs for each function for
x = -2, -1, 0, 1, 2.
29. -2.5
43. y = 3x + 7
Pre-Course Test
Intervention
44. y = (x - 3) 2
Skills Readiness, available on the
Easy Planner, provides review and
practice for the items on the
Pre-Course Test.
COMPARE AND ORDER REAL NUMBERS
Compare. Use <, >, or =.
3
8
_
30. _
5
15
31. 30%
0.030
8
32. _
ORDERED PAIRS
Identify each point on the coordinate grid.
45. D(-1, 3)
40%
20
46. E(4, 0)
GRAPH LINEAR FUNCTIONS
EVALUATE EXPRESSIONS
Evaluate each expression for the given value
of the variable.
Graph each function.
47. y = x + 4
1
1
48. y = -_ x + _
2
2
SOLVE AND GRAPH INEQUALITIES
33. 6g - 15 for g = 7
3
4
34. 13 + _d for d = -8
Solve and graph each inequality.
49. q - 5 ≤ -2
50. -3g < 12
SOLVE ONE-STEP EQUATIONS
Solve.
35. 6t = 144
36. 18 + u = -8
Items
Skill
1–3
43
4–5
44
6–7
45
8–9
46
10–11
47
12–13
48
14–15
51
16–17
52
18–19
14
20–21
55
22–23
56
24–25
13
26
58
27–29
18
30–32
16
33–34
60
35–36
68
37–38
57
39–40
69
41–42
77
43–44
78
45–46
79
47–48
75
49–50
74
COMBINE LIKE TERMS
Combine like terms to simplify each
expression.
37. 4c 2 - 23 + 5c 2
38. -4h + 5j - 4j + 7h
SOLVE MULTI-STEP EQUATIONS
Solve.
39. 3y + 13 = 40
40. 4(w - 3) - 6 = 42
M LAG1_MTNAESE476841_PT.indd TN69
8/30/10 9:14:00 AM
49. q # 3
22
0
2
4
6
50. g . 24
26
24
22
0
Skills Readiness
117
Additional Content
Algebra 1
Contents
Lesson 1.5A Use Precision and Significant Digits . . . . . . . . . . CC1
Extension 3.1A Use Real and Rational Numbers . . . . . . . . . . CC8
Extension 3.4A Apply Properties of Equality . . . . . . . . . . . CC11
Graphing Calculator Activity 4.7A Solve Linear
Equations by Graphing Each Side . . . . . . . . . . . . . . . . . . . . CC13
Extension 5.7A Assess the Fit of a Model . . . . . . . . . . . . . . CC15
Graphing Calculator Activity 7.4A Multiply
and Then Add Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . CC18
Lesson 10.7A Solve Systems with Quadratic Equations . . . CC21
Lesson 10.8A Model Relationships. . . . . . . . . . . . . . . . . . . . CC28
Graphing Calculator Activity 10.8B
Average Rate of Change. . . . . . . . . . . . . . . . . . . . . . . . . . . . CC35
Investigating Algebra Activity 13.5A
Investigating Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CC36
Lesson 13.6A Analyze Data . . . . . . . . . . . . . . . . . . . . . . . . . . CC37
Investigating Algebra Activity 13.7A
Investigate Dot Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CC42
Extension 13.8A Analyze Data . . . . . . . . . . . . . . . . . . . . . . . CC44
118
Additional Content
© Paul Burns/Photodisc/Getty Images
Precision and
1.5A Use
Measurement
Before
Now
Why?
1
You measured using a ruler and protractor.
Warm-Up Exercises
You will compare measurements for precision.
Perform the indicated operation.
1. 18.1 1 0.7 18.8
2. 3.1 3 2.5 7.75
3. 0.17 2 0.08 0.09
4. 24 4 0.2 120
5. Connie scored 13 points in
the first basketball game and
9 points in the second game.
How many total points did she
score? 22 points
So you can determine which measurement is more precise, as in Ex. 31.
You ask two friends for the time. Noah says that it is about 2:30. Mia says it is
2:28 and 19 seconds. Mia gives a more precise measurement of the time.
Key Vocabulary
• precision
• significant digits
PLAN AND
PREPARE
Noah’s
Watch
Mia’s
Watch
02:28:19
Pacing
Basic: 1 day
Average: 1 day
Advanced: 1 day
Block: 0.5 block
PRECISION Precision is the level of detail that an instrument can measure.
Mia’s watch is more precise than Noah’s watch because it gives the time to
the nearest second. In a similar way, a ruler marked in millimeters is more
precise than a ruler marked only in centimeters, since a millimeter is a
smaller unit than a centimeter.
EXAMPLE 1
2
Compare precision of measurements
Essential Question
Choose the more precise measurement.
a. 7 cm; 7.3 cm
b. 5 yd; 16 ft
Big Idea 1, p. 1
When comparing two measurements, how do you determine
which one is more precise? Tell
students they will learn how to
answer this question by looking
at the level of detail shown and the
units of measure used in the
measurement.
c. 1 pint; 16 ounces
Solution
AVOID ERRORS
a. The units are the same. Because tenths are smaller than ones,
Remember that the
smaller number is not
always the more precise
measurement. Always
examine the units of
measure.
✓
7.3 centimeters is more precise than 7 centimeters.
b. The units are different. Because a foot is a smaller unit of measure
than a yard, 16 feet is a more precise unit of measure.
c. The units are different. Because an ounce is a smaller unit of measure
than a pint, 16 ounces is a more precise measurement even though 1 pint
is equal to 16 ounces.
GUIDED PRACTICE
FOCUS AND
MOTIVATE
Motivating the Lesson
In many youth football leagues, the
athletes are assigned to the teams
in various divisions based on the
player’s weight. Lead students into
a discussion about this method by
asking the following question. Why
would it be inadvisable for league
officials to simply estimate a
player’s weight when assigning
them to a weight division?
for Example 1
Choose the more precise measurement.
5
8
1. 21.13 oz; 21.4 oz 21.13 oz
1
2. 14 }
in.; 2} in. 2 }5 in.
3. 14 mm; 2 cm 14 mm
4. 2.5 hr; 90 min 90 min
2
8
1.5A Use Precision and Measurement
CC1
Resource Planning Guide
Ch t Resource
Chapter
R
• Practice level B
• Study Guide
• Challenge
• Pre-AP notes
ESE612355_01-5A_EXPO.indd Sec1:1
Teaching
T
hi Options
• Activity Generator provides
editable activities for all ability
levels
Interactive Technology
12/10/10
• Activity Generator
• Animated Algebra
• Test Generator
• eEdition
12:12:50 AM
See also the Differentiated Instruction
Resources for more strategies for
meeting individual needs.
CC1
CC1
3
SIGNIFICANT DIGITS To the nearest centimeter, the
diameter of a United States quarter is 2 centimeters.
Measured to the nearest millimeter, the diameter of
the quarter is 24 millimeters. The measurement
24 millimeters is more precise because it is given
using a smaller unit of length.
TEACH
Extra Example 1
In the two coin measurements, notice that the numerical value 24 has
more digits than the value 2. You can use the number of significant digits
to describe the precision of a measurement. Significant digits are the digits
in a measurement that carry meaning contributing to the precision of the
measurement.
Choose the more precise
measurement.
a. 4.7 m; 11 m 4.7 m
b. 0.2 gal; 6 qt 6 qt
c. 7 in.; 2.02 ft 7 in.
For Your Notebook
Extra Example 2
KEY CONCEPT
Determine the number of significant digits in each measurement.
a. 250 2
b. 0.0620 3
c. 30.04 4
Determining Significant Digits
Rule
Key Question to Ask for
Example 2
•
In Example 2b, why is the first
zero in the number 0.8500 not a
significant digit? The first zero is
neither between significant
digits nor to the right of both the
last nonzero digit and the
decimal point.
Significant
digits
Number of
significant digits
All nonzero digits
281.39
281.39
5
Zeros that are to the right of
both the last nonzero digit
and the decimal point
0.0070
0.0070
2
500.7
500.7
4
Zeros between significant
digits
Zeros at the end of a whole number are usually assumed to be nonsignificant.
For example, 220 centimeters has 2 significant digits, while 202 centimeters
has 3 significant digits.
Reading Strategy
EXAMPLE 2
Be sure students notice that the
significant digits in the numbers in
the Key Concept box are shown in
color so they are easily identifiable.
Identify significant digits
Determine the number of significant digits in each measurement.
a. 290.01 g
b. 0.8500 km
c. 4000 mi
Solution
Teaching Strategy
Point out to students that the word
and in the second rule for determining significant digits given in
the Key Concept box means both
requirements must be met. Refocus
students’ attention on this rule
when discussing Example 2c. Point
out that the nonsignificant zeros in
4000 may be to the right of the nonzero digit 4 but they are to the left
of the decimal point.
Example
a. The digits 2, 9, and 1 are nonzero digits, so they are significant digits. The
zeros are between significant digits, so they are also significant digits.
There are 5 significant digits: 290.01.
b. The digits 8 and 5 are nonzero digits, so they are significant digits. The
AVOID ERRORS
Remember that not all
zeros are significant. Be
careful when deciding
whether a zero in a
number is significant
or not.
CC2
two zeros to the right of the last nonzero digit are also to the right of the
decimal point, so they are significant digits.
There are 4 significant digits: 0.8500.
c. The digit 4 is a nonzero digit, so it is a significant digit. The zeros at the
end of a whole number are not significant.
There is 1 significant digit: 4000.
Chapter 1 Expressions, Equations, and Functions
Differentiated Instruction
Advanced Students may be interested in the idea that the
more precise measurement may not be more correct than a
less precise measurement. Have them research the meaning of
accuracy. Accuracy describes how close the measurement is
to the actual value. Generally, you want precise and accurate
measurements, but you must decide the level of accuracy and
precision appropriate to a situation.
See also the Differentiated Instruction Resources for more
strategies.
LA1_CCESE612355_01-5A_EXPO.indd Sec1:2
CC2
12/10/10 12
SIGNIFICANT DIGITS IN CALCULATIONS When you perform calculations
involving measurements, the number of significant digits that you write
in your result depends on the number of significant digits in the given
measurements.
Extra Example 3
Perform the indicated operation.
Write the answer with the correct
number of significant digits.
a. 7.29 mm 2 4.1 mm 3.2 mm
b. 0.02 ft 3 17.1 ft 0.3 ft 2
For Your Notebook
KEY CONCEPT
Determining Significant Digits in Calculations
Operations
Addition and
Subtraction
Multiplication
and Division
Rule
Example
Round the sum or difference
to the same place as the last
significant digit of the least
precise measurement.
3.24 ← hundredths
1 7.3 ← tenths
10.54 ← tenths
The product or quotient
must have the same number
of significant digits as the
least precise measurement.
40 ← 1 sig digit
3 31 ← 2 sig digits
1240 ← exact answer
1000 ← 1 sig digit
Key Question to Ask for
Example 3
•
Zeros at the end of a whole number are usually assumed to be nonsignificant.
For example, 220 centimeters has 2 significant digits, while 202 centimeters
has 3 significant digits.
EXAMPLE 3
Calculating with significant digits
Closing the Lesson
Perform the indicated operation. Write the answer with the correct
number of significant digits.
a. 45.1 cm 1 19.45 cm
Have students summarize the
major points of the lesson and
answer the Essential Question:
When comparing two measurements, how do you determine
which one is more precise?
• When the units of measure are the
same, the measurement found to a
smaller place value is more precise. So, 8.1 millimeters is more
precise than 8 millimeters.
• When the units of measure are
not the same, the measurement
given using the smaller unit is
more precise. So, 100 centimeters is more precise than 1 meter.
To compare the precision of two
measurements, first look at the
units of measure. If the units are
the same, use the first rule above.
If different, use the second rule.
b. 6.4 ft 3 2.15 ft
Solution
a. 45.1 cm 1 19.45 cm 5 64.55 cm
The least precise measurement is 45.1 centimeters. Its last significant
digit is in the tenths place. Round the sum to the nearest tenth.
The correct sum is 64.6 centimeters.
b. 6.4 ft 3 2.15 ft 5 13.76 ft 2
The least precise measurement is 6.4 feet. It has two significant digits.
Round the product to two significant digits.
The correct product is 14 square feet.
✓
GUIDED PRACTICE
for Examples 2 and 3
Determine the number of significant digits in each measurement.
5. 800.20 ft 5
6. 0.005 cm 1
7. 36,900 mi 3
Perform the indicated operation. Write the answer with the correct
number of significant digits.
8. 27.23 m 2 12.7 m 14.5 m
Previously when you calculated
45.1 1 19.45, you simply gave your
answer as 64.55 and did not even
consider significant digits. Why
must you consider significant
digits for the sum 45.1 cm 1 19.45
cm? The sum 45.1 cm 1 19.45 cm
is the sum of two measurements,
not just two decimal numbers.
Because the precision of the two
measurements is not the same,
significant digits must be considered when giving the sum.
9. 45.16 yd 2 4 4.25 yd 10.6 yd
1.5A Use Precision and Measurement
CC3
Differentiated Instruction
Verbal Some students may have trouble determining the
number of significant digits in a number, especially when there
are zeros are to the right of the decimal point. Pair students up and
have them create a list of numbers. Students should take turns
explaining to their partner which digits are significant and why.
See also the Differentiated Instruction Resources for more
strategies.
ESE612355_01-5A_EXPO.indd Sec1:3
12/10/10 12:12:56 AM
CC3
EXERCISES
1.5A
4
5 WORKED-OUT SOLUTIONS
for Exs. 3, 11, 21, and 33
★ 5 STANDARDIZED TEST PRACTICE
PRACTICE
AND APPLY
Exs. 2, 20, 29, 30, and 37
SKILL PRACTICE
Assignment Guide
Basic:
Day 1: pp. CC4–CC6
Exs. 1–8, 10–16, 20, 21–27 odd,
33–38, 40–45, 52–58
Average:
Day 1: pp. CC4–CC6
Exs. 1–2, 3–31 odd, 33–36, 39–41,
43–49 odd, 50, 52–58
Advanced:
Day 1: pp. CC4–CC6
Exs. 1, 3–8, 20–32, 34–46 even,
48–51, 52–58 even
Block:
pp. CC4–CC6
Exs. 1–2, 3–31 odd, 34–43, 47–51
odd, 49–55
HOMEWORK
KEY
A
1. VOCABULARY Copy and complete: The level of detail that an instrument
can measure is known as its
2.
. precision
★ WRITING Which number, 0.023 or 301, has the fewer significant digits?
Explain. 0.023; the number 0.023 has two significant digits, while the number 301 has three
significant digits.
COMPARING PRECISION Choose the more precise measurement.
EXAMPLE 1
on p. CC1
for Exs. 3–10
3. 14.2 gal; 7 gal 14.2 gal
4. 0.02 mm; 0.1 mm 0.02 mm
5. 90 ft; 71 in. 71 in.
6. 57.65 lb; 34.9 lb 57.65 lb
7. 14.1 m; 29.3 cm 29.3 cm
8. 36 yd; 17.2 yd 17.2 yd
ERROR ANALYSIS Describe and correct the error in the statement.
9. Heidi told her friend Mike that 1.5 hours is a more precise measurement
Minutes are a smaller unit of measure than hours, therefore
85 minutes is more precise than 1.5 hours.
10. Eric’s new fishing rod was advertised as being 4 feet long. He measured
it to be 47 inches long. Eric’s friend says that 4 feet is the more precise
measurement. Inches are a smaller unit of measure than feet, therefore 47 inches
is more precise than 4 feet.
IDENTIFYING SIGNIFICANT DIGITS Determine the number of significant
digits in the measurement.
of time than 85 minutes.
EXAMPLE 2
on p. CC2
for Exs. 11–20
Differentiated
Instruction
11. 312.5 cm 4
12. 100 hr 1
13. 0.030 gal 2
14. 16.007 lb 5
15. 1020 mm 3
16. 0.0025 sec 2
See Differentiated Instruction
Resources for suggestions on
addressing the needs of a diverse
classroom.
17. 38.0 m 3
18. 8.375 ft 4
19. 205.7140 mi 7
Homework Check
For a quick check of student
understanding of key concepts,
go over the following exercises.
Basic: 3, 5, 11, 23, 33
Average: 3, 7, 13, 25, 36
Advanced: 3, 7, 23, 31, 37
20.
A 1
EXAMPLE 3 B
on p. CC3
for Exs. 21–30
C 3
D 4
CALCULATING WITH SIGNIFICANT DIGITS Perform the indicated operation.
Write the answer with the correct number of significant digits.
22. 8 ft 3 11.2 ft 90 ft 2
21. 97.2 m 2 16.04 m 81.2 m
25. 6.42 mm 3 7.51 mm 48.2 mm
24. 0.043 yd 1 0.22 yd 0.26 yd
2
27. 245 kg 2 18.32 kg 227 kg
26. 2.8 mi 1 3.56 mi 6.4 mi
28. 9.05 cm 2 4 18 cm 0.50 cm
29.
★ WRITING Describe how to find the number of significant digits to give
30.
★ MULTIPLE CHOICE The quotient 97.3 hr 4 5.5 hr contains how many
for the area of a rectangle with side lengths 8.2 meters and 20 meters.
Practice B in Chapter Resources
Avoiding Common Errors
significant digits? C
Exercises 18–25 Some students
may perform the indicated operation
and record this result as the correct
answer. Remind students to write
the answer with the correct number
of significant digits.
A 4
C
B 3
C 2
D 1
CHALLENGE Perform the indicated operation. Write the answer with the
correct number of significant digits.
31. 0.40 ft 3 2.25 ft 0.90 ft 2
32. 23.175 km 2 4 10.30 km
2.250 km
CC4
29. The area
must have the
same number
of significant
digits as the
least precise
measurement.
The value 20 is
less precise than
8.2, having one
significant digit.
Therefore the area
of the rectangle
should be given
with just one
significant digit.
Chapter 1 Expressions, Equations, and Functions
LA1_CCESE612355_01-5A_EXE.indd CC4
CC4
B 2
23. 257.64 oz 4 2.4 oz 110
Extra Practice
•
★ MULTIPLE CHOICE The measurement 0.007 grams contains how many
significant digits? A
12/10/10 12
PROBLEM SOLVING
EXAMPLE 1 A
on p. CC2
for Exs. 33–36
33. COINS According to the United States Mint, a one-dollar coin has a mass
of 8.1 grams. Justine finds the mass of a one-dollar coin and reports a
mass of 8.05 grams. Steven finds that the mass of his one-dollar coin is
8.2 grams. Whose measurement is more precise? Justine
Teaching Strategy
Exercises 31–33 Before students
begin these exercises, have a class
discussion on whether it is possible
for one measurement to be more
precise than a second measurement
even though the second measurement is closer to the actual length.
Some students may think that the
more precise measurement and the
measurement closest to the actual
length must be the same.
COMPARING MEASUREMENTS For Exercises 34–36, three students are asked
to measure a piece of string that has a length of exactly 15.2 centimeters.
Their measurements are shown in the table.
Student
Measurement
Alex
15.35 cm
Chandra
14.9 cm
Luis
154 mm
Avoiding Common Errors
34. Which student made the most precise measurement? Luis
Exercise 37 Watch for students
who identify the perimeter of the
garden to be 16.8 meters and the
area to be 12.8 square meters.
These students understand how to
find perimeter and area but do not
understand how to record an
answer using the correct number
of significant digits. Be sure to
reinforce what they did correctly
before pointing out their error.
35. Which student made the least precise measurement? Chandra
36. Which student’s answer is closest to the actual length of the string? Alex
EXAMPLES B
2 and 3
on pp. CC3–4
for Exs. 37–47
37.
★ SHORT RESPONSE Brian drives 426 miles and uses 19.3 gallons of gas
426
for the trip. Brian’s calculator shows that }
ø 22.07253886, so he states
19.3
that his car gets 22.07253886 miles per gallon. Do you agree with Brian’s
statement? Explain your answer?
38. REFLECTING POOL The Reflecting Pool is a rectangular
body of water in front of the Lincoln Memorial in
Washington, D.C. A surveyor determines that the length
of the pool to the nearest foot is 2029 feet and the width
of the pool to the nearest foot is 167 feet.
© Fuse/Getty Images
a. How should the surveyor report the perimeter of
the pool using the correct number of significant
digits? 4392 ft
b. How should the surveyor report the area of the
37. No. Sample
answer: Both
426 miles and
19.3 gallons are
measurements
with 3 significant
digits, so Brian’s
answer should
have 3 significant
digits. He should
say that his car
gets 22.1 miles
per gallon.
ESE612355_01-5A_EXE.indd CC5
pool using the correct number of significant digits?
339,000 ft 2
39. HEALTH When Kyle went for his annual physical the nurse weighed him
and told him he weighed 118.5 pounds. After seeing the doctor, Kyle was
sent for some tests where he was weighed again. This time he was told he
weighed 119 pounds. Which of the two measurements is more precise?
Explain your answer.
118.5 lb;
because tenths
are smaller
units than ones,
118.5 pounds is
more precise
40. GARDENING A student measures the length of a rectangular garden plot than 119 pounds.
to the nearest tenth of a meter and finds that the length is 6.4 meters.
Another student measures the width of the plot to the nearest meter and
finds that the width is 2 meters. Using the correct number of significant
digits, what are the perimeter and area of the plot? 17 m, 10 m 2
Chapter 1.5A Use Precision and Measurement
CC5
12/10/10 12:11:44 AM
CC5
41. CHARITY RUN Nicole and Renee are participating in a charity run to
5
raise money for their school’s library. Both girls have sponsors who will
pay them $1 for each mile they collectively run. If Nicole ran 7.2 miles
and Renee ran 6.03 miles, how should they report their cumulative miles
to their sponsors using the correct number of significant digits? 13.2 mi
ASSESS AND
RETEACH
★ OPEN-ENDED In Exercises 42–46, give an example of the described
measurement. 42–46. Sample answers are given.
