Download Plainfield Public Schools Mathematics Unit Planning Organizer

PPS Mathematics Curriculum Algebra I
Plainfield Public Schools
Mathematics
Unit Planning Organizer
Grade/Course
Unit of Study
Pacing
Dates
MP1.
MP2.
MP3.
MP4.
MP5.
MP6.
MP7.
MP8.
Algebra 1
Unit 3 Expressions and Equations
4 weeks; 3 instructional week , 1 weeks for reteaching and enrichment
January 5 – January 29.2016
CCSSM Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
I. Unit Standards
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.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the
previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to
justify a solution method.
A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by
letters.
A.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect
are the solutions of the equation f(x) = 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.*
A.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the
case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the
intersection of the corresponding half-planes.
“Unwrapped” Skills
“Unwrapped” Concepts
DOK Levels
(students need to be able to do)
(students need to know)
FOCUS STANDARD:
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.
Create
equations and inequalities
3
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
DOK Levels
(students need to know)
FOCUS STANDARD:
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales
Create
equations
3
graph
3
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
DOK Levels
(students need to know)
FOCUS STANDARD:
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For
example, rearrange Ohm’s law V = IR to highlight resistance R.
Rearrange
formulas
3
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
DOK Levels
(students need to know)
FOCUS STANDARD:
A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous
step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution
method.
Explain
equations
2
Construct
3
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
DOK Levels
(students need to know)
FOCUS STANDARD:
A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Solve
Equations
2
Inequalities
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
(students need to know)
DOK Levels
FOCUS STANDARD:
A.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = 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.*
Explain
Equations
1
“Unwrapped” Skills
(students need to be able to do)
“Unwrapped” Concepts
DOK Levels
(students need to know)
FOCUS STANDARD:
A.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict
inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.
Graph
Linear inequality
2
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
II Mathematical Practices………………………………………………… Explanation & Examples
Algebra: Creating Equations  (A-CED)
Create equations that describe numbers or relationships.
Standards
Mathematical
Explanations and Examples
Students are expected to:
Practices
HS.A-CED.A.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.
HS.A-CED.A.2. Create
equations in two or more
variables to represent
relationships between
quantities; graph equations
on coordinate axes with
labels and scales.
HS.MP.2. Reason
abstractly and
quantitatively.
Equations can represent real world and mathematical problems. Include equations and
inequalities that arise when comparing the values of two different functions, such as one
describing linear growth and one describing exponential growth.
HS.MP.4. Model with
mathematics.
Examples:
2
●
Given that the following trapezoid has area 54 cm , set up an equation to find the
length of the base, and solve the equation.
●
Lava coming from the eruption of a volcano follows a parabolic path. The height h in
feet of a piece of lava t seconds after it is ejected from the volcano is given by
After how many seconds does the
lava reach its maximum height of 1000 feet?
HS.MP.5. Use
appropriate tools
strategically.
HS.MP.2. Reason
abstractly and
quantitatively.
HS.MP.4. Model with
mathematics.
HS.MP.5. Use
appropriate tools
strategically.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
HS.A-CED.A.4. Rearrange
formulas to highlight a quantity
of interest, using the same
reasoning as in solving
equations. For example,
rearrange Ohm’s law V = IR to
highlight resistance R.
HS.MP.2. Reason abstractly
and quantitatively.
Examples:
●
HS.MP.4. Model with
mathematics.
HS.MP.5. Use appropriate
tools strategically.
HS.MP.7. Look for and
make use of structure.
●
The Pythagorean Theorem expresses the relation between the legs a and b of a right
2
2
2
triangle and its hypotenuse c with the equation a + b = c .
o Why might the theorem need to be solved for c?
o Solve the equation for c and write a problem situation where this form of the equation
might be useful.
o Solve
for radius r.
Motion can be described by the formula below, where t = time elapsed, u=initial velocity, a
= acceleration, and s = distance traveled
2
s = ut+½at
o
o
Why might the equation need to be rewritten in terms of a?
Rewrite the equation in terms of a.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Algebra: Reasoning with Equations and Inequalities  (A-REI)
Understand solving equations as a process of reasoning and explain the reasoning.
Standards
Mathematical Practices
Explanations and Examples
Students are expected to:
HS.A-REI.A.1. Explain each step
in solving a simple equation as
following from the equality of
numbers asserted at the
previous step, starting from the
assumption that the original
equation has a solution.
Construct a viable argument to
justify a solution method.
HS.MP.2. Reason abstractly
and quantitatively.
HS.MP.3. Construct viable
arguments and critique the
reasoning of others.
HS.MP.7. Look for and
make use of structure.
Properties of operations can be used to change expressions on either side of the equation to equivalent
expressions. In addition, adding the same term to both sides of an equation or multiplying both sides by a
non-zero constant produces an equation with the same solutions. Other operations, such as squaring both
sides, may produce equations that have extraneous solutions.
Examples:
 Explain why the equation x/2 + 7/3 = 5 has the same solutions as the equation 3x + 14 = 30. Does this
mean that x/2 + 7/3 is equal to 3x + 14?
 Show that x = 2 and x = -3 are solutions to the equation
Write the equation in a form
that shows these are the only solutions, explaining each step in your reasoning.
Algebra: Reasoning with Equations and Inequalities  (A-REI)
Solve equations and inequalities in one variable.
Standards
Mathematical Practices
Explanations and Examples
Students are expected to:
HS.A-REI.B.3. Solve linear
equations and inequalities in
one variable, including
equations with coefficients
represented by letters.
HS.MP.2. Reason abstractly
and quantitatively.
HS.MP.7. Look for and
make use of structure.
HS.MP.8. Look for and
express regularity in
repeated reasoning.
Examples:





7
 y  8  111
3
3x > 9
ax + 7 = 12
3 x x 9

7
4
Solve for x: 2/3x + 9 < 18
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Algebra: Reasoning with Equations and Inequalities  (A-REI)
Represent and solve equations and inequalities graphically.
HS.A-REI.D.11. Explain why the
x-coordinates of the points
where the graphs of the
equations
y = f(x) and y = g(x) intersect are
the solutions of the equation
f(x) = 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.
Connection: ETHS-S6C2-03
HS.MP.2. Reason abstractly
and quantitatively.
HS.MP.4. Model with
mathematics.
HS.MP.5. Use appropriate
tools strategically.
HS.MP.6. Attend to
precision.
Students need to understand that numerical solution methods (data in a table used to approximate an
algebraic function) and graphical solution methods may produce approximate solutions, and algebraic
solution methods produce precise solutions that can be represented graphically or numerically. Students
may use graphing calculators or programs to generate tables of values, graph, or solve a variety of
functions.
Example:
 Given the following equations determine the x value that results in an equal output for both
functions.
f ( x )  3x  2
g ( x )  ( x  3)2  1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Algebra: Reasoning with Equations and Inequalities  (A-REI)
Represent and solve equations and inequalities graphically.
Standards
Mathematical Practices
Students are expected to:
HS.A-REI.D.12. Graph the solutions
HS.MP.4. Model with
to a linear inequality in two
mathematics.
variables as a half-plane (excluding
HS.MP.5. Use appropriate
the boundary in the case of a strict
tools strategically.
inequality), and graph the solution
set to a system of linear inequalities
in two variables as the intersection
of the corresponding half-planes.
Explanations and Examples
Students may use graphing calculators, programs, or applets to model and find solutions for inequalities or systems of
inequalities.
Examples:

Graph the solution: y < 2x + 3.

A publishing company publishes a total of no more than 100 magazines every year. At least 30 of these are women’s
magazines, but the company always publishes at least as many women’s magazines as men’s magazines. Find a
system of inequalities that describes the possible number of men’s and women’s magazines that the company can
produce each year consistent with these policies. Graph the solution set.

