Download Pre Algebra - Cherokee County Schools

Eighth Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
Date
Implement
ed
The Number System
Know that there are numbers that are not rational, and approximate them by
rational numbers.
3
3
8.1
8.2
Know that numbers that are not rational are called irrational.
Understand informally that every number has a decimal
expansion; for rational numbers show that the decimal
expansion repeats eventually, and convert a decimal
expansion which repeats eventually into a rational number.
[8-NS1]
Use rational approximations of irrational numbers to compare
the size of irrational numbers, locate them approximately on
a number line diagram, and estimate the value of expressions
(e.g., 2).[8-NS2]
Example: By truncating the decimal expansion of
Real # Properties:
76237 (WS) MA7ZZ23(Q)
Rational/Irrational #’s:
M8003
M8004(Q)
Repeating Decimals to Fractions:
M8011
M8012
M8013(Q)
Rational # Equivalents:
AL109(WS) AL-2K02(Q)
Holt Grade 8: 1.1 and
3.7
Larson Pre-Algebra:
5.1 and 9.4
Compare/Order #’s:
M8023
M8024
M8026(R) M8027(R)
M8025(Q)
M8028(Q)
Holt Grade 8: 3.7
Extension
Larson Pre-Algebra:
5.1 and 9.4
Exponents:
M7001
M7002
M7003(Q)
2 , show
that 2 is between 1 and 2, then between 1.4 and 1.5, and
explain how to continue on to get better approximations.
Expressions and Equations
Work with radicals and integer exponents.
2
8.3
Know and apply the properties of integer exponents to
generate equivalent numerical expressions. [8-EE1]
2010 Alabama Course of Study Mathematics
Holt Grade 8: 3.1, 3.2,
and lab after 3.6
1
Eighth Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
Example: 3 2  3 5  3 3 
3
2
2
8.4
8.5
8.6
1
1

.
3
27
3
Suggested Lesson Resources/Activities
M7004(R)
M7005(R)
M7006(Q)
Lesson Plan
(description, number, etc.)
Larson Pre-Algebra:
4.5 and 4.6
Integers as Exponents:
8062(WS)
MA8ZZ24(Q)
Roots:
M8017
M8018
M8019(Q)
M8020(R) M8021(GA) M8022(Q)
Squares and Square Roots:
8066(GA/WS) MA8ZZ12(Q)
Powers and Roots:
AL021(GA/WS) AL-2B09(Q)
Irrational #’s as Decimals:
AL110(GA/WS) AL-2K03(Q)
Holt Grade 8: 3.5 and
lab after 3.6
Larson Pre-Algebra:
1.2 and 4.6
Use numbers expressed in the form of a single digit times an
integer power of 10 to estimate very large or very small
quantities, and to express how many times as much one is
than the other. [8-EE3]
Example: Estimate the population of the United States as 3 ×
108 and the population of the world as 7 × 109, and determine
that the world population is more than 20 times larger.
Scientific Notation:
M7007
M7008
M7009(Q)
M7010(R)
M7011
M7012(Q)
Exponents and Scientific Notation:
AL048(WS)
AL-2E03(Q)
Holt Grade 8:
3.3
Larson Pre-Algebra:
4.7
Perform operations with numbers expressed in scientific
notation, including problems where both decimal and
scientific notation are used. Use scientific notation and
choose units of appropriate size for measurements of very
large or very small quantities (e.g., use millimeters per year
for seafloor spreading). Interpret scientific notation that has
been generated by technology. [8-EE4]
Scientific Notation Representation:
M7013
M7014(Q)
Scientific Notation:
M8001
M8002(Q)
AL048(R)
Computing in Scientific Notation:
AL049
AL-2E04(Q)
Holt Grade 8: 3.4 and
lab following
Larson Pre-Algebra:
4.7
Use square root and cube root symbols to represent solutions
to equations of the form x 2  p and x 3  p , where p is a
positive rational number. Evaluate square roots of small
perfect squares and cube roots of small perfect cubes. Know
that
2 is irrational. [8-EE2]
2010 Alabama Course of Study Mathematics
Date
Implement
ed
2
Eighth Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
Date
Implement
ed
Understand the connections among proportional relationships, lines, and
linear equations.