Daily Homework Quiz
Choose the more precise
measurement.
1. 12.1 ft; 11 ft 12.1 ft
2. 29 gal; 3 oz 3 oz
Determine the number of significant digits in the measurement.
3. 10.08 yd 4
4. 250 gal 2
5. Shaun’s dad built a rectangular
ice rink measuring 60.1 feet by
49 feet. Using the correct
number of significant digits,
what is the area of the ice
rink? 2900 ft 2
Practice B in Chapter Resources
• Study Guide in Chapter Resources
•
43. A measurement greater than 1000 centimeters that has 2 significant digits 22,000 cm
44. A measurement less than 1 millimeter that has 4 significant digits 0.1472 mm
45. A 4-digit area that has 3 significant digits and 2 digits that are zeros 4020 m 2
46. A weight less than 10 pounds that has 5 significant digits 7.4032 lb
47. POSTERS The area of a rectangular poster is 852 square inches. The
length of the poster is 36 inches. Using the correct number of significant
digits, what is the width of the poster? 24 in.
48. Edmond;
because
milliliters are
smaller units of
measure than
liters, his is the
more precise
measurement.
48. SCIENCE Tanya and Edmond are lab partners in
science class. They each measure the volume of a
beaker of a solution. Tanya found the volume to be
2.25 liters, while Edmond reported the volume as
2300 milliliters. Who gave the more precise
measurement? Explain your answer.
© Creatas/Jupiterimages/Getty Images
Diagnosis/Remediation
42. A 5-digit distance in miles that has 3 significant digits 36,500 mi
49. REALTORS When a realtor first lists a home for
sale, it is very important to calculate the living
area of the home. Carrie measured the length
and width of a house she is about to list and
found that it measured 52.5 feet long by 35 feet
wide. Using the correct number of significant
digits, how should Carrie report the area of
the house? 1800 ft 2
Challenge
Additional challenge is available in
the Chapter Resources.
C
50. CHALLENGE A student measures the length of a cube and records the
length as 3.5 centimeters. Using the correct number of significant digits,
how should the student report the volume of the cube? 43 cm 3
51. CHALLENGE Suppose the average 12-ounce aluminum drink can weighs
approximately 13.6 grams and the liquid inside weighs approximately
453.59 grams. Using the correct number of significant digits, how much
do the 24 drink cans in a carton weigh? 11,000 g
MIXED REVIEW
PREVIEW
Evaluate the expression. (Lesson 1.2)
Prepare for
Lesson 1.6 in
Exs. 50–56.
52. 42 1 8 4 2 20
53. 42 2 1 3 5 37
54. 40 2 [23 2 1] 33
Evaluate the expression when x 5 22. (Lesson 1.2)
55. x 2 1 3 7
56. 25x 2 5 5
57. 24(x 2 2) 16
58. AREA A football field is 50 yards wide and 100 yards long. What is the
area of the field? (Lesson 1.5) 5000 yd 2
CC6
Chapter 1 Expressions, Equations, and Functions
LA1_CCESE612355_01-5A_EXE.indd CC6
CC6
12/22/10 12:
Tennessee Grade Six Mathematics Standards
Mastering the Standards
for Mathematical Practice
Mathematical Practices
The topics described in the Standards for Mathematical
Content will vary from year to year. However, the way in
which you learn, study, and think about mathematics will
not. The Standards for Mathematical Practice describe skills
that you will use in all of your math courses.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
Make sense of problems and persevere in solving them.
1 M
Mathematically proficient
M
students start by explaining
to themselves the meaning
of a problem... They
analyze givens, constraints,
relationships, and goals. They
make conjectures about the
form... of the solution and plan
a solution pathway...
In your book
Verbal Models and the Problem Solving Plan help you
translate the information in a problem into a model and
then analyze your solution.
a Problem
1.5 Use
Solving Plan
Before
Now
Why?
Key Vocabulary
• formula
You used problem solving strategies.
&9".1-&
You will use a problem solving plan to solve problems.
KEY CONCEPT
4PMWFBNVMUJTUFQQSPCMFN
+0#&"3/*/(4 You have two summer jobs at a youth
center. You earn $8 per hour teaching basketball and
$10 per hour teaching swimming. Let x represent the
amount of time (in hours) you teach basketball each
week, and let y represent the amount of time (in hours)
you teach swimming each week. Your goal is to earn at
least $200 per week.
So you can determine a route, as in Example 1.
For Your Notebook
A Problem Solving Plan
s 7RITEANINEQUALITYTHATDESCRIBESYOURGOALINTERMS
of x and y.
STEP 1 Read and Understand Read the problem carefully. Identify what
you know and what you want to find out.
s 'RAPHTHEINEQUALITY
STEP 2 Make a Plan Decide on an approach to solving the problem.
s 'IVETHREEPOSSIBLECOMBINATIONSOFHOURSTHATWILL
allow you to meet your goal.
STEP 3 Solve the Problem Carry out your plan. Try a new approach if the
first one isn’t successful.
4PMVUJPO
STEP 4 Look Back Once you obtain an answer, check that it is reasonable.
34%0 8SJUFAVERBALMODEL4HENWRITEANINEQUALITY
#BTLFUCBMM
QBZSBUF
Read a problem and make a plan
EPMMBSTIPVS
#BTLFUCBMM
UJNF
1
+
RUNNING You run in a city. Short blocks are north-south
8
and are 0.1 mile long. Long blocks are east-west and are
0.15 mile long. You will run 2 long blocks east, a number
of short blocks south, 2 long blocks west, and back to
your start. You want to run 2 miles at a rate of 7 miles
per hour. How many short blocks must you run?
For an alternative
method for solving the
problem in Example
1, turn to page 34 for
the Problem Solving
Workshop.
"70*%&33034
"70*
* % & 3 3034
0.1 mi
STEP 1 Read and Understand
What do you know?
x
+
4XJNNJOH
QBZSBUF
+
EPMMBSTIPVS
1
10
0.15 mi
5IFWBSJBCMFTDBO
5IFWBSJBCMFTDBOU
SFQSFTFOUOFHBUJWF
SFQSFTFOUOFHBUJW
OVNCFST4PUIFH
OVNCFST4PUIFHSBQI
PGUIFJOFRVBMJUZEPFT
PGUIFJOFRVBMJUZE
OPUJODMVEFQPJOUTJO
OPUJODMVEFQPJOUT
2VBESBOUT*****PS*7
2VBESBOUT*****P
4XJNNJOH
UJNF
q
IPVST
y
+
34%0 (SBQITHEINEQUALITYx 1 10y q 200.
Solution
ANOTHER WAY
IPVST
&
IRSTGRAPHTHEEQUATIONx 1 10y 5 200
IN1UADRANT)4HEINEQUALITYISq, so use
a solid line.
Next, test (5, 5) in 8x 1 10y q 200:
Swimming (hours)
EXAMPLE 1
8(5) 1 10(5) q 200
90 q 200 You know the length of each size block, the number of long blocks you
will run, and the total distance you want to run.
5PUBM
FBSOJOHT
EPMMBST
q
200
y
20
8x 1 10y ≥ 200
10
0
0
(5, 5)
10
20
30 x
Basketball (hours)
Finally, shade the part of Quadrant I that does not contain (5, 5),
BECAUSEISNOTASOLUTIONOFTHEINEQUALITY
You can conclude that you must run an even number of short blocks
because you run the same number of short blocks in each direction.
34%0 $IPPTFthree points on the graph, such as (13, 12), (14, 10), and (16, 9).
The table shows the total earnings for each combination of hours.
What do you want to find out?
#BTLFUCBMMUJNFIPVST
You want to find out the number of short blocks you should run so
that, along with the 4 long blocks, you run 2 miles.
STEP 2 Make a Plan Use what you know to write a verbal model that
4XJNNJOHUJNFIPVST
5PUBMFBSOJOHTEPMMBST
represents what you want to find out. Then write an equation and
solve it, as in Example 2.
28
Chapter 1 Expressions, Equations, and Functions
(6*%&%13"$5*$&
GPS&YBNQMF
8. 8)"5*' In Example 6, suppose that next summer you earn $9 per hour
TEACHINGBASKETBALLANDPERHOURTEACHINGSWIMMING7RITEAND
GRAPHANINEQUALITYTHATDESCRIBESYOURGOAL4HENGIVETHREEPOSSIBLE
combinations of hours that will help you meet your goal.
laa111se_0105.indd 28
10/20/10 12:50:34 AM
Comstock/Getty Images
$IBQUFS4PMWJOHBOE(SBQIJOH-JOFBS*OFRVBMJUJFT
Extension
1
Use after Lesson 3.1
PLAN AND
PREPARE
GOAL Identify whether sets of rational and irrational numbers are closed under
operations.
Warm-Up Exercises
Use the following list of numbers.
}
27.2, 25, 2Ï 2 , 0, }1, 4
3
Key Vocabulary
• closure
1. Which are integers? 25, 0, 4
2. Which are rational?
27.2, 25, 0, }1, 4
3
Use Real and Rational
Numbers
RATIONAL AND IRRATIONAL NUMBERS Recall that a rational number is a
a
number }
where a and b are integers with b Þ 0. An irrational number is any
b
number that cannot be written as a quotient of two integers.
EXAMPLE 1
}
3. Which are irrational? Ï 2
Sums of rational numbers
Prove that the sum of two rational numbers is rational.
2
FOCUS AND
MOTIVATE
Solution
Let x and y be two rational numbers.
a
By the definition of rational numbers, x can be written as }
and y can
b
c
be written as } where a, b, c, and d are integers with b Þ 0 and d Þ 0.
Essential Question
Big Idea 1, p. 131
How can you show that the sum of
a rational number and an irrational
number is irrational? Tell students
they will learn how to answer this
question by showing that the sum
is irrational for a specific case and
then use an indirect proof to establish this for all cases.
3
d
a
x 1 y 5 } 1 }c
b
d
ad 1 bc
x1y5 }
bd
CLOSURE As you saw in Example 1, the sum of two rational numbers is rational.
The set of rational numbers has closure or is closed under multiplication.
Closure
A set has closure or is closed under a given operation if the number that
results from performing the operation on any two numbers in the set is
also in the set.
b
written as }c where a, b, c, and d
d
are integers with b Þ 0 and d Þ 0.
ad 2 bc
x 2 y 5 }a 2 }c 5 }
Example: The sum of any two rational numbers is a rational number. The
set of rationals is closed under addition.
1
2
1
3
5
6
}1}5}
bd
Because the difference or product
of two integers will always be an
integer, the expressions ad 2 bc
and bd are both integers. Therefore,
the difference x 2 y is equal to the
ratio of two integers. So by
definition, the difference is a
rational number.
For Your Notebook
KEY CONCEPT
Prove that the difference of two
rational numbers is rational. Let x
and y be two rational numbers. By
the definition of rational numbers,
x can be written as }a and y can be
1
2
3
2
}1}52
Non-example: The quotient of two integers is not necessarily an integer.
The set of integers is not closed under division.
64253
CC8
6
26 4 5 5 2 }
5
Chapter 3 Solving Linear Equations
LA1_CCESE612355_03-01A_EXT.indd 8
CC8
c
d
Therefore, the sum x 1 y is equal to the ratio of two integers. So by definition,
this sum is a rational number.
Extra Example 1
d
a
b
Rewrite } 1 } using a common denominator.
Because the sum or product of two integers will always be integers, the
expressions ad 1 bc and bd are both integers.
TEACH
b
Add x and y.
12/10/10
11
LA1_CCE
EXAMPLE 2
1. Let x and y be two rational
numbers. By definition x 5 }a
b
and y 5 }c where a, b, c, and d
d
are integers with
b Þ 0 and d Þ 0.
Sum of a rational and an irrational number
}
Solve the equation x 2 3 5 Ï 2 . Is the solution rational or irrational.
Extra Example 2
Solution
}
x 2 3 5 Ï2
Write original equation.
}
xy 5 }a • }c
b d
ac
xy 5 }
bd
x 2 3 1 3 5 Ï2 1 3
Add 3 to both sides.
}
x 5 Ï2 1 3
Because the set of integers is
closed under the operation of
multiplication, the expressions
ac and bd are both integers.
Therefore, the product xy
is equal to the ratio of two
integers. So by definition, this
product is a rational number.
2. irrational; integers;
SUMS OF IRRATIONAL NUMBERS Example 2 shows a single case where the sum
of a rational number and an irrational number is irrational. To prove that this is
always true, you must first assume that such a sum is rational. This results in a
contradiction which proves that the assumption must be false.
Let a be rational and b be irrational. Let c be the sum of a and b, and assume
that c is rational.
a1b5c
d b
d
a
b c b
bc bc
• } y 5 } • } ; } ; y 5 } ; } ; xy;
a d a
b
ad ad
the product of a nonzero
rational number and an
irrational number is irrational
Key Question to Ask for
Example 2
Simplify.
c The solution is irrational.
rational; xy 5 }c ; }a • y 5 }c ; }ba
b5c2a
Assume c is rational.
Subtract a from each side.
By Example 1, you know that c 2 a is rational. But a rational number cannot be
equal to an irrational number, so this is a contradiction. Therefore the sum of a
rational number and an irrational number must be irrational.
PRACTICE
1. Use Example 1 as a model to prove that the product of two rational
numbers is rational.
2. Copy and complete: Prove that the product of a nonzero rational number
and an irrational number is irrational.
a
b
Let x be a rational number and y be an ? number. By definition, x 5 },
where a and b are ? with b Þ 0. Now assume that the product xy is a
? number. Therefore xy can be written as the quotient of integers c
and d with d Þ 0.
c
d
?
The product xy can be written as } .
?
a
Substitute } for x.
b
?
Multiply both sides by
?
Simplify.
By definition,
}
Solve the equation x 1 5 5 Ï7 . Is
the solution }rational or irrational?
x 5 25 1 Ï 7 ; irrational
? .
? is a rational number which means that y must be
rational. But y is an irrational number, meaning the assumption that
? is rational must be false. Therefore, ? .
•
Why can you conclude that the
solution to the equation in
Example} 2 is irrational? The
the
value Ï 2 1 3 contains
}
irrational number Ï 2 .
Closing the Lesson
Have students summarize the
major points of the lesson and
answer the Essential Question:
How can you show that the sum of
a rational number and an irrational
number is irrational?
• The sum or product of two
rational numbers is rational.
• The sum of a rational number and
an irrational number is irrational.
• The product of a nonzero rational
number and an irrational number
is irrational.
To prove that a 1 b is irrational
whenever either a or b is an
irrational number, use an indirect
proof. Begin the proof by assuming
that the sum is a rational number
and then continue until a
contradiction is reached.
4
PRACTICE
AND APPLY
Teaching Strategy
Exercise 3 Some students may be
unfamiliar with using an indirect
proof as shown below Example 2.
3. Use an indirect proof like the one following Example 2 to prove that the
Suggest that students use the
sum of a rational number and an irrational number is irrational.
following steps to help guide them.
Ask students to identify each step
as it pertains to the example.
1. Assume that the opposite of
what is to be proved is true.
Extension: Use Real and Rational Numbers
CC9
2. Show that this assumption leads
to a contradiction.
a
a c a
3. Let x be a rational number and y be an
}1y2}5}2}
3.
State that the contradiction
b
b
d
b
irrational
number. By definition, x 5 }a
bc 2 ad
implies the assumption was false
1:00:59
PM
ESE612355_03-01A_EXT.indd
9
12/22/10 12:25:28 AM
y5}
b
bd
where a and b are integers with b Þ 0. Now
and therefore its opposite must
Because the set of integers is closed under the operations
be true.
assume that the sum x 1 y is a rational
of subtraction and multiplication, the expression bc 2 ad
number. Therefore x 1 y can be written as
bc 2 ad
is an integer. So by definition }
is a rational number,
the quotient of integers c and d with d Þ 0.
bd
which means that y must be rational. But y is an irrational
x 1 y 5 }c
d
number, meaning the assumption that x 1 y is rational
a
c
}1y5}
must be false. Therefore, x 1 y is an irrational number.
b
d
CC9
Mastering the Standards
for Mathematical Practice
Mathematical Practices
The topics described in the Standards for Mathematical
Content will vary from year to year. However, the way in
which you learn, study, and think about mathematics will
not. The Standards for Mathematical Practice describe skills
that you will use in all of your math courses.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
4 M
Model with mathematics.
In your book
Application exercises and Mixed Reviews of Problem
Solving apply mathematics to other disciplines and in
real-world scenarios.
.**9
.
.*9
.*9&%3&7*&8
9&%
&% 3&7
3&7*&8
3&7*&8
*&
&8PG1SPCMFN4PMWJOH
&8
PGG 1SPCMFN
PG1SPCMFN4PMWJOH
PG1SP
PG1SPCMFN4
CMFN4
MFN
FN 4PMWJOH
WJO
45"5&5&4513"$5*$&
DMBTT[POFDPN
-FTTPOTo
1. .6-5*45&1130#-&. Flying into the wind,
a helicopter takes 15 minutes to travel
15 kilometers. The return flight takes
12 minutes. The wind speed remains
constant during the trip.
a. Find the helicopter’s average speed (in
kilometers per hour) for each leg of the trip.
b. Write a system of linear equations that
represents the situation.
c. What is the helicopter’s average speed in
still air? What is the speed of the wind?
4. 01&/&/%&% Describe a real-world problem
that can be modeled by a linear system.
Then solve the system and interpret the
solution in the context of the problem.
130#-&.40-7*/(
5. 4)0353&410/4& A hot air balloon is
launched at Kirby Park, and it ascends at
a rate of 7200 feet per hour. At the same
time, a second hot air balloon is launched
at Newman Park, and it ascends at a rate of
4000 feet per hour. Both of the balloons stop
ascending after 30 minutes. The diagram
shows the altitude of each park. Are the hot
air balloons ever at the same height at the
same time? Explain.
,JSCZ1BSL
&9".1-&
&
9".
58. %*7*/( A diver dives from a cliff when her center of gravity is 46 feet
above the surface of the water. Her initial vertical velocity leaving the cliff
is 9 feet per second. After how many seconds does her center of gravity
enter the water?
POQ
POQ
GPS&YT
GPS&YT
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
&9".1-&
&
9".
59. 4$3"1#00,%&4*(/ You plan to make a
scrapbook. On the cover, you want to show three
pictures with space between them, as shown. Each
of the pictures is twice as long as it is wide.
POQ
POQ
GPS&YT
GPS&YT
/FXNBO1BSL
a. Write a polynomial that represents the area of
2 cm
2x
4x
2 cm
2 cm
the scrapbook cover.
b. The area of the cover will be 96 square
2 cm
1 cm
1 cm
centimeters. Find the length and width of the
pictures you will use.
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
3940 ft
3. (3*%%&%"/48&3 During one day, two
computers are sold at a computer store. The
two customers each arrange payment plans
with the salesperson. The graph shows the
amount y of money (in dollars) paid for the
computers after x months. After how many
months will each customer have paid the
same amount?
y
SEA LEVEL
Not drawn to scale
6. &95&/%&%3&410/4& A chemist needs
500 milliliters of a 20% acid and 80% water
mix for a chemistry experiment. The chemist
combines x milliliters of a 10% acid and
90% water mix and y milliliters of a 30% acid
and 70% water mix to make the 20% acid and
80% water mix.
61. 1"35)&/0/ The Parthenon in Athens, Greece, is an ancient structure
that has a rectangular base. The length of the Parthenon’s base is
8 meters more than twice its width. The area of the base is about
2170 square meters. Find the length and width of the Parthenon’s base.
62.
a. Write a linear system that represents the
situation.
b. How many milliliters of the 10% acid
and 90% water mix and the 30% acid and
70% water mix are combined to make the
20% acid and 80% water mix?
200
0
2
4
6
8
10
Months since purchase
x
.6-5*1-&3&13&4&/5"5*0/4 An African cat
called a serval leaps from the ground in an attempt
to catch a bird. The serval’s initial vertical velocity
is 24 feet per second.
a. 8SJUJOHBO&RVBUJPO Write an equation that
gives the serval’s height (in feet) as a function
of the time (in seconds) since it left the ground.
c. The chemist also needs 500 milliliters of
400
(4)0353&410/4& You throw a ball into the air with an initial vertical
velocity of 31 feet per second. The ball leaves your hand when it is 6 feet
above the ground. You catch the ball when it reaches a height of 4 feet.
After how many seconds do you catch the ball? Explain how you can use
the solutions of an equation to find your answer.
b. .BLJOHB5BCMF Use the equation from part (a)
a 15% acid and 85% water mix. Does the
chemist need more of the 10% acid and
90% water mix than the 30% acid and
70% water mix to make this new mix?
Explain.
to make a table that shows the height of the
serval for t 5 0, 0.3, 0.6, 0.9, 1.2, and
1.5 seconds.
c. %SBXJOHB(SBQI Plot the ordered pairs in
the table as points in a coordinate plane.
Connect the points with a smooth curve.
After how many seconds does the serval
reach a height of 9 feet? Justify your answer
using the equation from part (a).
$IBQUFS4ZTUFNTPG&RVBUJPOTBOE*OFRVBMJUJFT
"MHFCSB
BUDMBTT[POFDPN
58
03,&%06540-65*0/4
$IBQUFS1PMZOPNJBMTBOE'BDUPSJOH
POQ84
( 545"/%"3%*;&%
5&4513"$5*$&
5.6-5*1-&
3&13&4&/5"5*0/4
PhotoDisc/Getty Images
customer pays a total of $9.70 for 1.8 pounds
of potato salad and 1.4 pounds of coleslaw.