Graph the system of linear inequalities below and determine if (3, 2) is a solution to the system.
x  3y  0

x  y  2
 x  3 y  3

Solution:
(3, 2) is not an element of the solution set (graphically or by substitution).
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Ill .Essential Questions ……………………………………………Corresponding Big ideas
Essential Questions
Corresponding Big Ideas
What can you learn about a function from
a table, graph, or equation that represents
the function?
For functions that map real numbers to real numbers, certain patterns of
covariation, or patterns in how two variables change together, indicate
membership in a particular family of functions and determine the type of
formula that the function has.
How can you determine whether the graph
of an equation is linear?
A rate of change describes how one variable quantity changes with respect
to another – in other words, a rate of change describes the covariation
between two variables.
Members of a family of functions share the same type of rate of change.
This characteristic rate of change determines the kinds of real-world
phenomena that the functions in the family can model.
How do the solution of inequalities relate
to the solution of equations?
How can you use an equations to
determine a function and the situation it
represents ?
How can you use graphs to find the
solutions of an inequality ?
How does applying the same operation to
each side on an inequality change ( or not)
the relationship of two quantities being
.
Changing the way that a function is represented does not change the
function, although different representations highlight different
characteristics, and some may only show part of the function.
Some representations of a function may be more useful than others,
depending on the context
Links between algebraic and graphical representations of functions are
especially important in studying relationships and change.
Real numbers, composing a function with “shifting” or “scaling” functions
changes the formula and graph of the function in readily predictable ways.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
compared ?
Solving an equation is the process of rewriting the equation to make what it
says about its variable(s) as simple as possible. Properties of number and
equality can be used transform an equation ( or inequality) into equivalent
,simpler equation to find solution . Solving equation will include factoring
as a means to acquire the zeroes of a function and on completing the
square as a means to determine the maximum or minimum of the function.
Quadratic equations can be solved by a variety of methods, finding the
square root , using the Quadratic formula completing the square, factoring
or Zero Product Property
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
IV. Student Learning Objective
Student Learning Objective
Create equations and inequalities in one variable
and use them to solve problems. Include
equations arising from linear and quadratic
functions, simple rational and exponential
functions and highlighting a quantity of interest in
a formula. A.CED.1, A.CED.4
Create linear relationship between two or more
variables. Graph equations on the coordinate
axes with labels and scale. A.CED.2,
Graph equations and inequalities, explain that
the solution to an equation is all points along the
curve A.REI.12
Describe constraints with linear equations and
inequalities to determine if solutions are viable or
non-viable A.REI.11
PARCC Instructional Clarification Mathematics Assessment Test
Specifications


