8th Grade Math Unit 1: Moving Straight Ahead
Enduring understanding (Big Idea): Students will be able to understand the connections between linear equations and the
patterns in the tables and graphs of those equations and use them to solve problems.
Essential Questions: What are the variables in the problem? Do the variables in the problem have a linear relationship to each other?
What patterns in the problem suggest that it is linear?How can the linear pattern be represented in a problem, in a table, in a graph, or with an equation? How do
changes in one variable affect changes in a related variable? How are these changes captured in a table, graph, or equation?
How can tables, graphs, and equations of linear relationships be used to express and answer questions?
BY THE END OF THIS UNIT:
Students will know…
Students will be able to…
𝑦 2 − 𝑦1
𝑚= 2
𝑥 − 𝑥1
y = mx + b; m = slope and b = y-intercept
Vocabulary:
Coefficient
Slope
Y-intercept
Linear Equation
Constant term
Linear Relationship
Unit Resources
Learning Task:
 MathematicalReflections
Performance Task:
 Check-Up(s) / Partner Quiz
Project:
 Unit Project: Conducting an Experiment
Unit Review:
 Looking Back Looking Ahead
 Recognize problem situations in which two or more variables have a linear relationship
to each other
 Construct tables, graphs, and symbolic equations that express linear relationships
 Translate information about linear relations given in a table, a graph, or an equation
to one of the other forms
 Understand the connections between linear equations and the patterns in the tables
and graphs of those equations: rate of change, slope, and y intercept
 Solve linear equations
 Solve problems and make decisions about linear relationships using information
given in tables, graphs, and symbolic expressions
 Use tables, graphs, and equations of linear relations to answer questions
Mathematical Practices Focus:
1.
2.
3.
4.
5.
6.
7.
8.
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
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
*If MSA was taught in 7th grade – please see page 4.
Investigation
Problem
Standard Review 7.EE.3; 7.EE.4; 1.1 Walking Marathons
Review 7.EE.4a. (skills to be
1.2 Walking Rates and Linear Relationships
maintained)
1.3 Raising Money
1.4 Using the Walkathon Money
Investigation 1
Math Reflections
Walking Rates
Standard Review 7.EE.3; 7.EE.4;
Review 7.EE.4a;Review 7.EE.4b.
(skills to be maintained)
Investigation 2
Exploring Linear Functions
with Graphs and Tables
Review RP.1; Review
PR.2a;Review PR.2d.
(skills to be maintained)
CC Investigation 1:
Graphing Proportions
Review 7.EE.1; Review 7.EE.2.
(skills to be maintained)
CC Investigation 2:
Equivalent Expressions
Suggested ACE Questions
1.1: ACE 1-2, 15-18
1.2: ACE 3-5, 19-22, 30
1.3: ACE 6-9, 23-26, 31, 32
1.4: ACE 10-14, 27-29, 33
2.1Walking to Win
2.2Crossing the Line
2.3Comparing Costs
2.4 Connecting Tables, Graphs, and Equations
Math Reflections
2.1: ACE 1, 29-34, 42
2.2: ACE 2-5, 35-37, 43
2.3: ACE 6-14, 38, 39, 44
2.4: ACE 15-28, 40- 41
Common Core Investigation 1: (Blue Book)
1.1Graphing Proportions
1.2Graphing Proportions
1.3Graphing Proportions
Common Core Investigations
1.1:ACE 1
1.2:ACE 2-9
1.3:ACE 10-16
Common Core Investigation 2: (Blue Book)
2.1Equivalent Expressions
2.2Equivalent Expressions
Common Core Investigations
2.1:ACE 1-17
2.2:ACE 18-23
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Standard Review 7.EE.1; 7.EE.3;
Review 7.EE.4; Review
7.EE.4a(skills to be maintained);
8.EE.7a
3.1 Solving Equations Using Tables and Graphs
3.2Exploring Equality
3.3From Pouches to Variables
3.4 Solving Linear Equations
3.5 Finding the Point of Intersection
Math Reflections
3.1 ACE 1-4, 28-30, 41
3.2 ACE 5-9, 31-33, 38
3.3 ACE 10-14, 39, 40, 43
3.4 ACE 15-23, 34-37, 44, 45
3.5ACE 24-27, 42, 46
Investigation 4
Exploring Slope
4.1 Climbing Stairs
4.2 Finding the Slope of a Line
4.3Exploring Patterns With Lines
4.4Pulling It All Together
Math Reflections
Looking Back and Looking Ahead
4.1 ACE 1, 36-38, 42
4.2 ACE 2-15, 39, 43, 45
4.3ACE 16-31, 40, 44
4.4ACE 32-35, 41, 46, 47
8.EE.5; 8.EE.6; 8.EE.7a; 8.F.1;
8.F.2.