Another customer pays a total of $6.55 for
1 pound of potato salad and 1.2 pounds of
coleslaw. How much do 2 pounds of potato
salad and 2 pounds of coleslaw cost? Explain.
0
60.
1705 ft
2. 4)0353&410/4& At a grocery store, a
Amount paid
(dollars)
M
Mathematically proficient
students can apply...
mathematics... to... problems...
in everyday life, society, and
the workplace...
Apply Properties of
E
Equality
Extension
Use after Lesson 3.4
1
GOAL Use algebraic properties to help solve equations.
Warm-Up Exercises
When you solve an equation, you use properties of real numbers. In particular
you use the algebraic properties of equality and the distributive property.
Key Vocabulary
• equation
• solve an equation
For Your Notebook
KEY CONCEPT
Algebraic Properties of Equality
Let a, b, and c be real numbers.
Addition Property
If a 5 b, then a 1 c 5 b 1 c.
Subtraction Property
If a 5 b, then a 2 c 5 b 2 c.
Multiplication Property
If a 5 b, then ac 5 bc.
Division Property
a
b
If a 5 b and c Þ 0, then }
c 5}
c.
Substitution Property
If a 5 b, then a can be substituted for b in
any equation or expression.
EXAMPLE 1
Solution
Explanation
Write original equation.
Given
Add 2x to each side.
Addition Property
of Equality
6x 1 7 5 25
Combine like terms.
Simplify.
6x 1 7 2 7 5 25 2 7
Subtract 7 from each
side.
Subtraction
Property of
Equality
6x 5 212
Combine like terms.
Simplify.
x 5 22
Divide each side by 6.
Division Property
of Equality
4x 1 7 1 2x 5 22x 2 5 1 2x
2. 13 2 2x 5 x 1 25 (Given)
13 5 3x 1 25 (Addition Prop.
of Equality)
212 5 3x ( Subtraction Prop.
of Equality)
24 5 x ( Division Prop.
of Equality)
ESE612355_03-04A_EXT.indd Sec1:11
Equation
Reason
Essential Question
3
TEACH
Extra Example 1
Solve 6x 2 8 5 2x 1 6. Write
reasons for each step. 6x 2 8 5
2x 1 6 (Given); 6x 2 8 1 8 5 2x 1
6 1 8 (Add Prop of Eq); 6x 5 2x 1
14 (Simplify); 6x 1 x 5 2x 1 14 1
x (Add Prop of Eq); 7x 5 14
(Simplify); x 5 2 (Div Prop Eq)
c The value of x is 22.
✓
FOCUS AND
MOTIVATE
Big Idea 1, p. 131
How do algebraic properties justify
the steps in the solution of an
equation? Tell students they will
learn how to answer this question
by reviewing the Algebraic
Properties of Equality and the
Distributive Property.
Write reasons for each step
4x 1 7 5 22x 2 5
Solve each equation.
1. x 2 3 5 11 14
2. 25x 5 35 27
3. 3x 2 2 5 10 4
4. 2x 1 3(x 2 1) 5 233 26
5. A rectangular playground has
an area of 1575 square yards.
The playground is 45 yards long.
What is its width? 35 yd
2
Solve 4x 1 7 5 2 2x 2 5. Write reasons for each step.
1. 5x 2 7 5 8 (Given)
5x 5 15 (Addition Prop. of
Equality)
x 5 3 ( Division Prop. of
Equality)
PLAN AND
PREPARE
Teaching Strategy
GUIDED PRACTICE
for Example 1
Solve the equation. Write a reason for each step.
1. 5x 2 7 5 8
2. 13 2 2x 5 x 1 25
Extension: Apply Properties of Equality
CC11
Students may object to the need
to justify each step in the solution
of an equation. Point out that
identifying the property that
justifies each step is an important
part of learning why the methods
we use to solve equations work.
You may wish to tell students that
they will not always have to
provide reasons for the steps
when solving equations.
12/10/10 11:07:08 PM
CC11
Extra Example 2
Solve 24(x 1 3) 5 20. Write
reasons for each step. 24(x 1 3) 5
20 (Given); 24x 2 12 5 20 (Distr
Prop); 24x 2 12 1 12 5 20 1 12
(Add Prop of Eq); 24x 5 32
(Simplify); x 5 28 (Div Prop Eq)
Key Question to Ask for
Example 2
•
Because the equation 7(5 2 x) 5
14 has the form ab 5 c, could the
first step of the solution have
been dividing both sides by 7
instead of applying the
distributive property? yes
Closing the Lesson
Have students summarize the
major points of the lesson and
answer the Essential Question:
How do algebraic properties
justify the steps in the solution
of an equation?
• The Algebraic Properties of
Equality and the Distributive
Property can be used to justify
each step in the solution of a
variety of equations.
In order to maintain the equality
of the original equation, each step
of the process when solving an
equation must follow from one of
the properties of equality or the
Distributive Property.
4
PRACTICE
AND APPLY
Avoiding Common Errors
Exercise 7 When solving an
equation like 19 2 2x 5 217,
some students will begin by
dividing both sides by 2 (or 22)
rather than subtracting 19 from
both sides first. By dividing first,
students unnecessarily introduce
fractions into the process. Instruct
them to think about reversing the
order of operations when solving
a multi-step equation.
12. 4(5x 2 9) 5 22(x 1 7) (Given)
20x 2 36 5 22x 2 14
(Distributive Prop.)
22x 2 36 5 214
(Addition Prop. of Equality)
22x 5 22
(Addition Prop. of Equality)
x 5 1 (Division Prop. of Equality)
CC12
3. 5x 2 10 5 240 (Given);
KEY CONCEPT
For Your Notebook
5x 5 230 (Addition Prop. of
Equality); x 5 26 (Division
Distributive Property
Prop. of Equality);
4. 4x 1 9 5 16 2 3x (Given);
a(b 1 c) 5 ab 1 ac, where a, b, and c are real numbers.
7x 1 9 5 16 (Addition Prop. of
Equality); 7x 5 7 (Subtraction
Prop. of Equality); x 5 1
(Division Prop. of Equality)
E X A M P L E 2 Use the Distributive Property
5. 5 2 x 5 17 (Given);
Solve 7(5 2 x) 5 14. Write reasons for each step.
2x 5 12 (Subtraction Prop. of
Equality); x 5 212 (Division
Prop. of Equality)
Solution
6. 2x 2 3 5 x 2 5 (Given);
Equation
Explanation
Reason
x 2 3 5 25 (Subtraction Prop.
Given
of Equality); x 5 22 (Addition
7(5 2 x) 5 14
Write original equation.
Prop. of Equality)
Distributive Property
35 2 7x 5 14
Multiply.
7. 19 2 2x 5 217 (Given);
27x 5 221
Subtract 35 from each side. Subtraction Property of
22x 5 236 (Subtraction Prop.
Equality
of Equality); x 5 18 (Division
Division Property of
x
5
3
Divide
each
side
by
27.
Prop. of Equality)
Equality
8. 23x 5 25x 1 12 (Given);
2x 5 12 (Addition Prop.
c The value of x is 3.
of Equality); x 5 6 (Division
Prop. of Equality)
PRACTICE
9. 5(3x 2 20)
5 210 (Given);
15x 2 100 5 210
(Distributive
Prop.); 15x 5 90
(Addition Prop.
of Equality);
x 5 6 (Division
Prop. of Equality)
10. 3(2x 1 11)
5 9 (Given);
6x 1 33 5 9
(Distributive
Prop.); 6x 5 224
(Subtraction
Prop. of
Equality);
x 5 24
(Division Prop.
of Equality)
Copy the logical argument. Write a reason for each step.
1.
3x 2 12 5 7x 1 8
Given
2. 5(x 2 1) 5 4x 1 3
Given
Distributive Property
Subtraction Property of Equality
24x 2 12 5 8
?
5x 2 5 5 4x 1 3
?
Subtraction Property of Equality
Addition Property of Equality
24x 5 20
?
x2553
?
Addition Property of Equality
Division Property of Equality
x 5 25
?
x58
?
For Exercises 3–14, solve the equation. Write a reason for each step.
3. 5x 2 10 5 240
4. 4x 1 9 5 16 2 3x
5. 5 2 x 5 17
6. 2x 2 3 5 x 2 5
7. 19 2 2x 5 217
8. 23x 5 25x 1 12
9. 5(3x 2 20) 5 210
12. 4(5x 2 9) 5 22(x 1 7)
10. 3(2x 1 11) 5 9
11. 2(2x 2 5) 5 12 12–14. See margin.
13. 13 2 x 5 22(x 1 3)
14. 3(7x 2 9) 2 19x 5 215
15. ERROR ANALYSIS Describe and correct the error in solving for x. 11. 2(2x 2 5) 5 12
7x 5 x 1 24
Given
8x 5 24
Addition Property of Equality
x53
Division Property of Equality
(Given); 22x 2 10 5 12
(Distributive Prop.);
22x 5 22 (Addition
Prop. of Equality);
x 5 211 (Division Prop.
of Equality)
16. DEBATE Mrs. Sinclair divided her 30 history students into 6 debate
teams, with each team consisting of a secretary to take notes during
the debates and x debaters. The solution of the equation 6(x 1 1) 5 30
represents the number of debaters on each team. Solve the equation and
write a reason for each step. See margin.
CC12
Chapter 3 Solving Linear Equations
13. 13 2 x 5 22(x 1 3) (Given)
13 2 x 5 22x 2 6 (Distributive Prop.)
LA1_CCESE612355_03-04A_EXT.indd Sec1:12
13 1 x 5 26 (Additive Prop. of Equality)
x 5 219 (Subtraction Prop. of Equality)
14. 3(7x 2 9) 2 19x 5 215 (Given);
21x 2 27 2 19x 5 215 (Distributive Prop.)
2x 2 27 5 215 (Simplify.)
2x 5 12 (Addition Prop. of Equality)
x 5 6 (Division Prop. of Equality)
15. In the initial step, x should have been
subtracted from each side, not added. The
second line should be 6x 5 24 and its reason
should be the Subtraction Property of Equality.
The third line should then begin with x 5 4.
16. Equation (Reason)
6(x 1 1) 5 30 (Given)
6x 1 6 5 30 (Distributive Prop.)
6x 5 24 (Subtraction Prop. of Equality)
x 5 4 (Division Prop. of Equality)
12/10/10 11
Graphing
Graphing
C
a
alculator
lc ulator
Calculator
ACTIVITY
AC
CTIVITY
Use a
Us
after Lesson 4.7
4.7 Solving Linear Equations
ations by
1
Graphing Each Side
e
QUESTION
Learn the Method
How can a graphing calculator be used to solve a
linear equation?
Students will solve a linear
equation by graphing each side.
• After the activity, students can
use a graphing calculator to
check their solutions to any
equation in one variable.
•
You can solve a linear equation in one variable by graphing each side of the
equation and fi nding the point of intersection. The x-value of the intersection
is the solution of the equation.
EXAMPLE 1
Solve a linear equation
4
Solve the linear equation }
x 1 8 5 20 using a graphing calculator.
2
5
STEP 1 Create two equations
Write two functions by setting each side of the equation equal to y.
TEACH
Tips for Success
4
5
4
y5}
x 1 8 and y 5 20
5
} x 1 8 5 20
STEP 2 Enter equations
STEP 3 Graph the equations
Enter the equations from Step 1
as Y1 and Y2.
Choose a viewing window that allows
you to see the intersection.
In Example 1, discuss how to select
a viewing window that will include
the point of intersection. Point out
that it is acceptable to begin with
an overly-large window at first and
then restrict the parameters after
seeing the graph in order to better
display the point of intersection.
q UNVAME
q!U#{Av
q k4ZAZ
q!UNVAME
q!U#{AvE
q!k4ZAZ
q j?kAZ
RYsZqRYsvqRYst
-!Z A ]FpE^ a@
-!v A v
-!t A
-!F A
-!E A
-!o A
-!n A
PLAN AND
PREPARE
Extra Example 1
Solve the linear equation
1
}x 2 5 5 –3 by graphing each
3
side. x 5 6
STEP 4 Find the point of intersection
STEP 5 Check the solution
Use the Intersect feature on the
graphing calculator to find the point
of intersection. The graphs intersect
at (15, 20).
The x-value of the point of
intersection, 15, is the solution of
the equation. Check by substituting
15 for x in the original equation.
4
5
4
5
}(15) 1 8
Vs?jk?4sNYV
AZEqqqqqqq!Av
Intersection
X=-2
Y=-3
} x 1 8 0 20
Check:
0 20
12 1 8 0 20
20 5 20 ✓
You can use this method to fi nd a solution for any type of equation in one variable.
You can also use this method to check a solution that you found algebraically.
ESE612355_04_07A_ACT.indd 13
4.7 Graph Linear Functions
CC13
12/10/10 4:06:51 AM
CC13
Graphing
Graphing
Ca
alculator
lc ulator
Calculator
Tips for Success
In Step 4 of Example 2, remind
students that they must place the
cursor relatively close to the point
of intersection of the two lines
when using the Intersect feature
on the graphing calculator.
Extra Example 2
Solve the equation 4w 1 7 5
26w 2 13 by graphing each
side. w 5 22
ACTIVITY
AC
CTIVITY
PR AC T IC E 1
Solve the equation using a graphing calculator.
1. 6x 2 5 5 19 x 5 4
2. 3 5 2x 1 5 x 5 21
7
8
4. 3 1 } x 5 21 x 5 2}
2
7
5. 7 2 } c 5 17 c 5 26
EXAMPLE 2
5
3
Set each side of the equation equal to y and change t to x.
y 5 2x 2 1
y 5 23x 1 9
STEP 3 Graph the equations
q UNVAMZ
q!U#{AZ
q k4ZAZ
q!UNVAMZ
q!U#{AZ
q!k4ZAZ
q j?kAZ
RYsZqRYsvqRYst
-!Z A v MZ
-!v A Mt aW
-!t A
-!F A
-!E A
-!o A
-!n A
STEP 4 Find the point of intersection
STEP 5 Check the solution
Use the Intersect feature on the
graphing calculator to find the
point of intersection. The graphs
intersect at (2, 3).
The x-value of the point of
intersection, 2, is the solution of the
equation.
Check:
ASSESS AND
RETEACH
2t 2 1 0 23t 1 9
2(2) 2 1 0 23(2) 1 9
353✓
Vs?jk?4sNYV
Avqqqqqqqq!At
PR AC T IC E 2
Solve the equation using a graphing calculator.
7. 25x 1 2 5 4x 2 7 x 5 1 8. 7x 2 4 5 9x 2 8 x 5 2 9. 23x 1 1 5 27x 2 11
x 5 23
12. 2x 1 4 5 x 2 2 x 5 3
x 5 218
13. DRAW CONCLUSIONS Describe the graphs when you solve an equation
with a variable on one side by graphing each side of the equation. What
is different about the graphs when the original equation has a variable
on each side? See margin
10. 8x 5 12x 2 20 x 5 5 11. 2x 2 7 5 3x 1 11
CC14
Chapter 4 Graphing Linear Equations and Functions
LA1_CCESE612355_04_07A_ACT.indd 14
CC14
5
STEP 1 Create two equations
Key Discovery
Solve the equation 25x 1 19 5
2x 2 2 by graphing each side.
1. What two linear equations
should be entered in a graphing
calculator? y 5 25x 1 19 and
y 5 2x 2 2
2. If the two lines from Exercise 1
intersect at the point (3, 4), what
is the solution of the equation?
x53
13. When the equation has one
side with no variable, you get a
horizontal line that intersects a
non-horizontal line. When the
equation has a variable on each
side, you get two non-horizontal
intersecting lines.
3
Solve the linear equation 2t 2 1 5 23t 1 9 using a graphing calculator.
Intersection
X=-2
Y=-1
3
2
1
6. }
x1}
x 5 22 x 5 30
Solve a linear equation
STEP 2 Enter equations
A graph can be used to solve a
linear equation. After graphing
the two sides of the equation as
separate functions, find the point
of intersection. The x-value of this
point is the solution of the original
equation.
3. 23q 1 4 5 13 q 5 23
12/10/10 4
Extension
Use after Lesson 5.7
Assess the Fit of a Model
PLAN AND
PREPARE
1
GOAL Assess the fit of a linear model by plotting and analyzing residuals.
Warm-Up Exercises
Key Vocabulary
• residual
You have found lines of fit using estimation and using linear regression. Most
lines of fit do not pass through every data point, so you can look at the residuals
to assess whether the model is a good fit for the data.
RESIDUALS Given a set of data and a model, the difference between an actual
value of the dependent variable y and the value predicted by the linear model ŷ
is called a residual. A residual plot is a scatter plot of points whose x-values are
those from the data set and whose y-values are the corresponding residuals.
EXAMPLE 1
Find the value of y when x 5 10, 15,
20, and 25.
1. y 5 8x 2 35 45, 85, 125, 165
2. y 5 5x 1 125 175, 200, 225, 250
3. Make a scatter plot of the data.
Draw a line of fi t. Write an equation of the line. Sample answer:
y5x
Calculate and interpret residuals
© Chris Rogers/Corbis
CRUISE SHIPS The table shows data for
ESE612355_05-07A_EXT.indd CC15
x
24
22
0
1
3
y
24
21
21
1
2
several cruise ships. Is the equation
y 5 4x 2 1500 a good model for the data.
Length, x (ft)
Passenger capacity, y
644
1090
720
1266
4
3
2
1
754
781
1748
866
1440
1870
915
2435
4
965
2
y
O
1 2 3 4x
2
3
4
1950
Solution
Make a table showing the passenger capacities predicted by the equation.
Then calculate the residuals.
Length, x (ft)
Predicted capacity, ŷ
Residuals, y 2 ŷ
644
720
754
781
866
915
965
1076
1380
1516
1624
1964
2160
2360
14
2114
232
2184
294
275
2410
300
150
0
2150
2300
500
700
900
x
GOODNESS OF FIT If a line is a good fit for a set of data, the absolute values of the
residuals are relatively small and more or less evenly distributed above and below
the x-axis in a residual plot. Residuals that are mostly positive or mostly negative
imply that the line is in the wrong place. Residuals that are steadily increasing
suggest the data is not linear, while wildly scattered residuals suggest that the
data might have relatively no correlation.
Extension: Assess the Fit of a Model
FOCUS AND
MOTIVATE
Essential Question
y
Plot the residuals on a residual plot.
The equation y 5 4x 2 1500 models the
data somewhat, but appears to predict
capacity better for shorter lengths than
it does for larger lengths.
2
CC15
Big Idea 3, p. 281
How do you know that a linear
equation is a good model for a set
of data? Tell students they will
learn how to answer this question
by examining the differences
between the actual values of the
dependent variable y and the
values of y predicted by the linear
model.
3
TEACH
Extra Example 1
The table shows the number of situps a student can do while being
timed. Is the equation y 5 11x 1 6 a
good model for the data? yes
12/10/10 11:10:27 PM
Time, x
(min)
1
2
3
4
Sit-Ups, y
16
29
40
50
CC15
EXAMPLE 2
SAFETY The table shows stopping distances for cars based on the speed
being traveled. Is the equation y 5 7x 2 105 a good model for the data?
Extra Example 2
The table shows the hand span and
the height of five students. Let x be
the hand span in inches and y be
the height in inches. Is the equation
y 5 4x 1 38 a good model for the
data? no
Hand
Span
6.7
7.3
8.3
9.4
9.6
Height
62
66
68
72
74
Speed, x (mi/hr)
10
20
30
Stopping distance, y (ft)
27
63
109
40
50
60
70
80
90
100
164 229 303 387 481 584 696
Solution
Create a residual plot.
The curve in the residuals suggests
that a linear model may not be the
best choice for this data, but for
values of x between 20 and 80, this
model appears to predict the actual
value fairly well.
Key Question to Ask for
Example 2
•
Calculate and interpret residuals
100
y
50
0
20
40
60
80
100
x
250
2100
Examine the residual plot. As the
value of x increases beyond 100,
what do you expect the values of
the residuals to do? As the
x-values increase beyond 100,
the plot seems to suggest that the
residuals will become increasingly positive.
PRACTICE
1. The
residuals are
consistently
positive; this
implies that the
line is in the
wrong place.
Closing the Lesson
Have students summarize the
major points of the lesson and
answer the Essential Question:
How do you know that a linear
equation is a good model for a set
of data?
• If a linear equation is a good
model for a set of data, the
residuals are more or less evenly
distributed above and below the
x-axis in a residual plot.
• For a line to be a good fit for a set
of data, the absolute values of
the residuals will be small.
For a given set of data and a model,
first calculate the residuals and
then create a residual plot. The
linear equation is a good model if
the plotted points all lie relatively
close to the x-axis.
For Exercises 1–4, the graph represents a residual plot for a data set and a
linear model. Based on the residual plot, discuss the goodness of fit of the
linear model.
y
1.
2.
y
x
x
3. The
distances
between the
points and the
x-axis appear
to be relatively
small and the
points are more
or less evenly
distributed
above and
below the
x-axis. The
linear model is
a good fi t.
2. The residuals are growing; this implies that the data is not linear.
y
4. y
3.
x
x
4. The residuals are wildly scattered; this implies that the data might have no correlation.
5. Create a residual plot for the data below using the model y 5 2x 1 0.2.
Time Walking, x (hr)
0
1
2
3
4
5
Distance Walked, y (mi)
0
2.1
4.3
6.1
8.6
10.1
The residuals are 20.2, 20.1, 0.1, 20.1, 0.4, 20.1; see margin for art.
PRACTICE
AND APPLY
4
CC16
Graphing Calculator
Exercise 5 A graphing calculator
can be used to create a residual
plot. Enter the times in list L1 and
the calculated residuals in list L2.
Choose an appropriate viewing
window and then use the STAT
PLOT feature of the calculator to
create the residual plot.