Graph proportional relationships, interpreting the unit rate as
the slope of the graph. Compare two different proportional
relationships represented in different ways. [8-EE5]
3
3
8.7
8.8
Example: Compare a distance-time graph to a distance-time
equation to determine which of two moving objects has greater
speed.
Use similar triangles to explain why the slope m is the same
between any two distinct points on a non-vertical line in the
coordinate plane; derive the equation y = mx for a line
through the origin and the equation y = mx + b for a line
intercepting the vertical axis at b. [8-EE6]
Remedial Intro to Proportions:
M7057
Slope of a Line:
M8207
M8208
M8209(Q)
M8210(R) M8211(R) M8212(Q)
AL089(WS) AL-2104(Q)
Holt Grade 8:
4.1, 4.2, and 8.2
Larson Pre-Algebra:
6.1, 6.2, 6.3, 8.4
Writing Equations in Slope-Intercept
Form:
M8213 M8214(Q)
Finding Function Rules:
M8215
M8216
M8217(Q)
M8218(R) M8219(R) M8220(Q)
Holt Grade 8:
Functions: 2.4, 2.5
Similar Figures: 4.3
Lab “Explore Slope”
following 8.1
Larson Pre-Algebra:
6.4 Similarity
8.1, 8.4, and 8.6
*See 8.9a and 8.9b
*See 8.9a and 8.9b
Analyze and solve linear equations and pairs of simultaneous linear
equations.
1
8.9
Solve linear equations in one variable. [8-EE7]
2010 Alabama Course of Study Mathematics
3
Eighth Grade Mathematics
Instr
Seq
1
COS #
8.9a
Course of Study Objective
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
Give examples of linear equations in one variable with one
solution, infinitely many solutions, or no solutions. Show which
of these possibilities is the case by successively transforming
the given equation into simpler forms until an equivalent
equation of the form x = a, a = a, or a = b results (where a and b
are different numbers). [8-EE7a]
Remedial Solving One-Step
Equations:
M7302(R)
M7304(Q)
Add/Subtract to Solve Equations:
8064(WS)
MA8ZZ26(Q)
Multiply/Divide to Solve Equations:
8120(WS)
MA8ZZ06(Q)
Holt Grade 8: 1.5, 1.6,
7.1-7.3 with labs and
extensions
Larson Pre-Algebra:
3.3
Solve linear equations with rational number coefficients,
including equations whose solutions require expanding
expressions, using the distributive property and collecting like
terms. [8-EE7b]
Solving Equations with Fractions:
AL029(WS)
AL-2C05(Q)
Remedial Solving Two-Step
Equations:
M7296
M7297
M7298(Q)
Solving Two-Step Equations:
8079(WS)
8121
MA8ZZ01(Q)
Solving Multi-Step Equations:
AL030(WS)
AL-2C06(Q)
Holt Grade 8: 1.5, 1.6,
7.1-7.3 with labs and
extensions
Larson Pre-Algebra:
2.3-2.7, 3.1-3.3, 5.7
1
8.9b
3
8.10
Analyze and solve pairs of simultaneous linear equations. [8EE8]
*Note: All listed activities for 8.10a-c
flow together.
8.10a
Understand that solutions to a system of two linear equations
in two variables correspond to points of intersections of their
graphs because points of intersection satisfy both equations
simultaneously. [8-EE8a]
Common Solutions/Intersecting
Lines:
AL099(WS)
AL-2J03(Q)
Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
Solve systems of two linear equations in two variables
algebraically, and estimate solutions by graphing the equations.
Solve simple cases by inspection. [8-EE8b]
Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because
3x + 2y cannot simultaneously be 5 and 6.
Solving Linear Equation Systems by
Substitution:
AL100(WS)
AL-2J04
Solving Linear Equation Systems by
Elimination:
AL101(WS)
AL-2J05(Q)
Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
3
3
8.10b
2010 Alabama Course of Study Mathematics
Date
Implement
ed
4
Eighth Grade Mathematics
Instr
Seq
3
COS #
8.10c
Course of Study Objective
Solve real-world and mathematical problems leading to two
linear equations in two variables. [8-EE8c]
Example: Given coordinates for two pairs of points, determine
whether the line through the first pair of points intersects the
line through the second pair.
