Mathematics
Curriculum Document for Algebra 1
Unit Title: Graphing Linear Equations, Inequalities, and
Functions
Time Frame: 10 blocks
Six Weeks: 2nd and 3rd
Unit Number: 4
Curriculum
The student will know:
Enduring Understandings (Big Ideas):
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Representing a situation in multiple ways leads to better
understanding and more effective communication.
Understanding how a parameter change affects the whole helps
us make predictions.
Graphs provide a visual representation of relationships
among data.
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Characteristics of the linear parent function
Independent variables are represented on the x-axis
Dependent variables are represented on the y-axis
Domain represents all reasonable input values
Range represents all output values based upon reasonable input values
Slope is rate of change
Slope is a ratio of change in y compared to change in x
Direct variation means proportional and the linear graph passes through
the origin
Slopes of parallel lines are equal
In slope-intercept form, m represents the slope (the coefficient of x)
In slope-intercept form, b represents the y-intercept (the constant)
Properties of horizontal and vertical lines
Solutions to linear inequalities are represented on a graph
The student will be able to:
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Unit Title: Graphing Linear Equations and Functions
Perform and describe transformations in a coordinate plane using
transformation notation {ex: (p,q)→(p + 3, q - 1)}
Identify the parent function (linear)
Determine if a situation is linear
Determine domain and range (with and without restrictions)
Determine slope from multiple representations, such as graphs, tables,
equations, and verbal models
Identify direct variation relationships in graphs, tables, and equations
Unit Number 4
Revised Spring 2013
Page 1 of 5
Mathematics
Curriculum Document for Algebra 1
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Solve literal equations (ex: solving for y)
Graph a linear equation using slope-intercept form
Describe the effects of the changes of m and b
Find and interpret x and y intercepts from tables, graphs, and equations
Graph linear equations using the intercepts
Graph linear inequalities
Formulate linear inequalities to solve problems
Determine reasonableness of solutions to linear inequalities
Interpret and make predictions from solutions of linear inequalities
Essential Questions:
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How do we visually represent mathematical ideas?
Why is it useful to represent mathematical ideas in different ways?
How can we be more effective in our communication?
How is the whole picture affected when one aspect is altered?
Why is it important to analyze effects of changing parameters?
Student Understanding (student friendly TEKS):
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I can represent a relationship as an inequality. (taken from A.1D)
I can identify and sketch the linear parent function (y = x). (taken from A.2A)
I can interpret and use function notation. (taken from A.4C)
I can tell if a situation is linear. (taken from A.5A)
I can determine the domain and range for linear relationships. (taken from A.5B)
I can switch back and forth between tables, graphs, words, and equations. (taken from A.5C)
I know slope is a rate of change. (taken from A.6A)
I can find and interpret the slope from tables, graphs, words, and equations. (taken from A.6A and A.6B)
I can find and interpret intercepts from tables, graphs, words, and equations. (taken from A.6B and A.6E)
I can tell how changes in m and b affect the graph of y = mx + b. (taken from A.6C)
I can graph equations given specific information. (taken from A.6D)
I know the slopes of parallel lines are equal. (taken from A.6D)
I can explain the effects of changing the slope and y-intercept in word problems. (taken from A.6F)
I can relate direct variation to linear functions through graphing. (taken from A.6G)
I know the line of a direct variation graph passes through the origin. (taken from A.6G)
Unit Title: Graphing Linear Equations and Functions
Unit Number 4
Revised Spring 2013
Page 2 of 5
Mathematics
Curriculum Document for Algebra 1
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I can solve equations and inequalities for a variable. (taken from A.7B)
I can graph linear inequalities. (taken from A.7)
TEKS:
(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can
be described in a variety of ways. The student is expected to:
(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions,
equations, and inequalities; and
(A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:
(A) identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions;
(A.4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve
problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in
problem situations. The student is expected to:
(C) connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.
(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their
various representations. The student is expected to:
(A) determine whether or not given situations can be represented by linear functions;
(B) determine the domain and range for linear functions in given situations; and
(C) use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.
(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of
linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical
situations. The student is expected to:
(A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;
(B) interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;
(C) investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;
(D) graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;
(E) determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic
representations;
(F) interpret and predict the effects of changing slope and y-intercept in applied situations; and
(G) relate direct variation to linear functions and solve problems involving proportional change.
(A.7) Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve
them, and analyzes the solutions in terms of the situation. The student is expected to:
(B) investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of
equality, select a method, and solve the equations and inequalities;
Unit Title: Graphing Linear Equations and Functions
Unit Number 4
Revised Spring 2013
Page 3 of 5
Mathematics
Curriculum Document for Algebra 1
Targeted College Readiness Standards:
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IID1, IID2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIC2, IXA1, IXA2, IXA3, IXB1, IXC1, IXC2, XA2, XB1, XB2
Targeted ELPs:
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1A, 2G, 2H, 2I, 3B, 3D, 3E, 3F, 3H, 3J, 4C, 4J, 5B, 5G
Academic Vocabulary:
 Direct variation
 Horizontal line
 Linear relation
 Parent function(linear)
 Slope
 Slope-intercept form
 Vertical line
 x-intercept
 y-intercept
Language of Instruction:
Coordinate plane, xy-plane(focus for PSAT preparedness)
Ordered pair
Origin
Parallel lines
Quadrant
Rate of change
Reflections
Transformations
Translations
x-axis
y-axis
Graph of an inequality in one variable and in two variables
Instruction
Instructional Resources:
Textbook:
 Chapter 4 Sections 1 (quick review only and include the
extension) , 2 (extension was done previously), 3, 4, 5, and
6
 Chapter 6 Section 7
Required Activities/Assessments:
Pool Problem
Region IV TAKS Preparation Grade 9Objective 3 Lessons and Obj 6
Transformation Lessons (translations and reflections)
Unit Title: Graphing Linear Equations and Functions
Unit Number 4
Revised Spring 2013
Page 4 of 5
Mathematics
Curriculum Document for Algebra 1
Engaging Mathematics Algebra 1Linear Functions Activities (p. 88146)
Closing the Distance Grade 9 Lesson 4 and 6
TEXTEAMS Algebra 2000 and Beyond Valentine’s Day
Algebra 1 Assessments (p.31-58, 65-68, 79-90, 105-110)
Instructional Suggestions/Examples for PSAT preparedness
Technology:
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Career Connections/Real Life Application:
Use calculator to see the effects of changes in m and b of
the linear parent function
Texas Instruments- Walk the Line Activity (motion detector
activity) www.education.ti.com
Exemplar Lessons:
Research Based Instructional Strategies:
Assessment
Student self-assessment & reflection:
Acceptable evidence or artifacts:
Performance Task Unit 4
Unit 4 Test- Common Assessment
Unit Title: Graphing Linear Equations and Functions
Unit Number 4
Revised Spring 2013
Page 5 of 5