CC16
Chapter 5 Writing Linear Equations
y
0.4
LA1_CCESE612355_05-07A_EXT.indd
0.3
0.2
0.1
0
1
2
20.1
20.2
20.3
20.4
5.
CC16
3
12/10/10 11
4
5
x
Tennessee Grade Six Mathematics Standards
Mastering the Standards
for Mathematical Practice
Mathematical Practices
The topics described in the Standards for Mathematical
Content will vary from year to year. However, the way in
which you learn, study, and think about mathematics will
not. The Standards for Mathematical Practice describe skills
that you will use in all of your math courses.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
Use appropriate tools strategically.
U
5 Us
Mathematically proficient
M
students consider the available
tools when solving a...
problem... [and] are... able
to use technological tools
to explore and deepen their
understanding...
In your book
Problem Solving Workshops explore alternative methods as
tools for problem solving. A variety of Activities use concrete
and technological tools to explore mathematical concepts.
*OWFTUJ
*OWFTUJ
*OWFTUJHBUJOH
WFT JH
HBUJOH
BUJOH
UJ H
UJO
"MHFCSB
"MHFCS
"MHFCSB
MHFC "MHFCSB
"$5*7*5:
"$
"$5
"
$
$5*7*5
$5*
$5*7*5:
$5
5*7*5
5*
7**5:
7
:
5SEBEFORE,ESSON
4PMWJOH-JOFBS4ZTUFNT6TJOH5BCMFT
. "5 & 3 * " - 4 tQFODJMBOEQBQFS
2 6 & 4 5 * 0 / )PXDBOZPVVTFBUBCMFUPTPMWFBMJOFBSTZTUFN
A system of linear equations, or linear system, consists of two or more linear
equations in the same variables. A solution of a linear system is an ordered
pair that satisfies each equation in the system. You can use a table to find a
solution to a linear system.
&91-03&
4PMWFBMJOFBSTZTUFN
-&440/
Bill and his brother collect comic books. Bill currently has 15 books and adds
2 books to his collection every month. His brother currently has 7 books and
adds 4 books to his collection every month. Use the equations below to find
the number x of months after which Bill and his brother will have the same
number y of comic books in their collections.
y 5 2x 1 15
/VNCFSPGDPNJDCPPLTJO#JMMTDPMMFDUJPO
y 5 4x 1 7
/VNCFSPGDPNJDCPPLTJOIJTCSPUIFSTDPMMFDUJPO
34%0 -AKEATABLE
Copy and complete the table of values shown.
34%0 &INDASOLUTION
"OPUIFS8BZUP4PMWF&YBNQMFQBHF
.6-5*1-&3&13&4&/5"5*0/4 In Example 5 on page 98, you saw how to solve
a problem about exercising using a verbal model and an equation. You can
also solve the problem by breaking it into parts.
1 30 # - & .
Y
Z5Y1
Z5Y1
&9&3$*4*/( Your daily workout plan involves a total of 50 minutes of
running and swimming. You burn 15 calories per minute when running
and 9 calories per minute when swimming. Find the number of calories
you burn in your 50 minute workout if you run for 20 minutes.
Find an x-value that gives the same y-value for
both equations.
34%0 )NTERPRETTHESOLUTION
.&5)0%
Use your answer to Step 2 to find the number of
months after which Bill and his brother have the
same number of comic books.
#SFBLJOHJOUP1BSUT You can solve the problem by breaking it into parts.
34%0 'JOEthe number of
calories you burn when
running.
:PVSSVOOJOHUJNFJT
NJOVUFTTPZPVS
TXJNNJOHUJNFJT
25NJOVUFT
% 3 " 8 $ 0 / $ - 6 4 * 0 / 4 6TFZPVSPCTFSWBUJPOTUPDPNQMFUFUIFTFFYFSDJTFT
1. When Bill and his brother have the same number of books in their
collections, how many books will each of them have?
34%0 'JOEthe calories you
burn when swimming.
34%0 "EEthe calories you
burn when doing each
activity. You burn a total
of 570 calories.
2. Graph the equations above on the same coordinate plane. What do
you notice about the graphs and the solution you found above?
15 calories
per minute + 20 minutes 5 300 calories
9 calories
per minute + 30 minutes 5 270 calories
300 calories 1 270 calories 5 570 calories
Use a table to solve the linear system.
3. y 5 2x 1 3
y 5 23x 1 18
4. y 5 2x 1 1
y 5 2x 2 5
1 3 "$ 5 * $ &
5. y 5 23x 1 1
y 5 5x 2 31
1. 7"$"5*0/*/( Your family is taking a
vacation for 10 nights. You will spend some
nights at a campground and the rest of the
nights at a motel. A campground stay costs
$15 per night, and a motel stay costs $60 per
night. Find the total cost of lodging if you
stay at a campground for 6 nights. Solve this
problem using two different methods.
$IBQUFS4ZTUFNTPG&RVBUJPOTBOE*OFRVBMJUJFT
2. 8)"5*' In Exercise 1, suppose the vacation
lasts 12 days. Find the total cost of lodging
if you stay at the campground for 6 nights.
Solve this problem using two different
methods.
3. '-03*45 During the summer, you work
35 hours per week at a florist shop. You get
paid $8 per hour for working at the register
and $9.50 per hour for making deliveries.
Find the total amount you earn this week if
you spend 5 hours making deliveries. Solve
this problem using two different methods.
4. &3303"/"-:4*4 Describe and correct the
error in solving Exercise 3.
$8 per hour + 5 hours 5 $40
$9.50 per hour + 30 hours 5 $285
Getty Images/Image Source
$40 1 $285 5 $325
$IBQUFS1SPQFSUJFTPG3FBM/VNCFST
Graphing
Graphing
C
a
alculator
lc ulator
Calculator
1
PLAN AND
PREPARE
Learn the Method
Students will use a graphing
calculator to show that the
elimination method for solving
a linear system of equations
results in the solution of the
system.
• After the activity, students can
use a graphing calculator to
check their solutions.
ACTIVITY
AC
CTIVITY
7.4 Multiply and Then
n Add Equations
Equation
QUESTION
How can you see why elimination works as a method for
solving linear systems?
•
2
TEACH
Tips for Success
In Example 1, make sure students
understand how to solve for y in
the equation Ax 1 By 5 C. Stress
that the form y 5 mx 1 b is needed
when entering an equation into a
graphing calculator. Also make
sure students know how to find
and use the Intersect feature of the
graphing calculator.
Extra Example 1
Solve the linear system.
24x 1 y 5 13
4x 1 y 5 211 (23, 1)
Use after
af Lesson 7.4
You have used elimination to solve systems of linear equations, but you may
think that it isn’t obvious why this method works. You can do an algebraic
proof by replacing the numbers in the system with variables, but this is
complicated to do. In this activity, you will graph each equation that you get
as you use elimination.
E X A M P L E 1 Solve the linear system using addition
Solve the linear system
22x 1 y 5 1
2x 1 y 5 5
Equation 1
Equation 2
Solution
STEP 1 Graph the System
Solve both equations for y.
–2x 1 y 5 1
2x 1 y 5 5
y 5 1 1 2x
y 5 5 2 2x
Graph the two equations using a graphing
calculator. Notice that the point of intersection
of the graphs is the solution of the system.
The solution is (1, 3).
STEP 2 Graph the sum of the equations
Add the two equations as you would if you were solving
the system algebraically. Graph the resulting equation.
22x 1 y 5 1
2x 1 y 5 5
2y 5 6
y53
Equation 1
Equation 2
Add.
Solve for y.
Now graph the equation y 5 3 on the same graphing
calculator screen with the two original equations.
STEP 3 Summarize the Results
All three equations intersect at (1, 3). So, (1, 3) is the solution of the system.
PR AC T IC E 1
1–3. Check students’ graphs.
Solve the system using elimination. Graph each resulting equation.
1. 2x 1 y 5 9
x 1 y 5 1 (24, 5)
CC18
3. 2x 2 3y 5 4
8x 1 3y 5 1 (0.5, 21)
Chapter 7 Systems of Equations and Inequalities
LA1_CCESE612355_07_04A_ACT.indd 18
CC18
2. 6x 2 7y 5 4
x 1 7y 5 17 (3, 2)
12/10/10
4
LA1_CCE
E X A M P L E 2 Solve a linear system using multiplication
Tips for Success
Solve the linear system:
In Step 3 of Example 2, ask students
why two of the new equations have
the same graphs as the two original
equations. Point out that if this step
results in different graphs, the
student must have made an error
in calculation or in entering the
equations.
2x 2 y 5 4
23x 1 2y 5 27
Equation 1
Equation 2
STEP 1 Graph the System
Solve each equation for y.
2x 2 y 5 4
23x 1 2y 5 27
27
y 5 3x
}
y 5 2x 2 4
2
Graph the two equations. The point of intersection of the
graphs is the solution of the system.
Extra Example 2
STEP 2 Use elimination to solve
Solve a linear system.
23x 2 y 5 2
4x 1 3y 5 4 (22, 4)
Multiply each equation by a constant so that you can eliminate
a variable x by adding.
2x 2 y 5 4
33
6x 2 3y 5 12
Multiply Equation 1 by 3.
23x + 2y 5 27
32
26x 1 4y 5 214
Multiply Equation 2 by 2.
y 5 22
Alternative Strategy
Ask students to rework Step 2
of Example 2 so that y will be
eliminated instead of x. The result
will be an equation of the form
x 5 a. Then have them examine the
graph shown in Step 3 to see how
a graph of their result for Step 2
would intersect the other lines in
the graph.
Add.
STEP 3 Graph the resulting equations
Graph the equations 6x 2 3y 5 12, 26x 1 4y 5 214, and
y 5 22 on the same graphing calculator screen with the
two original equations.
STEP 4 Summarize the Results
All of the equations intersect at (1, 22). So, (1, 22) is the
solution of the system.
3
PRACTICE
Solve the system using elimination. Graph each resulting equation. 4–6. Check students’ graphs.
4. x 2 y 5 25 (22, 3)
4x 1 3y 5 1
5. 2x 2 5y 5 3 (4, 1)
2x 1 2y 5 22
ASSESS AND
RETEACH
Solve the linear system.
1. x 1 2y 5 1
3x 2 2y 5 11 (3, 21)
2. 22x 1 3y 5 27
3x 2 7y 5 8 (5, 1)
3. 2x 1 4y 5 24
2x 1 3y 5 213 (4, 23)
4. 2x 1 2y 5 27
4x 1 5y 5 224 (21, 24)
6. 3x 1 5y 5 3 (6, 23)
x2y59
7. Solve the linear system using a graphing calculator. Now use a
x 2 2y 5 26
linear combination on the system to eliminate the variable x.
2x 1 y 5 8
Use a linear combination on the system to eliminate the
variable y. What do you notice?
The solution (2, 4) found using the graphing calculator has coordinates that are given by the equations
resulting from using linear combinations to eliminate one of the variables
D R A W C O N C L U S I O N S from the original system.
8. Explain how you could use this method to check whether you have correctly
solved a system of linear equations by graphing?
To check the solution of the system, you can add the equations and graph the sum. If the three lines intersect
9. Suppose you are trying to solve a system of linear equations that has no solution. in one point, the
solution is correct.
a. What happens when you use the elimination method?
You get a false equation such as 5 5 3.
b. What does the graph of the system look like?
The lines are parallel.
c. Will the method of graphing the resulting equations as in Example 2 work
with the system? When you add the equations, you don’t get an equation that can be graphed,
so the method does not work.
4:10:05
AM
ESE612355_07_04A_ACT.indd
19
7.4 Solve Linear Systems by Multiplying First
CC19
12/10/10 4:10:14 AM
CC19
Mastering the Standards
for Mathematical Practice
Mathematical Practices
The topics described in the Standards for Mathematical
Content will vary from year to year. However, the way in
which you learn, study, and think about mathematics will
not. The Standards for Mathematical Practice describe skills
that you will use in all of your math courses.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
Make sense of problems and persevere in solving them.
1 M
In your book
Verbal Models and the Problem Solving Plan help you
translate the information in a problem into a model and
then analyze your solution.
a Problem
1.5 Use
Solving Plan
Before
Now
Why?
Key Vocabulary
• formula
You used problem solving strategies.
&9".1-&
You will use a problem solving plan to solve problems.
KEY CONCEPT
4PMWFBNVMUJTUFQQSPCMFN
+0#&"3/*/(4 You have two summer jobs at a youth
center. You earn $8 per hour teaching basketball and
$10 per hour teaching swimming. Let x represent the
amount of time (in hours) you teach basketball each
week, and let y represent the amount of time (in hours)
you teach swimming each week. Your goal is to earn at
least $200 per week.
So you can determine a route, as in Example 1.
For Your Notebook
A Problem Solving Plan
s 7RITEANINEQUALITYTHATDESCRIBESYOURGOALINTERMS
of x and y.
STEP 1 Read and Understand Read the problem carefully. Identify what
you know and what you want to find out.
s 'RAPHTHEINEQUALITY
STEP 2 Make a Plan Decide on an approach to solving the problem.
s 'IVETHREEPOSSIBLECOMBINATIONSOFHOURSTHATWILL
allow you to meet your goal.
STEP 3 Solve the Problem Carry out your plan. Try a new approach if the
first one isn’t successful.
4PMVUJPO
STEP 4 Look Back Once you obtain an answer, check that it is reasonable.
34%0 8SJUFAVERBALMODEL4HENWRITEANINEQUALITY
EXAMPLE 1
#BTLFUCBMM
QBZSBUF
Read a problem and make a plan
EPMMBSTIPVS
RUNNING You run in a city. Short blocks are north-south
8
and are 0.1 mile long. Long blocks are east-west and are
0.15 mile long. You will run 2 long blocks east, a number
of short blocks south, 2 long blocks west, and back to
your start. You want to run 2 miles at a rate of 7 miles
per hour. How many short blocks must you run?
For an alternative
method for solving the
problem in Example
1, turn to page 34 for
the Problem Solving
Workshop.
"70*%&33034
"70*
* % & 3 3034
0.1 mi
STEP 1 Read and Understand
What do you know?
IPVST
x
+
4XJNNJOH
QBZSBUF
+
EPMMBSTIPVS
1
10
0.15 mi
5IFWBSJBCMFTDBO
5IFWBSJBCMFTDBOU
SFQSFTFOUOFHBUJWF
SFQSFTFOUOFHBUJW
OVNCFST4PUIFH
OVNCFST4PUIFHSBQI
PGUIFJOFRVBMJUZEPFT
PGUIFJOFRVBMJUZE
OPUJODMVEFQPJOUT
OPUJODMVEFQPJOUTJO
2VBESBOUT*****P
2VBESBOUT*****PS*7
4XJNNJOH
UJNF
q
IPVST
y
+
34%0 (SBQITHEINEQUALITYx 1 10y q 200.
Solution
ANOTHER WAY
#BTLFUCBMM
UJNF
1
+
&
IRSTGRAPHTHEEQUATIONx 1 10y 5 200
IN1UADRANT)4HEINEQUALITYISq, so use
a solid line.
Next, test (5, 5) in 8x 1 10y q 200:
Swimming (hours)
8(5) 1 10(5) q 200
90 q 200 You know the length of each size block, the number of long blocks you
will run, and the total distance you want to run.
5PUBM
FBSOJOHT
EPMMBST
q
200
y
20
8x 1 10y ≥ 200
10
0
0
(5, 5)
10
20
30 x
Basketball (hours)
Finally, shade the part of Quadrant I that does not contain (5, 5),
BECAUSEISNOTASOLUTIONOFTHEINEQUALITY
You can conclude that you must run an even number of short blocks
because you run the same number of short blocks in each direction.
34%0 $IPPTFthree points on the graph, such as (13, 12), (14, 10), and (16, 9).
The table shows the total earnings for each combination of hours.
What do you want to find out?
#BTLFUCBMMUJNFIPVST
You want to find out the number of short blocks you should run so
that, along with the 4 long blocks, you run 2 miles.
STEP 2 Make a Plan Use what you know to write a verbal model that
4XJNNJOHUJNFIPVST
5PUBMFBSOJOHTEPMMBST
represents what you want to find out. Then write an equation and
solve it, as in Example 2.
28
Chapter 1 Expressions, Equations, and Functions
(6*%&%13"$5*$&
GPS&YBNQMF
8. 8)"5*' In Example 6, suppose that next summer you earn $9 per hour
TEACHINGBASKETBALLANDPERHOURTEACHINGSWIMMING7RITEAND
GRAPHANINEQUALITYTHATDESCRIBESYOURGOAL4HENGIVETHREEPOSSIBLE
combinations of hours that will help you meet your goal.
laa111se_0105.indd 28
10/20/10 12:50:34 AM
$IBQUFS4PMWJOHBOE(SBQIJOH-JOFBS*OFRVBMJUJFT
Comstock/Getty Images
M
Mathematically proficient
students start by explaining
to themselves the meaning
of a problem... They
analyze givens, constraints,
relationships, and goals. They
make conjectures about the
form... of the solution and plan
a solution pathway...
Systems with
10.7A Solve
Quadratic Equations
© moodboard/Alamy
Before
Now
Why?
Key Vocabulary
• system of linear
equations
• zero-product
property
1
You solved systems of linear equations.
Warm-Up Exercises
You will solve systems that include a quadratic equation.
Solve the linear system using
substitution.
1. y 5 3 2 2x
y 5 x 1 9 (22, 7)
Solve the linear system using
elimination.
2. x 2 y 5 10
4x 1 y 5 215 (21, 211)
So you can predict the path of a ball, as in Example 4.
You have solved systems of linear equations using the graph-and-check
method and using the substitution method. You can use both of these
techniques to solve a system of equations involving nonlinear equations,
such as quadratic equations.
Recall that the substitution method consists of the following three steps.
STEP 1 Solve one of the equations for one of its variables.
Pacing
STEP 2 Substitute the expression from Step 1 into the other equation and
Basic: 1 day
Average: 1 day
Advanced: 1 day
Block: 0.5 block
solve for the other variable.
STEP 3 Substitute the value from Step 2 into one of the original equations
and solve.
EXAMPLE 1
2
Use the substitution method
y 5 3x 1 2
y 5 3x2 1 6x 1 2
Solve the system:
Equation 1
Big Idea 2, p. 627
How do you solve a system of
equations that includes a quadratic
equation? Tell students they will
learn how to answer this question
by applying techniques they
learned for solving systems of
linear equations.
STEP 1 Solve one of the equations for y. Equation 1 is already solved for y.
STEP 2 Substitute 3x 1 2 for y in Equation 2 and solve for x.
y 5 3x2 1 6x 1 2
Write original Equation 2.
2
Substitute 3x2 1 2 for y.
3x 1 2 5 3x 1 6x 1 2
Be sure to set all linear
factors equal to zero
when applying the zeroproduct property.
0 5 3x2 1 3x
Subtract 3x and 2 from each side.
0 5 3x(x 1 1)
Factor.
3x 5 0 or
x50
x1150
or
x 5 21
Motivating the Lesson
Zero-product property
Solve for x.
STEP 3 Substitute both 0 and 21 for x in Equation 1 and solve for y.
y 5 3x 1 2
y 5 3x 1 2
y 5 3(0) 1 2
y 5 3(21) 1 2
y52
y 5 21
FOCUS AND
MOTIVATE
Essential Question
Equation 2
Solution
AVOID ERRORS
PLAN AND
PREPARE
c The solutions are (0, 2) and (21, 21).
10.7A Solve Systems with Quadratic Equations
CC21
Suppose you missed your cruise
ship but you know that it is following
a path that can best be modeled by
the equation y 5 2x 2 2 4x 1 1.
Thinking quickly you hire the owner
of a speedboat to take you to the
cruise ship. The owner of the
speedboat suggests that you follow
a path that can best be modeled by
the equation y 5 4x 2 7. By solving
this system of equations, you can
determine the location where you
will meet up with the cruise ship.
Resource Planning Guide
Ch t Resource
Chapter
R
• Practice level B
• Study Guide
• Challenge
• Pre-AP notes
ESE612355_10-7A_EXPO.indd 21
Teaching
T
hi Options
• Activity Generator provides
editable activities for all ability
levels
Interactive Technology
12/10/10
• Activity Generator
• Animated Algebra
• Test Generator
• eEdition
4:11:01 AM
See also the Differentiated Instruction
Resources for more strategies for
meeting individual needs.
CC21
3
POINTS OF INTERSECTION When you graph a system of equations, the graphs
intersect at each solution of the system. For a system consisting of a linear
equation and a quadratic equation the number of intersections, and therefore
solutions, can be zero, one, or two.
TEACH
For Your Notebook
Extra Example 1
KEY CONCEPT
Solve the following system using
the substitution method.
y 5 23x 1 4
y 5 x 2 2 4x 1 2 (21, 7) and (2, 22)
Systems With One Linear Equation and One Quadratic Equation
There are three possibilities for the number of points of intersection.
y
Extra Example 2
2
Solve the following system using a
graphing calculator.
y 2 x 5 21
y 5 2x 2 1 1 (22, 23) and (1, 0)
y
y
1
x
1
No Solution
1
x
1
1
One Solution
x
Two Solutions
Key Question to Ask for
Example 2
•
EXAMPLE 2
Why is it important to check your
solutions? It is important to
check the solutions to make
sure you have done everything
correctly. For instance, the
Trace function of the graphing
calculator does not always give
you the best answer. You also
may have entered one or both of
your equations into your graphing
calculator incorrectly leading to
incorrect answers.
Use a graphing calculator to solve a system
Solve the system:
y 5 2x 2 4
y 5 x2 2 4x 1 1
Equation 1
Equation 2
Solution
STEP 1 Enter each equation into your graphing calculator.
Set Y1 5 2x 2 4 and Y2 5 x2 2 4x 1 1.