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
Graphing Systems of Linear
Equations:
AL102(WS)
AL-2J06(Q)
Holt Grade 8: 7.4, 8.6
Larson Pre-Algebra:
8.8
Understand that a function is a rule that assigns to each input
exactly one output. The graph of a function is the set of
ordered pairs consisting of an input and the corresponding
output. (Function notation is not required in Grade 8.) [8-F1]
Remedial Function Tables and
Graphs:
M7237(R)
M7238(Q)
Lines as Functions:
AL091(WS)
AL-2l06(Q)
Graphing Linear Equations Review:
8081(WS)
8123(R)
MA8ZZ48(Q)
Holt Grade 8: 2.4, 9.3
Larson Pre-Algebra:
8.1
Compare properties of two functions, each represented in a
different way (algebraically, graphically, numerically in tables,
or by verbal descriptions). [8-F2]
Example: Given a linear function represented by a table of
values and linear function represented by an algebraic
expression, determine which function has the greater rate of
change.
Tables and Ordered Pairs:
M8187(R)
M8188(Q)
Equations and Lines:
M8189(R) M8190(Q)
Finding a Function Rules:
M8215
M8216 M8217(Q)
M8218(R) M8219 M8220(Q)
Holt Grade 8: 2.5 and
“Use Multiple
Representations” lab,
9.4
Larson Pre-Algebra:
8.2-8.5
Interpret the equation y = mx + b as defining a linear function
whose graph is a straight line; give examples of functions that
are not linear. [8-F3]
Slope-Intercept Form:
M8213
M8214(Q)
Determine if a Function is Linear:
M8221
M8222
M8223(Q)
M8224(R) M8225 M8226(Q)
Holt Grade 8: Lab on
p.355
Larson Pre-Algebra:
8.2, Focus on
Functions p.412A, 8.5
Date
Implement
ed
Functions
Define, evaluate, and compare functions.
3
3
3
8.11
8.12
8.13
Example: The function A = s2 giving the area of a square as a
2010 Alabama Course of Study Mathematics
5
Eighth Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
function of its side length is not linear because its graph
contains the points (1,1), (2,4), and (3,9), which are not on a
straight line.
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
Date
Implement
ed
Graphing Equations:
AL087(WS)
AL-2l02(Q)
Use functions to model relationships between quantities.
3
3
8.14
8.15
Construct a function to model a linear relationship between
two quantities. Determine the rate of change and initial value
of the function from a description of a relationship or from
two (x,y) values, including reading these from a table or from
a graph. Interpret the rate of change and initial value of linear
function in terms of the situation it models and in terms of its
graph or a table of values. [8-F4]
Slope of a Line:
M8207
M8208
M8209(Q)
M8210(R) M8211
M8212(Q)
Slopes of Lines:
AL089(WS)
AL-2l04(Q)
Holt Grade 8: 8.3 and
8.4
Larson Pre-Algebra:
8.4-8.6
Describe qualitatively the functional relationship between
two quantities by analyzing a graph (e.g., where the function
is increasing or decreasing, linear or nonlinear). Sketch a
graph that exhibits the qualitative features of a function that
has been described verbally. [8-F5]
X- and Y- Intercepts:
M8205
M8206(Q)
Intercepts of Lines:
AL088(WS)
AL-2l03(Q)
Graphs Without Numbers:
AL095(WS)
AL-2l10(Q)
Holt Grade 8: 2.3, 8.1,
8.5
Larson Pre-Algebra:
8.2, 8.3, 8.6.
Geometry
Understand congruence and similarity using physical models, transparencies,
or geometry software.