Tasks have a real-world context.
The quantity of interest is linear in nature.
Mathematical
Practices
MP.2
MP.6
MP.7
MP.2
MP.4
•
Solve multi-step contextual word problems with degree of
difficulty appropriate to the course, requiring application of course-level
knowledge and skills articulated in A-CED, N-Q.2, A-SSE.3,A-REI.6,
A-REI.12, A-REI.11-1, limited to linear and quadratic equations
CED is the primary content; other listed content elements may be
involved in tasks as well.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
V. Unit Vocabulary
Unit Vocabulary Terms
Inequality
Equivalent Expression
Equivalent inequalities
Commutative Property of addition
Commutative Property of Multiplication
Distributive Property
Combining Expressions
Solution of an inequalities
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
V . Differentiating Instruction
Research Based Effective
Teaching Strategies
Task /Activities that solidifies
mathematical concepts
Use questioning techniques
to facilitate learning
Reinforcing Effort, Providing
Recognition
Practice , reinforce and
connect to other ideas within
mathematics
Modifications
( how do I differentiate
instruction?)
Modifications
Before or after school tutorial
program
Leveled rubrics
Increased intervention
Small groups
Change in pace
Calculators
Extended time
Alternative assessments
Tiered activities/products
Color coded notes
Use of movements
Use any form of technology
Promotes linguistic and
nonlinguistic representations
Cooperative Learning
Setting Objectives, Providing
Feedback
Varied opportunities for
students to communicate
mathematically
Use technological and /or
physical tools
Extension
Research sound frequencies
that can be heard by various
animals. Students present
ranges as inequalities. Student
can identify animals with the
best and worst hearing, those
that hear low best or high sound
best. Student describe in written
form how animals may use the
range to their advantage
Special Education
Strategies for English Language Learners
Change in pace
Calculators
Alternative assessments
Accommodations as per IEP
Modifications as per IEP
Use graphic organizer to clarify
mathematical functions for
students with processing and
organizing difficulties’.
Whiteboards
Small Group / Triads
Word Walls
Partially Completed Solution
Gestures
Native Language Supports
Pictures / Photos
Partner Work
Work Banks
Teacher Modeling
Math Journals
Constant review of math
concepts to strengthen
understanding of prior concepts
for difficulties recalling facts.
Use self-regulations strategies’
for student to monitor and
assess their thinking and
performance for difficultly
attending to task
Cooperative learning (small
group, teaming, peer assisted
tutoring) to foster communication
and strengthen confidence.
Use technology and/or hands on
devices to: clarify abstract
concepts and process for :
1. Difficulty interpreting pictures
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
.
PPS Mathematics Curriculum Algebra I
21st Century Learning
Skills :
Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information
and diagram.
2.difficulties with oral
communications
3. Difficulty correctly identifying
symbols of numeral
4.Difficulty maintaining attentions
Simplify and reduces strategies
/ Goal structure to enhance
motivation , foster independence
and self-direction for:
1.difficulty attending to task
2. difficulty with following a
sequence of steps to solution.
3.difficulty processing and
organizing
Scaffolding math idea/concepts
guided practice and questioning
strategies’ to clarify and
enhance understanding of math
big ideas for :
1.Difficulty with process and
organization
2.difficulty with oral and written
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Enrichment :
Use any form of technology
(graphing calculators)
Tiered activities/products
Use of movement
Use of realia, graphic
organizers, visuals.
communication
Teacher models strategies’ and
think out aloud strategies to
specify step by step process for
1.Difficulties processing and
organization
2. Difficulty attending to tasks.
Use bold numbers and/or words
to draw students’ attention to
important information.
**Use a straw or straight pasta to
with coordinate grids to deepen
students’ understanding of
slope, y-intercept, and point of
intersection and / or systems of
equations.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Instructional Resources
Instructional Resources and Materials
Formative Assessment
Short constructed responses
Extended responses
Checks for Understanding
Exit tickets
Teacher observation
Projects
Timed Practice Test – Multiple
Choice & Open-Ended Questions
Performance Tasks:
Illustrative Mathematics .Basketball
Summative Assessment:
End of Unit Assessment for
Algebra 1 Unit 3 Equations and
Inequalities
Print
Pearson Algebra 1 with Foundation © 2011 ( middle school) : Chapter 2 and Chapter 3
Holt McDougal Larson Algebra 1 ©2011 (high School) : Chapter 3 and Chapter 6
Technology
Resources for teachers
Annenberg Learning : Insight into Algebra 1
Mathematics Assessment Projects
Get the Math
Achieve the Core
Webmath.com
sosmath.com
Mathplanet.com
Interactive Mathematics.com
Illustrative Mathematics
Inside Mathmatics.org
Asia Pacific Economic Cooperation : :Lesson
Study Videos
Genderchip.org
Interactive Geometry
Mathematical Association of America
National Council of Teachers of Mathematics
learner.org
Math Forum : Teacher Place
Shmoop /common core math
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Resources for Students
Khan Academy
Math world : Wolfram.com
Webmath.com
sosmath.com
Mathplanet.com
Interactive Mathematics.com
Mathexpression.com.algebra
Math Words for Advance Algebra & Pre-Calculus
Math TV
Virtual Nerd : Algebra 1
PPS Mathematics Curriculum Algebra I
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Mathematics Curriculum Algebra I
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.