STEP 2 Graph the system. Set a good viewing window. For this system, a
good window is 210 # x # 10 and 210 # y # 10.
STEP 3 Use the Trace function to find the coordinates of each point of
intersection. The points of intersection are (1, 22) and (5, 6).
Graphing Calculator
In Example 2, students can also
use the Intersect function of the
graphing calculator when finding
the intersection points of the
system. While the points of
intersection of a system are not
always integers, the Intersect
function will provide an accurate
answer.
Intersection
X=1
Y=-2
c The solutions are (1, 22) and (5, 6).
CHECK Check the solutions. For example, check (1, 22).
Avoid Common Errors
When solving a system consisting
of a linear function and a quadratic
function using a graphing
calculator, students may forget to
look for a second solution if the
chosen viewing window only
shows one point of intersection.
Emphasize the need to look for a
second point of intersection by
adjusting the viewing window until
they can clearly establish whether
a second point of intersection
exists.
CC22
Intersection
X=5
Y=6
CC22
y 5 2x 2 4
y 5 x 2 2 4x 1 1
22 0 2(1) 2 4
22 0 (1)2 2 4(1) 1 1
22 5 22 ✓
22 5 22 ✓
Chapter 10 Quadratic Equations and Functions
LA1_CCESE612355_10-7A_EXPO.indd 22
12/10/10 4
✓
GUIDED PRACTICE
for Examples 1 and 2
Solve the system of equations first by using the substitution method and
then by using a graphing calculator.
1. y 5 x 1 4 (21, 3) and (3, 7) 2. y 5 x 1 1 (0, 1) and (5, 6)
y 5 2x2 2 3x 2 2
Extra Example 3
3. y 5 x2 2 6x 1 11
y 5 2x2 1 6x 1 1
y5x11
(2, 3) and (5, 6)
SOLVING EQUATIONS You can use a graph to solve an equation in one variable.
Treat each side of the equation as a function. Then graph each function on the
same coordinate plane. The x-value of any points of intersection will be the
solutions of the equation
Solve the equation 22x 2 1 x 1 1 5
5x 1 1 using a system of equations.
Check your solution(s). (22, 29)
and (0, 1)
Key Question to Ask for
Example 3
•
EXAMPLE 3
Solve an equation using a system
Solve the equation 2x 2 2 4x 1 2 5 22x 2 1 using a system of equations.
Check your solution(s).
Solution
STEP 1 Write a system of two equations by setting both the left and right
sides of the given equation each equal to y.
2x 2 2 4x 1 2 5 22x 2 1
AVOID ERRORS
If you draw your graph
on graph paper, be very
neat so that you can
accurately identify any
points of intersection.
y 5 2x 2 2 4x 1 2
Equation 1
y 5 22x 2 1
Equation 2
STEP 2 Graph Equation 1 and Equation 2
on the same coordinate plane or
on a graphing calculator.
STEP 3 The x-value of each point of
intersection is a solution of the
original equation. The graphs
intersect at (23, 5) and (1, 23).
Teaching Strategy
c The solutions of the equation are x 5 23
and x 5 1.
In Step 3 of Example 3, stress the
fact that the x-values of the points
of intersection are solutions of the
equation, not the two points of
intersection as in Examples 1
and 2.
CHECK: Substitute each solution in the original equation.
2x 2 2 4x 1 2 5 22x 2 1
2(23) 2 2 4(23) 1 2 0 22(23) 2 1
2x 2 2 4x 1 2 5 22x 2 1
2(1) 2 2 4(1) 1 2 0 22(1) 2 1
29 1 12 1 2 0 6 2 1
21 2 4 1 2 0 22 2 1
555✓
✓
GUIDED PRACTICE
In Step 3 of Example 3 you are
instructed to graph the equations
on the same coordinate plane or
on a graphing calculator. For this
system, both methods will lead to
the same solution provided you
are careful when graphing by
hand. Explain why this may not
always be the case? The
solutions to this system involve
integer coordinates. If the two
equations are carefully graphed
using paper and pencil the
solutions should be clearly
identifiable. However, many
systems have solutions that do
not have integer coordinates.
Graphing such a system using
paper and pencil will likely
not yield answers that are as
accurate as those found using
a graphing calculator.
Reading Strategy
23 5 23 ✓
for Example 3
Solve the equation using a system of equations.
4. x 1 3 5 2x2 1 3x 2 1 x 5 22 and x 5 1
5. x2 1 7x 1 4 5 2x 1 4 x 5 25 and x 5 0
6. 8 5 x2 2 4x 1 3 x 5 21 and x 5 5
7. 2x 1 4 5 3x x 5 1
10.7A Solve Systems with Quadratic Equations
While discussing Example 3, point
out that both of the potential
solutions are checked in the
original equation. Stress that
checking only one of the potential
solutions is not sufficient.
CC23
Differentiated Instruction
Kinesthetic Learners Have students work in groups to
verify each of the examples in this lesson using their own
graphing calculator. This active involvement will help students
who learn best by interacting with the content.
See also the Differentiated Instruction Resources for more
strategies.
ESE612355_10-7A_EXPO.indd 23
12/14/10 9:48:49 PM
CC23
EXAMPLE 4
Solve a multi-step problem
BASEBALL During practice, you hit a baseball
toward the gym, which is 240 feet away.
After being kicked, the height of a
football in feet can be modeled by
the equation y 5 216x 2 1 70x 1 3,
where y is the height of the ball
above the playing field x seconds
after being kicked. Suppose a large
scoreboard hangs over the field at
a height of 70 feet. The bottom
edge of the scoreboard can be
modeled by the equation y 5 70.
Does the football go high enough
to hit the scoreboard on its way
up? If so, how long after being
kicked does it reach a height of
70 feet? yes; about 1.4 sec
The path of the baseball after it is hit can be
modeled by the equation:
y 5 20.004x2 1 x 1 3
The roof of the gym can be modeled by the
equation:
2
y5}
x 2 120
3
for values of x greater than 240 feet and less than 320 feet.
The wall of the gym can be modeled by the equation:
x 5 240
for values of y between 0 feet and 40 feet.
Does the baseball hit the roof of gym?
Solution
Closing the Lesson
Have students summarize the
major points of the lesson and
answer the Essential Question:
How do you solve a system of
equations that includes a quadratic
equation?
• A system with one linear
equation and one quadratic
equation can have one, two,
or no solutions.
• An equation in one variable can
be solved using a system of two
equations, created by setting
each side of the equation equal
to y .
To solve a system with one linear
equation and one quadratic
equation, the substitution method
or a graphing calculator can be
used. Using the substitution
method, one of the equations is
solved for one of the variables
and the resulting expression is
substituted into the second
equation. That equation is then
solved for the remaining variable.
The known value is then
substituted into either of the
original equations to find the value
of the other variable. To use a
graphing calculator to solve the
system, solve each of the
equations for the variable y . Graph
both equations and use the Trace
or Intersect function to find the
point(s) of intersection.
CC24
© Tetra Images/Alamy
Extra Example 4
STEP 1 Write a system of two equations for the baseball and the roof.
y 5 20.004x2 1 x 1 3
Equation 1 (baseball)
2
y5}
x 2 120
3
Equation 2 (roof)
STEP 2 Graph both equations on the same coordinate plane.
y
ball’s path
60
roof
40
20
O
wall
20
40
60
80
100
120
140
160
180
200
220
x
240
STEP 3 The x-value where the graphs intersect is between 200 feet and
230 feet which is outside the domain of the equation for the roof.
c The baseball does not hit the roof.
✓
GUIDED PRACTICE
for Example 4
8. WHAT IF? In Example 4, does the baseball hit the gym wall? If it does,
how far up the wall does it hit? If it does not, how far away from the gym
wall does the ball land?
Yes, the baseball will hit the gym wall at a height of 12.6 feet.
9. WHAT IF? In Example 4, if you hit the ball so that it followed a path that
had a smaller number as the coefficient of x2, would it be more or less
likely to hit the gym? Explain. Less; try graphing an equation with a smaller
value such as 20.005. Then the ball does not reach as high or travel as far.
CC24
Chapter 10 Quadratic Equations and Functions
LA1_CCESE612355_10-7A_EXPO.indd 24
12/10/10 4
10.7A
EXERCISES
HOMEWORK
KEY
5 WORKED-OUT SOLUTIONS
for Exs. 5, 15, 19, and 23
★ 5 STANDARDIZED TEST PRACTICE
Exs. 2, 11, 28, and 35
SKILL PRACTICE
A
1. VOCABULARY Describe how to use the substitution method to solve a
2.
EXAMPLE 1
on p. CC21
for Exs. 3–8
4
system of linear equations. See margin.
Assignment Guide
★
y 5 3x2 2 6x 1 4
Equation 1
y54
Equation 2
y 5 3(4) 2 2 6(4) 1 4
Substitute.
Basic:
Day 1: pp. CC25–CC27
Exs. 1–4, 13–27 odd, 34, 36, 38,
41–44
Average:
Day 1: pp. CC25–CC27
Exs. 1–9 odd, 10–12, 14–20 even,
22–30, 35–38, 41–44
Advanced:
Day 1: pp. CC25–CC27
Exs. 2, 6, 8, 13–17 odd, 18–28 even,
31–33, 35, 37, 39–44
Block:
Day 1: pp. CC25–CC27
Exs. 1–9 odd, 10–12, 14–20 even,
22–30, 35–38, 41–44
y 5 3(16) 2 24 1 4 5 28
Simplify
Differentiated Instruction
WRITING Describe the possible number of solutions for a system
consisting of a linear equation and a quadratic equation.
The system could have two solutions, one solution, or no solutions.
SUBSTITUTION METHOD Solve the system of equations using the
substitution method.
3. y 5 x2 2 x 1 2
4. y 5 2x2 1 4x 2 2
y 5 x 1 5 (21, 4) and (3, 8)
5. y 5 x2 2 x
y 5 4x 2 6 (22, 214) and (2, 2)
6. y 5 2x2 1 x 2 1
7. y 5 3x2 2 6
y 5 2x 2 3 no solution
5
y 5 2}
x11
2
(22, 6) and 1 }1 , 2}1 2
8. y 5 22x2 2 2x 1 3
2
4
7
y5}
21 , 7
2 1 } }2
y 5 23x (22, 6) and (1, 23)
2 2
9. ERROR ANALYSIS Describe and correct the error in the solution steps
shown. The student substituted incorrectly. Substitute 4 for y and then the solutions are (0, 4)
and (2, 4).
equation and a quadratic equation, there will (always, sometimes, never)
be an infinite number of solutions. never
See Differentiated Instruction
Resources for suggestions on
addressing the needs of a diverse
classroom.
★
Homework Check
10. COPY AND COMPLETE When a system of equations includes a linear
11.
EXAMPLE 2 B
on p. CC22
for Exs. 12–17
MULTIPLE CHOICE Which equation intersects the graph of
y 5 x2 2 4x 1 3 twice? C
A y 5 21
B x52
C y115x
D y 1 x 5 21
12. y 5 3x2 2 2x 1 1
1 2
15. y 5 }
x 2 3x 1 4
2
y 5 x 2 2 (2, 0) and (6, 4)
on p. CC23
for Exs. 18–21
ESE612355_10-7A_EXE.indd CC25
For a quick check of student
understanding of key concepts,
go over the following exercises.
Basic: 3, 13, 19, 23, 34
Average: 7, 16, 24, 29, 36
Advanced: 5, 17, 24, 32, 35
GRAPHING CALCULATOR Use a graphing calculator to find the points of
intersection, if any, of the graph of the system of equations.
y 5 x 1 7 (21, 6) and (2, 9)
EXAMPLE 3
PRACTICE
AND APPLY
13. y 5 x2 1 2x 1 11
(21, 10) and
y 5 22x 1 8
(23, 14)
1 2
16. y 5 }
x 1 2x 2 3
3
14. y 5 22x2 2 4x
Extra Practice
y 5 2 (21, 2)
•
Practice B in Chapter Resources
2
17. y 5 4x 1 5x 2 7
y 5 23x 1 5
(23, 14) and (1, 2)
SOLVE THE EQUATION Solve the equation using a system. Check each answer.
y 5 2x (23, 26) and (3, 6)
18. 25x 1 5 5 x2 2 4x 1 3 22 and 1
19. 26 5 x2 1 2x 2 5 21
20. 23 5 x2 1 5x 2 3 25 and 0
21. 2x2 1 4x 5 2x 1 4 1 and 22
10.7A Solve Systems with Quadratic Equations
CC25
1. First solve one of the equations
for a variable. Then substitute that
expression for the variable in the
other equation. Solve the resulting
equation in one variable. Use that
solution to substitute into one of
the original equations to find the
value of the other variable.
12/10/10 4:10:35 AM
CC25
GRAPHING CALCULATOR Use a graphing calculator to find the points of
intersection, if any, of the graph of the system of equations.
Graphing Calculator
22. y 5 2x2 1 4 no solution
Exercise 27 Students may think
that this system has only one point
of intersection. Suggest they take a
closer look using the ZBox function
found in the ZOOM menu. They may
have to apply the ZBox function
multiple times before they can see
both points of intersection.
23. y 5 21
y55
y 5 22
25. y 5 2x2 1 2x no solution
24. y 5 x 1 6 (22, 4)
(0, 21)
x
y 5 0.5x
26. y 5 3x 2 1 (1, 2) and (3, 8)
27. y 5 21.5x 1 1 (21, 2.5), (0, 1)
y 5 2x
y 5 22x 1 5
y 5 0.4x
★ WRITING Describe the possible number of solutions for a system
consisting of a quadratic equation and an exponential equation.
The system of equations could have two solutions, one solution, or no solutions.
SOLVE THE EQUATION Solve the equation using a system.
28.
Teaching Strategy
29. 2x 1 1 5 2x 1 1
Exercise 33 Initiate a discussion
about how many points of
intersection are possible when a
system consists of two quadratic
equations. To help students
visualize the possibilities, suggest
that they look back at the Key
Concept box above Example 2.
Have students draw figures
representing all of the possibilities.
31. 22x 1 11 5 2x 2 3 3
C
2
30. 4x 5 2 } x 1 9 1.5
3
1 and 2
32. 3x 2 5 5 6x 2 8 2 and 1
33. CHALLENGE Using a graphing calculator, find the points of
intersection, if any, of the graphs of the equations y 5 x2 2 3x 1 1 and
y 5 x2 2 x 2 1. What are the solutions of the system? (1, 21)
PROBLEM SOLVING
EXAMPLES A
1 AND 2
34. RECREATION Marion and Reggie are driving boats on the same lake.
Marion’s chosen path can be modeled by the equation y 5 2x2 2 4x 2 1
and Reggie’s path can be modeled by the equation y 5 2x 1 8. Do their
paths cross each other? If so, what are the coordinates of the point(s)
where the paths meet? yes; (23, 2)
on p. CC21–22
for Exs. 34–36
★
SHORT RESPONSE Two dogs are running in a fenced dog park. One
dog is following a path that can be modeled by the equation y 5 4.
Another dog is following a path that can be modeled by the equation
y 5 2x2 1 3. Will the dogs’ paths cross? Explain your answer.
No; Sample answer: The graphs of the equations that model the paths do not intersect, so the dogs’
36. ARCHITECTURE The arch of the Sydney Harbor Bridge in Sydney, paths will not cross.
Australia, can be modeled by y 5 20.00211x2 1 1.06x where x is the
distance (in meters) from the left pylons and y is the height (in meters)
of the arch above the water. The road can be modeled by the equation
y 5 52. To the nearest meter, how far from the left pylons are the two
points where the road intersects the arch of the bridge? 55 meters and 447 meters
35.
y
© Ron Chapple Stock/Alamy
y 5 52
5 WORKED-OUT SOLUTIONS
CC26 Chapter 1 Expressions,
Equations,
for Exs. 5, 15,
19, and 23and Functions
★ 5 STANDARDIZED
TEST PRACTICE
Differentiated Instruction
English Language Learners For Exercises 34–38, consider
pairing any English Language Learners with students who are
proficient in English. While ELL students may understand the
necessary mathematics, they may find it difficult to decode
these word problems and identify the information needed to
answer the questions being asked.
See also the Differentiated Instruction Resources for more
strategies.
LA1_CCESE612355_10-7A_EXE.indd CC26
CC26
12/14/10 11
EXAMPLES B
3 AND 4
on p. CC22–24
for Exs. 37–39
37. The graphs
intersect when
the two girls
have the same
amount of money
saved. Miranda
has more money
saved for the
first 20 months,
and then again
after 104 months,
because the
graphs intersect
near x 5 20 and
x 5 104.
37. SAVINGS Nancy and Miranda are looking at different ways to save
money. Graph the two equations. Explain what happens when the graphs
intersect. When will Miranda have more money saved than Nancy?
Nancy
Miranda
I will save $15 each month.
My money will not earn interest.
I will put $200 into an account
that earns 2% annually. I will not
save any more money.
A model for my savings is y 5 15x.
5
Daily Homework Quiz
If the interest is compounded monthly,
y 5 200(1.02) x models my savings.
x is the number of months
y is my total savings
x is months and y is my total savings.
38. SPACE Suppose an asteroid and a piece of space debris are traveling in
the same plane in space. The asteroid follows a path that can be modeled
locally by the equation y 5 2x2 2 3x 1 1. The space debris follows a path
that can be modeled locally by the equation y 5 8x 2 13.
a. Will the paths of the two objects intersect? Is it possible for the two
objects to collide? If so, what are the coordinates of the point where
the paths intersect? yes; yes; (2, 3), (3.5, 15)
b. What additional information would you need to decide whether the
two objects will collide? Explain. In order to know whether the two objects will collide
you would need to know their positions at the same time and their speeds.
39. MULTI-STEP PROBLEM Keno asks Miguel if the graphs of all three of the
equations shown below ever intersect in a single point.
y 5 3x 1 1
y 5 2x2 2 4x 1 6
y 5 22x 1 6
a. Find any points of intersection of the graphs of y 5 3x 1 1 and
• Practice B in Chapter Resources
• Study Guide in Chapter
Resources
b. Find any points of intersection of the graphs of y 5 3x 1 1 and
y 5 22x 1 6. (1, 4)
c. Find any points of intersection of the graphs y 5 2x2 2 4x 1 6 and
y 5 22x 1 6. (0, 6) and (1, 4)
Challenge
d. Do the three graphs ever intersect in a single point? If so, what are
C
Solve the system of equations
using the substitution method.
1. y 5 x 2 2 2x 1 2
y 5 23x 1 4 (22, 10), (1, 1)
2. y 5 2x 2 1 6
y 5 2x 1 4 (21, 5), (2, 2)
Use a graphing calculator to find
the points of intersection, if any,
of the graph of the system of
equations.
3. y 5 2x 2 1 x 1 1
y 5 22x 1 1 (0, 1), (3, 25)
4. y 5 2x 2 1 9
y 5 4x 1 14 no solution
5. Solve the equation 3x 2 1 2x 5
27x 2 6 using a system. x 5 22
and x 5 21
Diagnosis/Remediation
y 5 2x2 2 4x 1 6. (1, 4) and (2.5, 8.5)
the coordinates of this point of intersection?
ASSESS AND
RETEACH
Additional challenge is available in
the Chapter Resources.
yes; (1, 4)
40. CHALLENGE Find the point(s) of intersection, if any, for the line with
equation y 5 2x 2 1 and the circle with equation x2 1 y 2 5 41. (25, 4) and (4, 25)
MIXED REVIEW
PREVIEW
Prepare for
Lesson 10.8 in
Exs. 41–43.
ESE612355_10-7A_EXE.indd CC27
Determine if the set of ordered pairs represents a function. (Lesson 1.6)
41. (22, 3), (3, 1), (22, 5)
42. (4, 1), (27, 1), (0.5, 1)
43. (3, 22), (3, 0.7), (3, 6)
not a function
function
not a function
44. John’s family is holding a garage sale and he needs to make a sign. His
dad gives him a piece of cardboard to use that is (2x 2 5) inches long and
(3x 1 2) inches wide. Write a quadratic expression in standard form that
represents the area of the piece of cardboard. (Lesson 9.2)
(6x2 2 11x 2 10) square inches
10.7A Solve Systems with Quadratic Equations
CC27
12/22/10 12:53:34 AM
CC27
1
10.8A
PLAN AND
PREPARE
Before
Warm-Up Exercises
You studied linear, exponential, and quadratic functions.
Now
You will compare representations of these functions.
Why
So you can model the height of water, as in Example 1.
Sometimes you will find it helpful to model a function with a graph even
if you don’t have enough information to write an equation to model the
function.
Key Vocabulary
• Verbal Model
• Slope
• Vertex
Sketching a graph based on a description of a situation can help you
understand the situation and identify key features of the model.
EXAMPLE 1
Pacing
Sketch a graph of a real-world situation
FIRE-FIGHTING The water from one water cannon on a fire-fighting
boat reaches a maximum height of 25 feet and travels a horizontal
distance of about 140 feet.
Basic: 1 day
Average: 1 day
Advanced: 1 day
Block: 0.5 block
2
© George Hall/Corbis
Find the slope of the line that
passes through the points.
1. (23, 210) and (2, 5) 3
2. (4, 23) and (4, 2) undefined
slope
Identify the slope of the line and
indicate whether the line rises or
falls from left to right.
3. y 5 26x 1 3 26; falls
4. 22y 1 8x 5 9 4; rises
Model
Relationships
a. What type of function should you use to represent the path of the
water? Sketch a graph of the path of the water.
b. In the context of the given situation, what do the intercepts and
FOCUS AND
MOTIVATE
maximum point represent?
Solution
Essential Question
a. The path of the water can be modeled by a parabola. Let x represent the
horizontal distance in feet and let y represent the vertical distance in feet.