4
8.16
Verify experimentally the properties of rotations, reflections,
and translations: [8-G1]
2010 Alabama Course of Study Mathematics
6
Eighth Grade Mathematics
Instr
Seq
COS #
Course of Study Objective
a. Lines are taken to lines, and line segments are taken to
line segments of the same length. [8-G1a]
4
4
4
Holt Grade 8: Lab
p.220, 5.6
Larson Pre-Algebra:
12.4-12.6
b. Angles are taken to angles of the same measure. [8-G1b]
Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
Holt Grade 8: Lab
p.220, 5.6
Larson Pre-Algebra:
12.4-12.6
c. Parallel lines are taken to parallel lines. [8-G1c]
Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
Holt Grade 8: Lab
p.220, 5.6
Larson Pre-Algebra:
12.6
Understand that a two-dimensional figure is congruent to
another if the second can be obtained from the first by a
sequence of rotations, reflections, and translations; given two
congruent figures, describe a sequence that exhibits the
congruence between them. [8-G2]
Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
Holt Grade 8: 5.5, Lab
p.237
Larson Pre-Algebra:
6.3, 6.4, 12.4-12.6
Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates. [8-
Show Me Transformations M8133
Let Me Try Transformations M8134
Holt Grade 8: Lab
p.174, 4.4, 5.7, 5.8
8.16b
8.16c
8.17
4
8.18
Lesson Plan
(description, number, etc.)
Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
8.16a
42
Suggested Lesson Resources/Activities
2010 Alabama Course of Study Mathematics
Date
Implement
ed
7
Eighth Grade Mathematics
Instr
Seq
4
COS #
8.19
Course of Study Objective
Lesson Plan
(description, number, etc.)
G3]
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
Larson Pre-Algebra:
12.4-12.7
Understand that a two-dimensional figure is similar to
another if the second can be obtained from the first by a
sequence of rotations, reflections, translations, and dilations;
given two similar two-dimensional figures, describe a
sequence that exhibits the similarity between them. [8-G4]
Show Me Transformations M8133
Let Me Try Transformations M8134
Quiz 1 Transformations M8135
Reteach Transformations M8136
Let Me Practice Transformations
M8137
Quiz 2 Transformations M8138
Holt Grade 8: Lab
p.168, 4.3
Larson Pre-Algebra:
6.4, 12.4-12.7
Use informal arguments to establish facts about the angle
sum and exterior angle of triangles, about the angles created
when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. [8-G5]
Interior and Exterior Angles:
M7125
M7126(Q)
Angle Measurement:
M7127
M7128
M7129(Q)
M7130(R) M7131(R) M7132(Q)
M7151
M7152
M7153(Q)
M7154
M7155
M7156(Q)
Angles and Lines:
76267(WS)
MA7ZZ41(Q)
Lines and Angles I:
8083(WS)
Lines and Angles II:
8125 MA8ZZ02(Q)
Angle Measures in a Triangle:
AL120(WS)
AL-2L03(Q)
Holt Grade 8: 5.2, 5.3,
Lab p.212
Larson Pre-Algebra:
Focus p.494, Concept
Activity p.691, 12.2,
12.3
Example: Arrange three copies of the same triangle so that the
sum of the three angles appears to form a line, and give
argument in terms of transversals why this is so.
4
Suggested Lesson Resources/Activities
8.20
Date
Implement
ed
Understand and apply the Pythagorean Theorem.
2010 Alabama Course of Study Mathematics
8
Eighth Grade Mathematics
Instr
Seq
4
COS #
8.21
4
8.22
4
8.23
Course of Study Objective
Explain a proof of the Pythagorean Theorem and its converse.
[8-G6]
Suggested Lesson Resources/Activities
Pythagorean Theorem:
8092(WS)
8130
MA8ZZ02(Q)
Lesson Plan
(description, number, etc.)