Big Idea 3, p. 627
How can you identify key features
of linear, exponential, and quadratic
functions when they are modeled in
different ways? Tell students they
will learn how to answer this
question by using their previous
experiences in algebra class when
they studied linear, exponential,
and quadratic functions.
1. The function is
increasing as x
increases from 0 to
about 70. This is when
the water is moving
upward until it reaches
its maximum height. The
function is decreasing
as x increases from
about 70 to about 140.
This is when the water
is traveling downward
until it reaches the
surface of the water that
the boat is on.
Motivating the Lesson
Explain to students that when a
decision needs to be made, people
often gather data and analyze it to
make an informed decision. The
data they collect may be modeled
in a variety of different ways, but
they need to be able to compare
and contrast these models.
✓
25
y
0
25
50
75
100
125
x
b. Because the water cannon is on a boat, the graph has only one x-intercept
where the water reaches the surface of the water or ground. The
maximum point of the graph is where the water reaches its maximum
height, about 70 feet from the boat.
GUIDED PRACTICE
for Example 1
1. Using the graph in Example 1, describe the intervals in which the function
is increasing and decreasing. Explain what the intervals mean in the given
situation.
CC28
Chapter 10 Quadratic Equations and Functions
Resource Planning Guide
Ch t Resource
Chapter
R
• Practice level B
• Study Guide
• Challenge
• Pre-AP notes
CC28
Teaching
T
h
Options
• Activity Generator provides
editable activities for all ability
levels
LA1_CCESE612355_10-8A_EXPO.indd 28
Interactive Technology
• Activity Generator
• Animated Algebra
• Test Generator
• eEdition
See also the Differentiated Instruction
Resources for more strategies for
meeting individual needs.
12/23/10 4:
EXAMPLE 2
Compare properties of two linear functions
Decide which linear function is increasing at a greater rate.
•
Linear Function 1 has an x-intercept of 4 and a y-intercept of 22.
•
Linear Function 2 includes the points in the table below.
x
22
21
0
1
2
3
y
211
26
21
4
9
14
3
Extra Example 1
Ali is competing in a 10-meter
diving event. When he dives, he
reaches a maximum height of
12 meters and travels a horizontal
distance of about 3.4 meters
before he hits the water.
a. What type of function should
you use to represent the path
of Ali’s dive? Sketch a graph of
the path. parabola;
Solution
AVOID ERRORS
In calculating the slope
of a linear function,
remember to divide
the change in y by the
change in x.
The slope of a linear equation indicates how rapidly a linear function is
increasing or decreasing. The points (4, 0) and (0, 22) are on the graph of
0 2 (22)
420
1
Linear Function 1, so its slope is } 5 }
.
2
The table for Linear Function 2 shows that for each increase of 1 in the value
5
of x there is an increase of 5 in the value of y, so its slope is }
5 5.
1
y
c Linear Function 2 is increasing more rapidly.
EXAMPLE 3
2. The rate of change of
y 5 4x 1 5 is 4. The rate
of change of
y 5 3 2 4x is 24.
The first function is
increasing at the same
rate that the second
function is decreasing.
8
6
4
2
Use the given information to decide which
quadratic function has the lesser minimum value.
Quadratic Function 1: The function whose
equation is y 5 3x2 2 12x 1 1.
•
Quadratic Function 2: The function whose
graph is shown at the right.
y
O
2
Review the lesson Graph
y 5 ax2 1 bx 1 c for
information on finding
the coordinates of the
minimum value of a
quadratic function.
3. The minimum value of
Quadratic Function
1 is now 216. As seen in
the graph of
Quadratic
Function 2, its minimum
value is 29. Quadratic
Function 1 again has the
lesser minimum value.
✓
The minimum value of Quadratic Function 1 is the y-value of the vertex of
b
212
12
its parabola. The x-coordinate of the vertex is 2 }
5 2}
5}
5 2. When
2a
1 2
2(3)
2
3
4 x
Extra Example 2
6
x 5 2, y 5 3(2)2 2 12(2) 1 1 5 12 2 24 1 1 = 211. So the vertex is (2, 211) and
the minimum value is 2 11.
The minimum value of Quadratic Function 2 can be seen on the graph of the
function; it is 29.
Decide which linear function is
decreasing at a greater rate.
• Linear Function 1 has a
y-intercept of 2 and a slope of 23.
• Linear Function 2 has the equation
y 5 24x 2 7. Linear Function 2
c Quadratic Function 1 has the lesser minimum value.
GUIDED PRACTICE
1
b. In the context of the given
situation, what do the intercepts
represent? The y -intercept
represents Ali on the 10-meter
diving board. The x-intercept is
the point where Ali enters the
water after traveling a horizontal
distance of 3.4 meters.
x
1
Solution
STUDY HELP
ESE612355_10-8A_EXPO.indd 29
12
10
Compare properties of two quadratic functions
•
TEACH
Extra Example 3
for Examples 2 and 3
2. COMPARE Compare the rates of change in the linear functions y 5 4x 1 5
and y 5 3 2 4x.
3. WHAT IF? In Example 3, replace the equation for Quadratic Function 1 with
y 5 x2 2 6x 2 7. Which function now has the lesser minimum value?
10.8A Model Relationships
CC29
Use the given information to decide
which quadratic function has the
greater maximum value.
• Quadratic Function 1: The
function whose equation is
y 5 2x 2 1 4x 1 1.
• Quadratic Function 2: The
function whose graph is
shown below.
12/14/10 9:53:47 PM
4
3
2
1
22 21 O
21
22
23
y
1
2
3
Quadratic Function 1
4 x
CC29
EXAMPLE 4
Choose a model for a real-world situation
BUSINESS The table shows the revenue generated by a company during each
of the previous five years. Based on the change per unit interval, choose an
appropriate type of function to model the situation.
Extra Example 4
Based on the change per unit
interval, choose an appropriate
function to model the situation.
Year
Revenue ($)
2008
2009
2010
2011
2012
50,000
51,500
53,045
54,636
56,275
Year
Value ($)
2008
288,000
Solution
2009
276,480
2010
265,421
The revenue is increasing each year by about 3%. Because the quantity grows
by a constant percent rate per unit interval, you should use an exponential
growth model for the situation.
2011
254,804
2012
244,612
exponential
decay model
EXAMPLE 5
Extra Example 5
FURNITURE You are a furniture salesperson and earn $200 a week
plus a 5% commission on the total value of all sales you make during
the week.
a. Based on the given information, choose an appropriate type of function
to model your potential weekly earnings as a function of sales.
b. Sketch a graph representing your potential earnings for any given week
as a function of sales. Identify the function’s intercept(s) and interpret
the meaning of each intercept in the context of the given situation.
Solution
a. For every $100 of sales, your earnings
STUDY HELP
Remember that the
graph of a real-world
function does not
necessarily have both
an x-intercept and a
y-intercept.
✓
Closing the Lesson
Have students summarize the
major points of the lesson and
answer the Essential Question:
How can you identify key features
of linear, exponential, and
quadratic functions when they
are modeled in different ways?
Students should recognize that
it is possible to extract the key
information from each of the
possible data models. When
comparing two models, students
should look for the characteristics
in each model that allow them to
decipher the information they
need.
CC30
Furniture Sales
increase by $5. Earnings are increasing by
a constant rate. Use a linear function.
b. Let x represent the weekly sales and let y
represent total earnings. The y-intercept
is 200 and represents your weekly salary
when you do not sell any furniture during
that week. The function only makes sense
for x $ 0, so there is no x-intercept.
GUIDED PRACTICE
Earnings ($)
The Wildlife Adventure Club is
planning a safari to Africa. At the
beginning of the safari, they will
have 210 pounds of food. They
anticipate that each day they will
reduce the weight of the food
being carried by 10 pounds.
a. Based on the given information,
choose an appropriate function
to model the amount of food
being carried as the safari
progresses. linear function
b. Identify the function’s
intercept(s) and interpret the
meaning of each in the context
of the given situation? The
y -intercept, 210, represents the
amount of food on the day the
safari begins. The x-intercept,
21, represents the day the club
runs out of food.
Choose a model for a real-world situation
y
500
400
300
200
100
0
0 1000 3000 5000 x
Sales ($)
for Examples 4 and 5
4. RUNNING The table shows the distance that Juan covered per hour in the first
four hours of a triathlon. Based on the change per unit interval, choose an
appropriate function to model the situation. The distance Juan travels per hour is
decreasing by a constant percent rate
per unit interval of time. The decay
Hour
1
2
3
4
rate is 10%. The best function to model
Miles
6
5.4
4.86
4.374
this situation is an exponential decay
model.
CC30
Chapter 10 Quadratic Equations and Functions
Differentiated Instruction
English Language Learners In Example 5, some students
may not be familiar with the idea of earning a commission on
sales. Take the time to explain that in some jobs employees not
only earn an hourly wage but are also rewarded for the sales
they make. Point out that commissions are usually a percentage
of the employee’s sales for a specific time period, such as a
week or month.
See also the Differentiated Instruction Resources for more
strategies.
LA1_CCESE612355_10-8A_EXPO.indd 30
12/10/10 4
EXERCISES
10.8A
3c. The function
is increasing
throughout
its domain, SKILL
x $ 0. As the
time since
A
1.
it resumed
its ascent
increases,
the altitude
2.
of the balloon
increases.
3.
EXAMPLE 1
on p. CC28
for Exs. 3–5
HOMEWORK
KEY
5 WORKED-OUT SOLUTIONS
for Exs. 3, 5, 11, and 15
★ 5 STANDARDIZED TEST PRACTICE
4
Exs. 2, 6, 11, 18, and 19
PRACTICE
2. A linear function
VOCABULARY Copy and complete: A
describes a real-world
situation using words as labels and using math symbols to relate the with a positive slope
is an increasing
words. verbal model
function. A linear
★ WRITING Explain the relationship between the slope of a linear function with a
function and the concept of an increasing/decreasing linear function.negative slope is a
decreasing function.
CHOOSE A MODEL A hot air balloon has already
risen 20 feet above the ground. At this point in
time it begins to rise at a steady rate of 2 feet
per second.
a. What type of function would be a good
b. Sketch a graph representing the balloon’s
altitude y in terms of the time x since it
resumed its ascent. See margin.
4c. The
x-intercept and
the y-intercept
are both 0.
The intercepts
represent the
fact that before
he starts riding
his motorcycle
Neil has not left
his starting point.
c. Identify the intervals on which the graph is
increasing or decreasing and explain what these
intervals mean in the context of the situation.
a. What type of function would be a good model for this situation? linear
b. Sketch a graph representing the distance he will travel y in terms of
the number of hours x that he rides. See margin.
275
5. CHOOSE A MODEL A juggler throws a ball into the air. It reaches a
maximum height of about 25 feet, and the juggler catches it again after
2.5 seconds.
a. What type of function would be a good model for this situation? quadratic
b. Sketch the graph of an equation that could model the height of the ball
Extra Practice
as a function of time. See margin.
• Practice B in Chapter Resources
c. Identify the intervals on which the graph is increasing or decreasing
3b.
and explain what these intervals mean in the context of the situation.
★ MULTIPLE CHOICE Marvin is making a rectangular quilt. Suppose the
30
width of the quilt is x meters and length of the quilt is (3 2 x) meters.
Which type of function should you use to model the area y of the quilt in
terms of its width? B
28
A linear
B quadratic
C exponential growth
D exponential decay
Neils’ Motorcycle Ride
5b.
220
165
110
26
24
22
20
0
0
1
2
3
4
Time (seconds)
5
12/15/10 12:38:56 AM
20
10
0
55
CC31
Balloon’s Height
30
Height (feet)
Miles Traveled
For a quick check of student
understanding of key concepts, go
over the following exercises.
Basic: 3, 6, 9, 13, 14
Average: 3, 5, 10, 13, 17
Advanced: 4, 8, 11, 16, 19
each intercept in the context of the situation.
ESE612355_10-8A_EXE.indd Sec1:31
0
Homework Check
c. Use the graph to identify the intercept(s) and interpret the meaning of
10.8A Model Relationships
4b
See Differentiated Instruction
Resources for suggestions on
addressing the needs of a diverse
classroom.
plans to average 55 miles per hour.
6.
Basic:
Day 1: pp. CC31–CC34
Exs. 1–3, 6, 7, 9, 13–15, 21–26
Average:
Day 1: pp. CC31–CC34
Exs. 1–3, 5, 7, 10, 11, 13, 17, 18,
21–26
Advanced:
Day 1: pp. CC31–CC34
Exs. 3, 4, 7, 8, 10–12, 14, 16, 18–20,
21–25 odd
Block:
Day 1: pp. CC31–CC34
Exs. 1–3, 5, 7, 10, 11, 13, 17, 18,
21–26
Differentiated Instruction
4. CHOOSE A MODEL During a weekend trip riding his motorcycle, Neil
5c. The graph is
increasing from
x 5 0 to about x
5 1.25. This is
the time during
which the ball is
traveling upward
until it reaches
its maximum
height at about
1.25 seconds.
The graph is
decreasing
from about x 5
1.25 to x 5 2.5.
This is the time
during which the
ball is traveling
downward
until the juggler
catches it at 2.5
seconds.
Assignment Guide
Height (ft)
© Wes Thompson/Corbis
model for this situation? linear
PRACTICE
AND APPLY
0
1
2
3
4
5
Time (seconds)
0
1
2
3
Hours
4
5
CC31
ERROR ANALYSIS In Exercises 7 and 8, describe and correct the error in the model.
7. A student uses a quadratic function to model a population that is
Teaching Strategy
Exercise 9 Some students may be
confused as to how to determine
which function is decreasing more
rapidly. Consider revisiting the
concept of slope. Provide students
with the equations of two or more
lines. Have them determine the
slope of each line. Then graph
the lines and draw a comparison
between the numerical slopes
of each line and their visual
representation.
EXAMPLES B
2 and 3
on p. CC29
for Exs. 9–10
increasing by 4% per year. A function that increases by a constant percent should be
modeled by an exponential growth function.
8. A student uses an exponential decay function to model the distance
traveled over time of a car traveling at a steady speed of 50 miles per hour.
A function that increases by a constant amount should be modeled by a linear function.
9. LINEAR FUNCTIONS Use the given information to decide which linear
function is decreasing more rapidly. The slope of Linear Function 1 is 21 while the
slope of Linear Function 2 is 22. So Linear Function 2 is decreasing more rapidly.
• Linear Function 1 has a y-intercept of 23 and a slope of 21.
• The table shows the coordinates of six points found on the line
representing Linear Function 2.
x
24
22
0
2
4
6
y
8
4
0
24
28
212
10. QUADRATIC FUNCTIONS Use the given information
Reading Strategy
2
to decide which quadratic function has the greater
maximum value.
Exercise 11 Point out that
students are asked to decide
which relationship grows by a
constant percent rate per unit
interval. Suggest that a careful
examination of the tables of data
can lead to the elimination of
those choices that do not model
growth over time. Students should
recognize that choices B and D
both model decay, and therefore
they can be eliminated from
consideration.
y
1
x
• Quadratic Function 1: The function whose
equation is y 5 2x2 1 4x 1 2.
• Quadratic Function 2: The function whose graph
is shown at the right.
EXAMPLES
4 and 5
11.
on p. CC30
for Exs. 11–12
★ MULTIPLE CHOICE Decide which relationship grows by
a constant percent rate per unit interval. C
A
B
Hours
1
2
3
4
Miles
5
10
15
20
Year
Revenue ($)
C
D
C
1
2
3
4
2000
1500
1125
843.75
Days
1
2
3
4
Windows Installed
2
4
8
16
Minutes
1
2
3
4
Pancakes Made
27
9
3
1
10. Quadratic
Function 1 has a
maximum value of 6.
Quadratic Function 2
has a maximum value
of 2. So Quadratic
Function 1 has the
greater maximum
value.
12. CHALLENGE In 2010, the United States Census Bureau estimated that
there were approximately 310 million people in the United States. By
some estimates the population is growing by about 0.9% per year.
a. See margin for art;
exponential growth.
represent the year 2010. What type of function will be a good model?
a. Sketch a graph relating the population y at any time x. Let x 5 0
b. Interpret the meaning of the x- and y-intercepts, if they exist, in terms
The y-intercept is 310
which is the population
c. Is the graph of the function increasing or decreasing? Explain. in 2010. There is no
This is an increasing function because the population continues to grow. x-intercept.
of the context of this situation.
5 WORKED-OUT SOLUTIONS
CC32
Chapter 10
Quadratic
Equations
and Functions
for Exs.
2, 5, 11, and
15
U.S. Population (millions)
12a.
TEST PRACTICE
U. S. Population
LA1_CCESE612355_10-8A_EXE.indd Sec1:32
CC32
★ 5 STANDARDIZED
y
400
375
350
325
300
0
0 1 2 3 4 5 6 7 8 9 x
Time Since 2010 (yr)
12/10/10 4
PROBLEM SOLVING
on p. CC27
for Exs. 13–15
14. Tim’s ball
reached a height
of 30 feet while
Matt’s ball
reached a height
of approximately
19 feet. Tim
threw the ball B
higher.
13. MUSIC Celia has already downloaded 14 songs to her cell phone. In the
future she intends to download 2 songs per week. Her friend Connie has
already downloaded 12 songs to her cell phone and she plans to download
songs based on the table below. Which girl’s playlist is growing faster?
Connie’s playlist is growing faster.
Week
1
2
3
4
Total Number of Songs
on Connie’s Cell Phone
17
22
27
32
14. BASEBALL Tim threw a baseball in the air.
Avoiding Common Errors
Exercise 14 Students often
mistakenly interpret this type of
graph as representing not just the
height of the ball but also the
distance that the ball was thrown.
The fact that the exercise begins
with the phrasing “Tim threw a
baseball” immediately focuses
some students on the idea of how
far he threw the baseball. Explain
to students that the distance the
ball traveled at any moment in time
is not the same as the height of
the ball at any moment in time.
Stress that the x-axis of this
graph shows the amount of time
(in seconds) that has elapsed since
the ball was thrown, not the
horizontal distance the ball
travels.
Baseball’s Height
Suppose the ball’s height in feet can be
modeled by the equation y 5 216x2 1 40x 1 5.
Matt threw the same baseball in the air. The
graph models the height in feet of Matt’s ball
as a function of time. Which ball reached
a greater height?
Height (ft)
EXAMPLES A
3 and 4
y
20
15
10
5
0
0
1
3 x
2
Time (Sec)
15. SCIENCE Tanya placed mold spores in a Petri dish. The table shows the
number of spores in the dish at the end of each hour. Indicate whether
the number of spores in the Petri dish represents growth, decay, or neither.
Identify the growth or decay rate, if it exists, expressing it as a percent.
1
2
3
4
Number of Spores
16
24
36
54
The number of spores in the Petri
dish represents growth; the
growth rate is 50%.
x
16. CHICKENS You have 100 meters of fencing to build
a chicken pen.
a. Use the diagram to help sketch a graph
50 2 x
representing the area y of the pen in terms
of the width x of the pen. See margin.
b. Use the graph to identify the intercept(s) and
interpret the meaning of each intercept in the
context of the situation.
17. ROWING The table shows the distance in miles that a
rowing crew covered during each 15-minute interval
in the first hour of practice. Based on the change per
unit interval, choose an appropriate function
to model the situation.
Minutes
15
30
45
60
Miles
2
1.6
1.28
1.024
The rowing crew’s distances are decreasing by a
constant percent rate per unit interval of time. The decay
rate is 20%.
10.8A Model Relationships
CC33
Differentiated Instruction
Below Level For Exercises 13 and 14, consider reading each
ESE612355_10-8A_EXE.indd
Sec1:33
problem
aloud in class. Guide students through a series of
questions that leads them to a meaningful conclusion. For
instance, in Exercise 13, students may not recognize the table
modeling Connie’s growing playlist as that of a linear function.
Consider visually modeling each girl’s growing playlist graphically
on the board.
See also the Differentiated Instruction Resources for more
strategies.
16.
Chicken Pen
y
700
Area (sq m)
© Robert Michael/Corbis
16b. There are
no intercepts.
If there was
an x-intercept
there would
be no area.
If there was
y-intercept the
pen would have
no measurable
length or width.
Hour
12/15/10 12:39:17 AM
500
300
100
0
0
10
20 30 40
Width (m)
50 x
CC33
18.
5
ASSESS AND
RETEACH
Daily Homework Quiz
1. Which linear function is
decreasing more rapidly?
Linear Function 2
Linear Function 1: y 5 22x 1 5
Linear Function 2: x-intercept of
2 and y-intercept of 6
2. Which quadratic function has
the greater maximum value?
Quadratic Function 1:
y 5 2x 2 1 16x
Quadratic Function 2:
x-intercepts of 4 and 24, and
vertex at (0, 16) Quadratic
Function 1
3. Mack has already sent 15 text
messages. In the future he
intends to send 5 text messages
per day. Sven has already sent
10 text messages and he plans
to send text messages based
on the table below. Who will
be sending text messages at a
faster rate? Sven
Day
1
2
3
4
Sven’s
Messages
16
22
28
34
4. The table shows the volume
of a melting ice cube (in cubic
centimeters) at the end of
several 10-minute intervals.
Indicate whether the volume
of the remaining ice cube
represents exponential
growth, exponential decay, or
neither. exponential decay
10-Minute
Intervals
0
1
2
3
Volume of
27 24.3 21.9 19.7
Ice Cube
Diagnosis/Remediation
20. Sample
answer: In
the case of the
linear function
y 5 ax 1 b,
successive
range values
increase/
decrease by a
units each time.
In the case of
the exponential
function y 5
a (b) x , the range
values increase/
decrease by a C
factor of b units
each time. For
the family of
linear functions,
successive
range values
increase/
decrease by
the value of the
slope of the
linear function
each time. For
the family of
exponential
functions,
successive
range values
increase/
decrease by
a factor of the
growth/decay
factor of the
C
exponential
function each
time.