Date
Implement
ed
Holt Grade 8: Lab
p.131, Lab p.136
Larson Pre-Algebra:
Activity p.493A
Apply the Pythagorean Theorem to determine unknown side
lengths in right triangles in real-world and mathematical
problems in two and three dimensions. [8-G7]
Remediation on Pythagorean
Theorem:
M7133(R) M7134(R/Q) M7136(R)
M7137(Q) M7138(R)
M7139(R)
M7140(R/Q) 76270(R/WS) 76271(R)
MA7ZZ15(R/Q)
Grade-level Pythagorean Theorem:
M8121
M8122
M8123(Q)
M8124 M8125 M8126(Q)
AL033(WS) AL-2C09(Q)
Holt Grade 8: 3.8
Larson Pre-Algebra:
9.3, 9.4, 9.6, 10.6
Apply the Pythagorean Theorem to find the distance between
two points in a coordinate system. [8-G8]
*No activities found in Compass*
Holt Grade 8: 3.9
Larson Pre-Algebra:
9.4, 9.5
Statistics and Probability
Solve real-world and mathematical problems involving volume of cylinders,
cones, and spheres.
4
8.24
Know the formulas for the volumes of cones, cylinders, and
spheres, and use them to solve real-world and mathematical
problems. [8-G9]
Volume:
M8145
M8146
M8147(Q)
M8148
M8149
M8150(Q)
Volumes of Prisms and Cylinders:
8090(WS)
MA8ZZ07(Q)
Volumes of Pyramids and Cones:
8091(WS)
MA8ZZ09(Q)
Holt Grade 8: Lab
p.266, 6.2, Lab p.274,
6.3, 6.4
Larson Pre-Algebra:
10.7, pgs. 578-583,
pgs. 586-591
Investigate patterns of association in bivariate data.
2010 Alabama Course of Study Mathematics
9
Eighth Grade Mathematics
Instr
Seq
1
1
3
4
Course of Study Objective
8.25
Construct and interpret scatter plots for bivariate
measurement data to investigate patterns of association
between two quantities. Describe patterns such as clustering,
outliers, positive or negative association, linear association,
and nonlinear association. [8-SP1]
8.26
Know that straight lines are widely used to model
relationships between two quantitative variables. For scatter
plots that suggest a linear association, informally fit a straight
line, and informally assess the model fit by judging the
closeness of the data points to the line. [8-SP2]
Scatter Plots I: 8096(WS)
Scatter Plots II:
8134
MA8ZZ39(Q)
Holt Grade 8: Lab
p.394
Larson Pre-Algebra:
8.6, Technology
Activity p.445
*No activities found in Compass*
8.27
Use the equation of a linear model to solve problems in the
context of bivariate measurement data, interpreting the slope
and intercept. [8-SP3]
Example: In a linear model for a biology experiment, interpret a
slope of 1.5 cm/hr as meaning that an additional hour of
sunlight each day is associated with an additional 1.5 cm in
mature plant height.
Holt Grade 8: 9.2
Larson Pre-Algebra:
8.4, 8.5, p.436-437B,
8.6
Histograms:
8095(WS)
8133
MA8ZZ10(Q)
Organizing Data:
AL067(WS)
AL-2G01(Q)
Holt Grade 8:
Extension p.396
Larson Pre-Algebra:
Two-Way Tables
Focus p.647A-647B
8.28
Understand that patterns of association can also be seen in
bivariate categorical data by displaying frequencies and
relative frequencies in a two-way table. Construct and
interpret a two-way table summarizing data on two
categorical variables collected from the same subjects. Use
relative frequencies calculated for rows or columns to
describe possible association between the two variables. [8SP4]
Example: Collect data from students in your class on whether
or not they have a curfew on school nights, and whether or not
they have assigned chores at home. Is there evidence that
those who have a curfew also tend to have chores?
2010 Alabama Course of Study Mathematics
Suggested Lesson Resources/Activities
Lesson Plan
(description, number, etc.)
COS #
Scatter Plots I: 8096(WS)
Scatter Plots II:
8134
MA8ZZ39(Q)
Date
Implement
ed
Holt Grade 8: 9.1
Larson Pre-Algebra:
1.8, 2.6, 3.1, 3.6, 7.7,
8.6, Focus p.447A447B, 11.3
10
Eighth Grade Mathematics
The Number System [NS]
• Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations [EE]
• Work with radicals and integer exponents.
• Understand the connections among proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions [F]
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.
Geometry [G]
• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability [SP]
• Investigate patterns of association in bivariate data.
*Key: (R) –remediation; (Q)-quiz; (WS)-worksheet
2010 Alabama Course of Study Mathematics
11