★ MULTIPLE CHOICE Choose the situation in which one quantity changes
by a constant amount per unit interval relative to a second quantity. B
A Michael rented tables and chairs for a party. The cost for the rental
was $10 for the first day. If he keeps them for more than one day the
cost per day is double the preceding day.
B Alexi’s stamp collection already contains 12 stamps. Each time he
goes to the post office he will buy 2 stamps to add to his collection.
C Sue has an ant farm. The number of ants can be modeled by the
equation y 5 100(1.05)x, where y is the number of ants on any given
day and x is the number of days since she started the farm.
D Pam accidently dropped her watch from her tree house. The equation
y 5 216x2 1 37 models the height of the watch as it is falling to the
ground. The variable y represents the height of the watch and x
represents the time in seconds since Pam dropped the watch.
19.
★ EXTENDED RESPONSE Use the information to answer each question.
a. Graphs Using a single coordinate system, graph the functions y 5 2x,
y 5 x2, and y 5 2x. Which function eventually has the greatest y-value
for a given value of x? the exponential function y 5 2 x
b. Tables Complete a table similar to the one below for each of the three
given functions. Which function eventually has the greatest y-value for
a given value of x? the exponential function y 5 3 x 1 1
19c.The exponential growth
Linear Function: y 5 3x 1 1
function; because
the y-value increases
Quadratic Function: y 5 3x2 1 1
x
exponentially as x
Exponential Function: y 5 3 1 1
increases, an exponential
growth function will
x
0
2
4
6
8
10
21
eventually exceed both
a linear and a quadratic
y
?
?
?
?
?
?
?
function.
c. Challenge Given any quantity that can be modeled by a linear function,
any quantity that can be modeled by a quadratic function, and any
quantity that can be modeled by an exponential growth function, can you
predict which quantity will eventually exceed the other two? Explain.
20. CHALLENGE Evaluate the functions y 5 ax 1 b and y 5 a(b)x for x equal to
0, 1, 2, 3, 4, and 5. In the case of the linear function, how does the value of
the function change as the x-values increase 1 unit at a time? In the case
of the exponential function how does the value of the function change
as the x-values increase 1 unit at a time? Extend these findings to the
families of linear and exponential functions.
MIXED REVIEW
PREVIEW
Evaluate the expression. (Lesson 2.7)
Prepare for
Lesson 11.1 in
Exs. 21–23
21. Ï 49 7
}
}
22. 2Ï 81 29
}
}
23. 6Ï 200 610Ï 2
Solve the equation. Round your solutions to the nearest hundredth, if
necessary. (Lesson 10.5)
24. 32 5 x2 1 7 65
25. 2q2 2 5 5 62 65.83 26. 3x2 2 25 5 38 64.58
5 WORKED-OUT SOLUTIONS
CC34 Chapter 8 Exponents
Functions
for Exs. 2,and
5, 11,Exponential
and 15
★ 5 STANDARDIZED
TEST PRACTICE
• Practice B in Chapter Resources
• Study Guide in Chapter
Resources
Challenge
Additional challenge is available in
the Chapter Resources.
CC34
LA1_CCESE612355_10-8A_EXE.indd Sec1:34
12/10/10 4
Graphing
Graphing
C
a
alculator
lc ulator
Calculator
ACTIVITY
AC
CTIVITY
Use a
after Lesson 10.8A
10.8B Average Rate off Change
QUESTION
1
What is the average rate of change between two points?
Learn the Method
The average rate of change is useful for some real-world situations, like fi nding
the average growth rate of a tree over a 20-year period. You can use the slope
formula to fi nd the average rate of change between two points on the graph of
a non-linear function.
EXAMPLE
Students will find the average
rate of change between two
points on a graph.
• After the activity, students will
understand rate of change in
nonlinear functions.
•
Find an average rate of change
Find the average rate of change between points on the graph of
y 5 2x 2 2 3x 21. How does the choice of the points impact the
average rate of change?
2
STEP 1 Graph the function
Make sure students recall how to
find the slope of a line between
two points using the slope formula,
and also be sure they understand
the use of function notation, f (x),
in Exercise 5.
STEP 2 Calculate average rate of change
Calculate the average rate of change between the points in each pair by
calculating the slope of the line through the two points. Record the results.
Add a column for the absolute values of the average rates of change.
Average Rate of
Change
(2, 1), (3, 8)
(21, 20.68) (0, 21)
Extra Example
Absolute Value of the
Average Rate of Change
7
7
20.32
0.32
Find the average rate of change
between points on the graph of
y 5 22x 2 1 x 2 3. How does the
choice of the points impact the
average rate of change?
Depending on the pair of points
chosen for an interval, the average
rate of change can be positive or
negative, and either very large or
very small.
Depending on the pair of points chosen for an interval, notice that the
average rate of change can be positive or negative, and either very large or
very small.
DR AW CONCLUSIONS
Key Discovery
In Exercises 1–4, repeat Steps 1 and 2 for the given function.
1. y 5 2x 2 3
2. y 5 24x2 1 2x 2 1
1
4. y 5 2 }
3. y 5 10 p 2x
The average rate of change
between two points on the graph
of a linear function is constant,
while the average rate of change
for quadratic and exponential
functions can vary widely
depending on the points chosen.
x
132
5. Graph the functions given in the table below. Estimate the average rate of
change for each graph. Copy and complete the table. Generalize the results.
Function
f(10) 2 f(0)
10 2 0
}
f(100) 2 f(10)
100 2 10
}}
y5x11
1
1
y 5 x2 1 1
10
110
102.3
?
y52
x
1.4 3 10 28
1. For y 5 2x 2 3, the average rate of
change is the constant 2.
ESE612355_10-8B_ACT.indd 35
2. For y 5 24x2 1 2x 2 1, the average
rate of change is positive but decreasing
as x increases for x < 0 and negative and
increasing as x increases for x > 0.
3. Depending on the interval, the average
rate of change can be very large or very
small, but it is always positive.
f(1000) 2 f(100)
1000 2 100
}}
TEACH
Tips for Success
Graph the function on a graphing calculator. Then use the Trace feature to
identify the coordinates of points on the graph. Record four pairs of points in
a table like the one shown.
Points
PLAN AND
PREPARE
f(10,000) 2 f(1000)
10,000 2 1000
}}
? 1
?1
? 1100
? 11,000
?
?
very large
extremely large
10.8A Model Relationships
3
CC35
ASSESS AND
RETEACH
Find the average rate of change
between two points on the graph
x
of y 5 31 }1 2 . How does the choice
2
x
4. For y 5 2 }1 , the average rate of change
3
12
is always negative and becomes smaller as
x increases.
5. As x becomes greater, the average
rate of change of the exponential function
increases much more rapidly than the
average rate of change of the quadratic
function. The linear function maintains a
constant rate of change.
12/14/10
of the points impact the average
rate of change? The average rate
9:58:06 PM
of change is always negative and
becomes smaller as x increases.
CC35
IInvestigating
nvestigating
Algebra
Algebra
1
PLAN AND
PREPARE
Explore the Concept
• Students will form several
samples from a known population
and compare how well the
samples represent the population.
• This activity helps students
distinguish between a
convenience sample and
a random sample.
Materials
Each student or group of students
will need 80 pinto beans, 20 red
beans, and a container such as a
bag or jar. If you use other varieties
of beans, the two types should be
about the same size and shape as
well as easily recognizable by color.
M AT E R I A L S • red beans, pinto beans, container
QUESTION
EXPLORE
Select a sample
Place 20 red beans directly on top of the pinto beans. Then out of
100 beans in the jar, twenty percent of the beans are red beans.
STEP 2 Take a sample Without stirring, reach in and pull a handful of
beans out of the jar. Count the number of red beans and the total
number of beans in your handful. Record your results in a table
like the one below. Return the beans to the jar.
STEP 3 Take a second sample Stir the jar thoroughly. Pull a handful of
beans out of the jar. Record your results of this sample in your table.
Return the beans to the jar.
STEP 4 Take a third sample Stir the jar thoroughly. Pull a handful of beans
out of the jar. Add your results to your table.
Sample
Grouping
TEACH
How well do different samples represent a situation?
STEP 1 Create the population Drop 80 pinto beans into a container.
Work activity: 15 min
Discuss results: 10 min
2
Use be
before Lesson 13.5
13.5 Investigating Samples
ples
Recommended Time
Students can work in small groups.
For each group, assign the tasks of
preparing the population, taking the
samples, and recording the samples.
ACTIVITY
CTIVITY
Number of red
beans, b
Total number of
beans, T
Percent that is
red (b/T)
one handful, not stirred
?
?
?
one handful, stirred
?
?
?
two handfuls, stirred
?
?
?
DR AW CONCLUSIONS
Use your observations to complete these exercises
1. Compare the first two samples.
a. How does stirring affect the results? answers may vary
Tips for Success
b. Which sample seems to be more representative of the beans in the jar? Why
Be sure students calculate the
percent of red beans, not just the
number, in each sample.
c. How could you accomplish the same effect as stirring the beans when
Key Questions
• What percent of red beans
would be the best representation
of the population? 20%
• Do all of the samples show the
same percent of red beans? no
do you think this occurred? Sample answer: The one handful, stirred because the beans were stirred up.
choosing a real-world sample for a survey or study? doing a random sample
2. Compare the last two samples. Which of these samples seems to be more
representative of the beans in the jar? Explain. Sample answer: two handfuls; larger sample
3. You would like to perform a fourth trial. Which of the samples below do you
think would produce the most representative sample? Explain your reasoning.
A 20 beans poured out, unstirred
C three handfuls, stirred
D three handfuls, unstirred
C. Sample answer: Mixing allows randomness and the larger sample reduces bias.
Key Discovery
The way in which a sample of a
population is taken will affect
whether the sample is a good
representation of the entire
population.
3
ASSESS AND
RETEACH
Use Exercises 2 and 3 to assess
student understanding.
CC36
B two handfuls, stirred
CC36
Chapter 13 Probability and Data Analysis
LA1_CCESE612355_13-05_ACT.indd 36
12/10/10 4
© Dave De Lossy/Photodisc/Getty Images
13.6A Analyze Data
Before
Now
Why?
1
You found measures of central tendency.
PLAN AND
PREPARE
You will find relative frequencies in a two-way frequency table.
Warm-Up Exercises
So you can use data about dogs in a store in Exercise 3 on p. CC39.
Find the mean, mode(s), and
median of the data set.
1. number of push-ups: 2, 11, 15, 9,
3, 7, 11, 8, 5, 1 8.2, 11, 8.5
2. temperatures: 468, 528, 768, 648,
688, 718, 828, 568, 618, 708, 788,
748 66.58, no mode, 698
3. Malik collected the following
data for numbers of rooms in
houses: 7, 9, 15, 5, 4, 5, 6, 9, 12,
10, 11, 16, 10, 9, 6, 8, 8, 9, 10, 12,
7, 6, 9, 10, 4, 7, 9. Find the mean,
mode(s), and median of this
data. about 8.6, 9, 9
A two-way frequency table shows the number of items in various categories.
Key Vocabulary
• marginal frequency Every element in the sample must fit into one of the categories and there
must be no overlap between categories.
• joint frequency
For Your Notebook
KEY CONCEPT
Two-way frequency table
A two-way frequency table divides the data into categories across the top
and down the side.
Apples
Oranges
Total
Boys
15
18
33
Girls
21
16
37
Total
36
34
70
EXAMPLE 1
The body of the table gives the
joint frequencies.
Pacing
The row and column totals give
the marginal frequencies.
Basic: 1 day
Average: 1 day
Advanced: 1 day
Block: 0.5 block
Read information from a two-way frequency table
2
The table shows the results of students naming their favorite subject.
Math
Science
English
Miss Bailey’s homeroom
8
6
5
19
Mr. Cole’s homeroom
4
7
9
20
Total
12
13
14
39
Essential Question
Total
Big Idea 2, p. 841
How do you find a marginal
frequency in a two-way frequency
table? Tell students they will learn
how to answer this question by
finding the appropriate cell.
a. How many students in Miss Bailey’s homeroom prefer math?
b. How many students from both homerooms prefer science?
Motivating the Lesson
Solution
Are children more likely to enjoy
classical music if one or more of
their parents enjoy classical
music? A frequency table showing
the results of a survey could be
used to determine such a
relationship.
a. The cell in the row for Miss Bailey’s homeroom and in the column for
Math contains 8, so 8 students in her homeroom prefer math.
b. The cell in the total row and in the column for Science contains 13, so
13 students prefer Science.
13.6A Analyze Data
FOCUS AND
MOTIVATE
CC37
Resource Planning Guide
Ch t Resource
Chapter
R
• Practice level B
• Study Guide
• Challenge
• Pre-AP notes
ESE612355_13-06A_EXPO.indd CC37
Teaching
T
hi Options
• Activity Generator provides
editable activities for all ability
levels
Interactive Technology
12/10/10
• Activity Generator
• Animated Algebra
• Test Generator
• eEdition
12:14:27 AM
See also the Differentiated Instruction
Resources for more strategies for
meeting individual needs.
CC37
CC37
EXAMPLE 2
Make a two-way frequency table
Make a two-way frequency table for the following data.
3
There are 175 freshmen taking a foreign language. Of these, 88 take Spanish,
46 take French, and the rest take German. No one takes more than one
language. There are 42 boys taking Spanish, 31 girls taking French, and a
total of 89 girls taking a language.
TEACH
Extra Example 1
The table shows the number of days
that were rainy, cloudy, or sunny.
Solution
The categories are Spanish, French, German, boys, and girls. Fill in the given
information. Then look for ways to calculate the missing values.
Rainy Cloudy Sunny Total
July
3
4
24
31
Aug
5
6
20
31
Total
8
10
44
62
a. How many July days were
sunny? 24
b. How many days in these
2 months were rainy? 8
Extra Example 2
There are 35 girls among the 67
students who play piano, clarinet,
or violin. Ten students play violin
and 26 play piano. Nineteen boys
play clarinet and 9 boys play piano.
Make a two-way frequency table
for this data.
Piano Clarinet Violin Total
Boys
9
19
4
32
Girls
17
12
6
35
Total
26
31
10
67
For example, the number of girls taking Spanish is 88 2 42 5 46. The number
of boys taking a foreign language is 175 2 89 5 86. The total number of
students taking German is 175 2 (88 1 46).
Spanish
French
German
Total
AVOID ERRORS
Boys
42
15
29
86
Be sure to enter the
given information in the
correct cells of the table.
Girls
46
31
12
89
Total
88
46
41
175
✓
GUIDED PRACTICE
for Examples 1 and 2
1. Using the table in Example 1, tell whether more students in Mr. Cole’s
homeroom prefer science or English. English
2. There are 152 students who play golf, basketball, or soccer. No one plays more
than one of these sports. There are 22 who play golf, 50 who play basketball,
and the rest play soccer. There are 10 boys who play golf, 26 girls who play
basketball, and a total of 80 boys who play one of these sports. Make a two-way
frequency table for the data. See margin.
EXAMPLE 3
Analyze a situation in a two-way table
The table shows where students at a university live.
Live on
Campus
Extra Example 3
Live off
Campus
Total
7226
Use the table in Extra Example 2.
If you randomly choose a student
who plays piano from the group,
are you more likely to choose a
boy or a girl ? girl
Men
3216
4010
Women
3824
3758
7582
Total
7040
7768
14,808
Closing the Lesson
b. Is it also true that more women live off campus than on campus?
a. Do more students live on campus or off campus?
Have students summarize the major
Solution
points of the lesson and answer the
a. Look at the marginal frequencies in the Total row. More students live
Essential Question: How do you
off campus.
find the relative frequency in a
b.
No. Even though the marginal frequencies show that more students live
two-way frequency table?
off campus, looking at just the row for women, you can see that more
• The body of a two-way
women live on campus than off campus.
frequency table gives the joint
frequencies of the categories.
CC38
Chapter 13 Probability and Data Analysis
• The row and column totals give
the marginal frequencies.
Differentiated Instruction
• To find the relative frequency
2.
Below Level
you read the number in the
LA1_CCESE612355_13-06A_EXPO.indd CC38
Golf Basketball Soccer Total
appropriate cell of the table.
Have students work in pairs to make a two-way frequency
table for the data in Guided Practice Exercise 2. Suggest that
they work together to be sure that they are setting up the table
correctly and entering the given data in the appropriate cells.
See also the Differentiated Instruction Resources for more
strategies.
CC38
Boys
10
24
46
80
Girls
12
26
34
72
Total
22
50
80
152
12/10/10 12
13.6A
EXERCISES
HOMEWORK
KEY
5 WORKED-OUT SOLUTIONS
for Exs, 3, 7, and 15
★ 5 STANDARDIZED TEST PRACTICE
Exs. 2, 8, 15, and 18
4
SKILL PRACTICE
A
Assignment Guide
1. VOCABULARY copy and complete: The body of a two-way frequency table
gives the ? of the categories involved.
2.
joint frequency
Basic:
Day 1: pp. CC39–CC41
Exs. 1-11, 20, 21, 27
Average:
Day 1: pp. CC39–CC41
Exs. 1-11, 13-16, 20-27
Advanced:
Day 1: pp. CC39–CC41
Exs. 1-27
★ WRITING Explain how you find the marginal frequency of a category
in a two-way frequency table. Give an example. Find the total of a row or column. For
example, in the table for Exercises 3-5 the marginal frequency of labradors is 11.
READING A TWO-WAY TABLE Answer the questions based on the table showing
the number of different kinds of puppies at a pet store.
EXAMPLE 1
© Getty Images
on p. CC37
for Exs. 3–5
Labradors
Poodles
Yorkies
Males
7
5
3
15
Females
4
8
6
18
Total
11
13
9
33
Total
Differentiated Instruction
3. How many male poodles does the pet store have? 5
See Differentiated Instruction
Resources for suggestions on
addressing the needs of a diverse
classroom.
4. How many female puppies does the pet store have? 18
5. How many more labradors than yorkies does the pet store have? 2
6. COPY AND COMPLETE Copy and complete the two-way table showing
EXAMPLE 2
Homework Check
data about cars sold.
on p. CC38
for Exs. 6–8
2 door
6 cylinder
4 door
586
? 724
8 cylinder
? 315
840
Total
? 901
1564
For a quick check of student
understanding of key concepts,
go over the following exercises:
Basic: 3, 6, 8, 9, 11
Average: 4, 6, 7, 10, 13
Advanced: 5, 7, 12, 17, 18
Total
? 1310
? 1155
2465
7. MAKING A TWO-WAY TABLE You surveyed 82 students in your grade and
Extra Practice
found that twenty-three have 2 brothers and twenty-eight have 1 brother.
Nine students are only children, ten have only 1 sister, seven have only
1 brother, six have 2 sisters and 1 brother, twenty-two have 2 sisters,
twenty-seven have no sisters, and eight have 1 sister and 2 brothers.
Make a two-way frequency table of the given information. See margin.
B
8.
Practice B in Chapter Resources
Vocabulary
Exercise 2 Have students look
up the meanings of the words
marginal and frequency and use
these definitions to help them
remember where in a two-way
table to find the marginal
frequencies.
★ MULTIPLE CHOICE Use this two-way table to find how many 4 bedroom
houses with 3 baths are for sale. D
3 Bedroom
4 Bedroom
Total
1 Bath
10
1
11
2 Bath
68
47
115
3 Bath
31
75
106
Total
109
122
232
A 31
B 47
C 68
PRACTICE
AND APPLY
D 75
13.6A Analyze Data
CC39
7.
0 brothers
1 brother
2 brothers
Total
0 sisters
9
7
11
27
1 sister
10
15
8
33
2 sisters
12
6
4
22
Total
31
28
23
82
ESE612355_13-06A_EXE.indd CC39
12/10/10 12:15:54 AM
CC39
Differentiated Instruction
EXAMPLE 3
ANALYZING A TWO-WAY TABLE The table shows the number of votes each student
on p. CC38
for Exs. 10–12
received from the various classes in the Student Government President Election.
Advanced
Exercises 9 – 11 Ask the students
to find the percent of votes each
candidate received from each
class and of the total.
See also the Differentiated
Instruction Resources for more
strategies.
Freshmen
Sophomores
Juniors
Seniors
Total
92
86
110
71
359
Olivia
77
99
82
68
326
Katy
115
94
90
149
448
Total
284
279
282
288
1133
Matt
9. If Matt received the most votes from the students in his class, what year
student is Matt? Junior
10. Did any candidate have the most votes from more than one class? If so,
Avoiding Common Errors
who and which classes? Explain. Katy had most votes from freshmen and seniors.
Exercise 10 This question refers
to the most votes from more than
one class, not just the most votes.
Discuss the difference between
these concepts with the students.
11. Which student won the election? Katy
C
12. CHALLENGE Create a two-way table from the given information.
Water and iced tea come in 12-ounce and 16-ounce bottles. The number
of 16-ounce bottles is one less than the number of 12-ounce bottles.
There are 11 more bottles of iced tea than water. There are 16 bottles of
water and the number of 12-ounce bottles of water is 2 less than twice the
number of 16-ounce bottles of water. See margin.
Study Strategy
Exercise 12 Let x represent the
total number of 12-ounce bottles.
Then the total number of 16-ounce
bottles can be represented by x 2 1.
You can use the equation
x 1 x 2 1 5 27 to solve for x.
Also, use algebra to represent the
number of 12-ounce and 16-ounce
bottles of water, and write an
equation.
PROBLEM SOLVING
A
In Exercises 13–15, use the given two-way table showing sandwiches sold
at a deli to answer the questions.
Ham
EXAMPLE 1
on p. CC37
for Exs. 14–16
16.c. choir;
in the choir,
the number of
students in this
height range is
about double
the number of
others, but in
the band, the
numbers are
closer to equal.
Chicken
Salami
Total
White bread
65
41
37
143
Wheat bread
97
75
62
234
Total
162
116
99
377
13. SANDWICHES How many more ham sandwiches on wheat bread were
sold than chicken sandwiches on white bread? 56
14. PREDICT If you choose one sandwich at random would it be more likely
to be chicken on wheat bread or ham on white bread? Explain.
chicken on wheat bread because more of this kind were sold
15. ★ SHORT RESPONSE If you know that a customer is going to order a
sandwich on wheat bread, what is the most likely type of sandwich that
customer will order? Explain.
ham because 97 is the greatest number of wheat bread sandwiches sold
16. MUSIC There are 33 students in choir and 74 in band. No one is in both.
Twenty-three of these students are less than 5 feet tall and 24 are more
than 6 feet tall. Six choir members are less than 5 feet tall while twentytwo choir members are between 5 and 6 feet tall.
a. How many students in the choir are more than 6 feet tall? 5
b. How many students in the band are between 5 and 6 feet tall? 38
c. If you choose a student at random from the choir and from the band,
which student is more likely to be between 5 and 6 feet tall? Explain.
5 WORKED-OUT SOLUTIONS
CC40 Chapter 8 Exponents
Exponential
Functions
for Exs. 3,and
7, and
15
★ 5 STANDARDIZED
TEST PRACTICE
5 MULTIPLE
REPRESENTATIONS
12.
12 ounce 16 ounce
LA1_CCESE612355_13-06A_EXE.indd CC40
CC40
Total
Water
10
6
16
Iced Tea
12
15
27
Total
22
21
43
12/22/10 12:
17. VEGETABLES A gardener planted two tomato and green pepper plants
© Danilo Calilung/Corbis
in each of two types of soil to test fertilizers. The table shows the number
of tomatoes and green peppers harvested from each set of plants. Which
type of soil seems better for each vegetable?
5
ASSESS AND
RETEACH
Tomatoes
Green
Peppers
Total
Fertilizer- fortified soil
56
37
93
Soil fertilized every
2 weeks
Daily Homework Quiz
65
19
84
Total
121
56
177
Use the two-way table showing the
number of students who have each
type of pet to answer the questions.
a. Does one treatment appear to better for tomatoes?
Dog Cat No Total
Pet
Soil fertilized every 2 weeks
b. Does one treatment appear to better for green peppers?
17.c. Fertilizerfortified soil;
no, this is the
better choice
for green
peppers, but is
not as good for
tomatoes.
Fertilizer-fortified soil
c. Looking at just the totals, which treatment appears to be better?
18.
★ EXTENDED RESPONSE Sangee, Tom, and Maleho have classical
46
29
127
Sophomores 47
61
20
128
107 49
255
1. How many freshmen have no
pet? 29
2. How many students have a cat?
107
3. Do more freshmen have a dog or
a cat? dog
4. One hundred boys and one
hundred girls were asked
whether they would rather
watch a movie or play a video
game. Seventy-six girls said
they would rather watch a
movie. If 58 boys said they
would rather play a video
game, make a frequency
table for the data.
b. Calculate If Sangee bought a classical CD, how would his classical
CD total compare to Maleho’s rock CD total? It would be 10 less.
c. Analyze If a CD is chosen at random from those owned by these three
boys, would it be more likely to be classical or rock? rock
19. CHALLENGE There were 1809 tickets sold to a play, of which 800 were for
the main floor. These tickets consisted of 2x 1 y adult tickets on the main
floor, x 2 40 child tickets on the main floor, x 1 2y adult tickets in the
balcony, and 3x 2 y 2 80 child tickets in the balcony.
a. Find the values of x and y. x 5 249, y 5 93
b. Find the number of adult balcony tickets sold. 435
c. Find the number of child main floor tickets sold. 209
MIXED REVIEW
PREVIEW
Prepare for
Lesson 13.7
in Ex. 20
99
Total
and rock CDs. They have a total of 141 CDs, of which 47 are classical.
Sangee has 19 rock CDs and 26 classical CDs, Tom has 38 rock CDs,
and Maleho has 49 CDs.
a. Model Make a two-way table to display this data.
C
52
Freshmen
Is this the best choice for both types of plants? Explain.
Watch
Movie
Play
Video
Game
Total
Boys
42
58
100
Girls
76
24
100
Total
118
82
200
Factor the polynomial. (Lesson 9.5)
20. 4x2 2 8x
21. a2 1 5a 1 4
4x (x 2 2)
(a 1 1) (a 1 4)
Factor the polynomial. (Lesson 9.6)
2
2
23. 2x 1 x 2 3
22. h2 2 h 2 72
(h 2 9) (h 1 8)
2
24. 36x 2 60x 1 25
25. 9y 2 3y 2 2
(2x 1 3) (x 2 1)
(6x 2 5) 2
(3y 1 1)(3y 2 2)
26. The value of Michael’s car decreases by about 10% per year. If you write a
model for the value of his car over time, should you use a linear function,
a quadratic function, or an exponential function? (Lesson 10.8A)
exponential function
27. Over the last several years, Maria’s collection of lunchboxes has increased
by about 5 lunchboxes a year. If you write a model to predict the size of
her collection in 3 years, should you use a linear function, a quadratic
function, or an exponential function? (Lesson 10.8A) linear function
13.6A Analyze Data
Diagnosis/Remediation
• Practice B in Chapter Resources
• Study Guide in Chapter
Resources
Challenge
CC41
Additional challenge is available in
the Chapter Resources.
18a.
Classical
Rock
Total
Sangee
26
19
45
Twan
9
38
47
Maleho
12
37
49
Total
47
94
141
ESE612355_13-06A_EXE.indd CC41
12/22/10 12:37:19 AM
CC41
IInvestigating
nvestigating
Algebra
Algebra
PLAN AND
PREPARE
Explore the Concept
• Students will collect data
and draw a dot plot. They will
examine the plot to see if the
data are spread out or tightly
clustered.
• This activity leads into the study
of data distribution.
Materials
Each student or group of students
will need a ruler and a sheet of
graph paper.
Recommended Time
Work activity: 15 min
Discuss results: 10 min
Use be
before Lesson 13.7
13.7 Investigate Dot Plots
ots
M AT E R I A L S p ruler, graph paper
QUESTION
© Ken Gillespie Photography/Corbis
1
ACTIVITY
CTIVITY
How do you represent data in a dot plot?
Data can be represented by dots in a display called a dot plot. A dot plot
shows the frequency of data and how the data are distributed.
EXPLORE
Draw a dot plot
STEP 1 Collect data
Look up the low temperature for a city in the northern
United States for each day in January of last year.
STEP 2 Make a dot plot
Use graph paper to draw a horizontal axis. Label it Temperatures and
number it using a reasonable scale. Place a dot above the appropriate
temperature to represent the low temperature for each day in January.
For example, put a dot over the temperature 4 to indicate that the low
temperature on one day was 48F. The sample graph shows that it was 48F
on two days and 238F on one day.
Grouping
Students can work individually or
in pairs. If students work in pairs,
one can read the temperatures and
the other can graph them.
2
TEACH
Tips for Success
Tell students to note the highest
and lowest data values before
deciding on the scale for their dot
plot. Make sure that the scale on
your horizontal axis is in equal
increments.
Alternative Strategy
10
10
15
20
2. Are the data tightly clustered or spread apart?
3. Is there a value that occurs more often than the others? If so, what does
this mean in the context of the data?
4. If you were to add the temperature for February 1st to your dot plot, what
would you expect it to be? Explain your reasoning. What types of values
would be surprising? Why?
5. How would your dot plot change if you collected temperatures from a
summer month rather than from January?
Sample answer: The temperatures would be higher and would not include negative values.
6. Compare the data in the dot plots.
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
Plot A
CC42
Plot B
Sample answer: The
data in Plot A are
closer together than
the data in Plot B. The
values in Plot A are
more predictable.
Chapter 13 Probability and Data Analysis
ASSESS AND
RETEACH
What does each dot on a dot plot
represent? a data value
What can you tell about data from
a dot plot? the frequency and how
the data are distributed
CC42
5
Use your observations to complete these exercises
1–4. Answers will vary.
1. Examine your dot plot. What is the range of the data values?
Key Discovery
3
0
DR AW CONCLUSIONS
This activity could be done as a
class demonstration. Students
could take turns coming up to the
board to put the dots on the dot plot.
A dot plot shows the frequency of
data and how the data are
distributed.
5
LA1_CCESE612355_13-07_ACT.indd 42
12/15/10 3
Tennessee Grade Six Mathematics Standards
Mastering the Standards
for Mathematical Practice
Mathematical Practices
The topics described in the Standards for Mathematical
Content will vary from year to year. However, the way in
which you learn, study, and think about mathematics will
not. The Standards for Mathematical Practice describe skills
that you will use in all of your math courses.
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
4 M
Model with mathematics.
Mathematically proficient
M
students can apply...
mathematics... to... problems...
in everyday life, society, and
the workplace...
In your book
Application exercises and Mixed Reviews of Problem
Solving apply mathematics to other disciplines and in
real-world scenarios.
.*9
.*9&%
.*9
.*9&%3&7*&8
9&%
&% 3&7
3&7
&7*&8
*&
*&8
&8
&
8PG1SPCMFN4PMWJOH
PG1SPCMFN4PMWJOH
PG
PG1SP
PG1SPCMFN4
1SP
SPCMFN
CMFN4
FN 4PMWJOH
PMWJOH
WJO
45"5&5&4513"$5*$&
DMBTT[POFDPN
-FTTPOTo
1. .6-5*45&1130#-&. Flying into the wind,
a helicopter takes 15 minutes to travel
15 kilometers. The return flight takes
12 minutes. The wind speed remains
constant during the trip.
a. Find the helicopter’s average speed (in
kilometers per hour) for each leg of the trip.
b. Write a system of linear equations that
represents the situation.
c. What is the helicopter’s average speed in
still air? What is the speed of the wind?
4. 01&/&/%&% Describe a real-world problem
that can be modeled by a linear system.
Then solve the system and interpret the
solution in the context of the problem.
130#-&.40-7*/(
5. 4)0353&410/4& A hot air balloon is
launched at Kirby Park, and it ascends at
a rate of 7200 feet per hour. At the same
time, a second hot air balloon is launched
at Newman Park, and it ascends at a rate of
4000 feet per hour. Both of the balloons stop
ascending after 30 minutes. The diagram
shows the altitude of each park. Are the hot
air balloons ever at the same height at the
same time? Explain.
,JSCZ1BSL
&9".1-&
&
9".
58. %*7*/( A diver dives from a cliff when her center of gravity is 46 feet
above the surface of the water. Her initial vertical velocity leaving the cliff
is 9 feet per second. After how many seconds does her center of gravity
enter the water?
POQ
POQ
GPS&YT
GPS&YT
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
&9".1-&
&
9".
59. 4$3"1#00,%&4*(/ You plan to make a
scrapbook. On the cover, you want to show three
pictures with space between them, as shown. Each
of the pictures is twice as long as it is wide.
POQ
POQ
GPS&YT
GPS&YT
/FXNBO1BSL
a. Write a polynomial that represents the area of
2 cm
2x
4x
2 cm
2 cm
the scrapbook cover.
b. The area of the cover will be 96 square
2 cm
1 cm
1 cm
centimeters. Find the length and width of the
pictures you will use.
GPSQSPCMFNTPMWJOHIFMQBUDMBTT[POFDPN
3940 ft
customer pays a total of $9.70 for 1.8 pounds
of potato salad and 1.4 pounds of coleslaw.
Another customer pays a total of $6.55 for
1 pound of potato salad and 1.2 pounds of
coleslaw. How much do 2 pounds of potato
salad and 2 pounds of coleslaw cost? Explain.
3. (3*%%&%"/48&3 During one day, two
computers are sold at a computer store. The
two customers each arrange payment plans
with the salesperson. The graph shows the
amount y of money (in dollars) paid for the
computers after x months. After how many
months will each customer have paid the
same amount?
Amount paid
(dollars)
y
SEA LEVEL
Not drawn to scale
6. &95&/%&%3&410/4& A chemist needs
500 milliliters of a 20% acid and 80% water
mix for a chemistry experiment. The chemist
combines x milliliters of a 10% acid and
90% water mix and y milliliters of a 30% acid
and 70% water mix to make the 20% acid and
80% water mix.
200
0
2
4
6
8
10
Months since purchase
x
(4)0353&410/4& You throw a ball into the air with an initial vertical
velocity of 31 feet per second. The ball leaves your hand when it is 6 feet
above the ground. You catch the ball when it reaches a height of 4 feet.
After how many seconds do you catch the ball? Explain how you can use
the solutions of an equation to find your answer.
61. 1"35)&/0/ The Parthenon in Athens, Greece, is an ancient structure
that has a rectangular base. The length of the Parthenon’s base is
8 meters more than twice its width. The area of the base is about
2170 square meters. Find the length and width of the Parthenon’s base.
62.
a. Write a linear system that represents the
situation.
b. How many milliliters of the 10% acid
and 90% water mix and the 30% acid and
70% water mix are combined to make the
20% acid and 80% water mix?
.6-5*1-&3&13&4&/5"5*0/4 An African cat
called a serval leaps from the ground in an attempt
to catch a bird. The serval’s initial vertical velocity
is 24 feet per second.
a. 8SJUJOHBO&RVBUJPO Write an equation that
gives the serval’s height (in feet) as a function
of the time (in seconds) since it left the ground.
c. The chemist also needs 500 milliliters of
400
0
60.
1705 ft
2. 4)0353&410/4& At a grocery store, a
b. .BLJOHB5BCMF Use the equation from part (a)
a 15% acid and 85% water mix. Does the
chemist need more of the 10% acid and
90% water mix than the 30% acid and
70% water mix to make this new mix?
Explain.
to make a table that shows the height of the
serval for t 5 0, 0.3, 0.6, 0.9, 1.2, and
1.5 seconds.
c. %SBXJOHB(SBQI Plot the ordered pairs in
the table as points in a coordinate plane.
Connect the points with a smooth curve.
After how many seconds does the serval
reach a height of 9 feet? Justify your answer
using the equation from part (a).
$IBQUFS4ZTUFNTPG&RVBUJPOTBOE*OFRVBMJUJFT
PhotoDisc/Getty Images
"MHFCSB
BUDMBTT[POFDPN
58
03,&%06540-65*0/4
$IBQUFS1PMZOPNJBMTBOE'BDUPSJOH
POQ84
( 545"/%"3%*;&%
5&4513"$5*$&
5.6-5*1-&
3&13&4&/5"5*0/4
Extension
Use after Lesson 13.8
PLAN AND
PREPARE
1
GOAL Choose an appropriate display, measure of central tendency, and measure
of spread based on the shape of a data distribution.
Warm-Up Exercises
1. The histogram shows the number
of people who caught fish in
a contest. How many people
caught between 9 and 11 fish? 6
When you are presenting a set of data, you should consider the distribution of
the data before deciding what type of measure of central tendency and graph to
use for the data.
DATA THAT ARE CLOSELY GROUPED Use
a histogram to display the data. Use the
mean as a measure of central tendency.
Use standard deviation as a measure of
the spread.
10
8
6
4
2
0
DATA VALUES THAT ARE SPREAD OUT Use
5
a box-and-whisker plot to display the data.
Use the median as a measure of central
tendency. Use the interquartile range as
a measure of the spread.
6–
8
9–
11
12
–1
4
3–
0–
2
People
Fishing Contest
Number of Fish
2. What is the median cost of the
recliners? $375
EXAMPLE 1
Cost of Recliners
150
2
350
550
Choose a display for data
A used car dealer has 21 cars for sale at the prices shown in the table.
Choose an appropriate display, measure of central tendency, and measure
of spread for this data set.
750
FOCUS AND
MOTIVATE
$2150
$2800
$3500
$5100
$6050
$7100
$7250
$8000
$8850
$9100
$9225
$9900
$10,200
$10,800
$11,750
$12,200
$12,640
$13,020
$14,700
$15,500
$16,400
Solution
The data are close together with no outliers. Use a histogram. The center
of the data can be represented by the mean, which is $9,345. The spread
can be represented by the standard deviation, which is about $3946.
Essential Question
Big Idea 3, p. 841
When should you display data
using a histogram instead of a
box-and-whisker plot?
Tell students they will learn how to
answer this question by studying
the distributions of data sets.
3
Analyze Data Distribution
Cars Available
Number
8
6
4
2
0
TEACH
0–2
2–4
4–6
6–8 8–10 10–12 12–14 14–16 16–18
Price (in thousands)
Extra Example 1
The high temperatures on ten
summer days (8F) are shown in the
table. Choose an appropriate display,
measure of central tendency, and
measure of spread for this data set.
76
74
83
91
71
96
94
82
87
85
The data are close together with
no outliers. Use a histogram. The
mean is 83.98F. The standard
deviation is about 8.08F.
CC44
CC44
Chapter 13 Probability and Data Analysis
LA1_CCESE612355_13-08A_EXT.indd 44
12/10/10 11
EXAMPLE 2
1. Since the data are close
together with no outliers, it is
appropriate to use a histogram.
The mean is 15.44 and the
standard deviation is about 3.49.
2. Since three of the values
appear to be much larger than
the rest, it is appropriate to use
a box-and-whisker plot. The
median is 29 points and the
interquartile range is 17 points.
3. Since the data are close
together with no outliers, it is
appropriate to use a histogram.
The mean is 9.51 minutes and
the standard deviation is about
1.44 minutes.
Choose a display for data
Another used car dealer has 24 cars for sale at the prices shown in the table.
Choose an appropriate display, measure of central tendency, and measure
of spread for this data set.
$3,800
$5,100
$7,100
$7,250
$8,850
$9,225
$9,900
$10,200
$10,500
$10,800
$11,400
$11,750
$12,200
$12,350
$12,640
$13,020
$13,890
$14,700
$15,500
$15,990
$17,000
$17,800
$22,900
$38,775
Extra Example 2
Another city recorded the
temperatures in degrees
Fahrenheit shown in the table.
Choose an appropriate display,
measure of central tendency, and
measure of spread for this data set.
Solution
84
82
93
81
74
The data value $38,775 appears to be an outlier. Use a box-and-whisker plot to
display the data. The outlier will affect the mean and standard deviation, so
they do not represent the data well. The median is $11,975. The interquartile
range is $5537.50.
96
94
51
86
85
Used Cars
4. Since one of the values
appears to be much smaller
than the rest, it is appropriate
to use a box-and-whisker plot.
The median is 10.5 hours and
the interquartile range is
1.75 hours.
The data value 51 appears to be
an outlier. Use a box-and-whisker
plot to display the data. The median
is 84.58F and the interquartile range
is 128F.
Temperatures
0
20
10
30
40
Price (in thousands)
5. Since the data are close together with no outliers, it is appropriate to use a
histogram. The mean is 25.7 cookies and the standard deviation is about 6.27 cookies.
EXERCISES
6. Since the
data are close
together with
no outliers, it is
appropriate to
use a histogram.
The mean is
35,890.75 people
and the standard
deviation is
about 3161.98
people.
ESE612355_13-08A_EXT.indd 45
6, 9, 10, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19,
20, and 20.
2. FOOTBALL The points scored by twenty of the top 25 college football
teams on Saturday, September 25, 2010 were 24, 73, 37, 42, 17, 31, 70, 35,
10, 20, 37, 65, 22, 31, 20, 24, 12, 27, 14, and 34.
3. RUNNING The time (in minutes) it took twenty freshmen to run the mile
Closing the Lesson
in physical education class were 7, 7.5, 8, 8, 8.2, 8.4, 8.5, 9, 9, 9, 9.6, 9.8, 10,
10.5, 10.5, 10.8, 11.2, 11.5, 11.7, and 12 minutes.
4. HOMEWORK The numbers of hours that twenty-five students spent doing
homework last week were 1, 8, 8, 8.5, 9, 9.5, 9.5, 10, 10, 10, 10, 10, 10.5, 10.5,
10.5, 11, 11, 11, 11, 11.5, 11.5, 12, 12, 12, and 12.
5. COOKIES The numbers of cookies in 20 boxes at a bake sale are 16, 16, 18,
18, 20, 20, 24, 24, 24, 24, 26, 28, 28, 30, 30, 30, 30, 36, 36, and 36.
6. BASEBALL The attendance at a professional baseball team’s home games
during September are shown in the table.
40,788
31,647
31,596
33,623
36,364
37,285
34,481
36,553
39,316
38,057
Extension: Analyze Data Distribution
90°F
• How can you check to see if
$38,775 is an outlier? Multiply
the interquartile range by 1.5
and add this value to the upper
quartile, giving $23,406.25.
Since $38,775 > $23,406.25,
$38,775 is an outlier.
1. QUIZ SCORES The scores on the first quiz in Mr. Stuart’s math class were
31,424
70°F
Key Question to Ask for
Example 2
For Exercises 1–6, choose an appropriate display, measure of central
tendency, and measure of spread for the data set. Explain your reasoning.
39,555
50°F
CC45
Have students summarize the
major points of the lesson and
answer the Essential Question:
When should you display data
using a histogram instead of a
box-and-whisker plot?
• Data that are closely grouped
should be displayed in a
histogram. Use the mean and
the standard deviation.
• Data that are spread out should
be displayed in a box-andwhisker plot. Use the median
and the interquartile range.
4
PRACTICE
AND APPLY
12/10/10 11:20:47 PM
Graphing Calculator
Exercises 2 and 4 Have students
enter the numbers in a list under
the STAT menu and choose 1-Var
Stats to find the minimum,
maximum, median, and quartiles.
CC45