Common Core Investigation 2: Functions
(Green Book)
Common Core Investigations
2.1 ACE 1-4
2.2 ACE 5
2.3 ACE 6-13
2.4 ACE14-22
Investigation 3
Solving Equations
8.F.2; 8.F.4;
CC Investigation 2:
Functions
2.1
2.2
2.3
2.4
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Alternative 1: (Common CoreUnits and Investigations 3 & 4)
Review 7.EE.1; Review
Common Core Investigation 2: Equivalent Expressions
7.EE.2.
(Blue Book)
(skills to be maintained)
2.1
2.2
CC Investigation 2:
Common Core Investigations
2.1 ACE 1-17
2.2 ACE 18-23
Equivalent Expressions
Standard Review 7.EE.1;
7.EE.3; Review 7.EE.4;
Review 7.EE.4a (skills to
be maintained); 8.EE.7a
3.1 Solving Equations Using Tables and Graphs
3.2Exploring Equality
3.3From Pouches to Variables
3.4 Solving Linear Equations
3.5 Finding the Point of Intersection
Math Reflections
3.1 ACE 1-4, 28-30, 41
3.2 ACE 5-9, 31-33, 38
3.3 ACE 10-14, 39, 40, 43
3.4 ACE 15-23, 34-37, 44, 45
3.5ACE 24-27, 42, 46
Investigation 4
Exploring Slope
4.1 Climbing Stairs
4.2 Finding the Slope of a Line
4.3Exploring Patterns With Lines
4.4Pulling It All Together
Math Reflections
Looking Back and Looking Ahead
4.1 ACE 1, 36-38, 42
4.2 ACE 2-15, 39, 43, 45
4.3ACE 16-31, 40, 44
4.4ACE 32-35, 41, 46, 47
8.EE.5; 8.EE.6; 8.EE.7a;
8.F.1; 8.F.2.
Common Core Investigation 2: Functions
(Green Book)
Common Core Investigations
2.1 ACE 1-4
2.2 ACE 5
2.3 ACE 6-13
2.4 ACE 14-22
Investigation 3
Solving Equations
8.F.2; 8.F.4;
CC Investigation 2:
Functions
2.1
2.2
2.3
2.4
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Alternative 2: (Common CoreUnits and MARsTasks/Lessons)
Review 7.EE.1; Review 7.EE.2.
Common Core Investigation 2: Equivalent Expressions
(skills to be maintained)
(Blue Book)
2.1
CC Investigation 2:
2.2
Equivalent Expressions
Standard Review 7.EE.1; 7.EE.3; Review 7.EE.4;
Review 7.EE.4a (skills to be maintained); 8.EE.7a
MARs Assessment Tasks (MS)
A12 Fencing
N03: Short Tasks - Expressions and Equations
MARs Assessment Lessons (MS)
Solving Real-Life Problems: Baseball Jerseys(Problems-Solving Section)
Steps to Solving Equations(Concept Development)
Solving Linear Equations in One Variable(Concept Development)
*Lessons are not in order of completion
8.F.2; 8.F.4;
PH.5.4. - Unit 5 Investigation 4: Exploring Slope (pp. 70 - 89)
Investigation 4
Exploring Slope
8.EE.5; 8.EE.6; 8.EE.7a; 8.F.1; 8.F.2.
CC Investigation 2:
Functions
Common Core Investigation 2: Functions
(Green Book)
2.1
2.2
2.3
2.4
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
CORE CONTENT
Cluster Title: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard 8.EE.7a: Solve linear equations in one variable.
b) Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions
using the distributive property and collecting like terms.
Concepts and Skills to Master
 Identify and provide examples of equations that have one solution, infinitely many solutions or no solutions.
 Solve multistep linear equations with rational coefficients and variables on both sides.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Solve one- and two-step equations (7.EE.4a).
 Use properties of algebra to simplify algebraic expressions.
Academic Vocabulary
solve, variable, order of operations, solution, like terms, distributive property
Suggested Instructional Strategies
 Build on the equations solved in seventh grade and move
toward increased fluency and procedural skill in solving
more complex linear equations.
 Examine solutions in the context of the original equation.
 Consider teaching unique solutions, no solutions, and
infinitely many solutions with 8.EE.8.
Resources

Textbook Correlation
o Moving Straight Ahead (CMP2)
 Investigations 3
o Common Core Investigations (CMP2)
 Investigation 2: Function
 MARS Concept Formative AssessmentLesson (MS):
Steps to Solving Equations
Classifying Solutions to Systems of Equations
Solving Linear Equations in One Variable
 MARS Concept AssessmentTaskLesson (MS):
A09: Buying Chips and Candy; A12: Fencing;
A14: How old are they?
 Texas Instrument 8.EE.7(a)Lessons:
http://education.ti.com/calculators/downloads/US/Activities/Searc
h/Standards
 NCTM 9-12 Activity: Two Terrains
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Sample Formative Assessment Tasks
Skill-based task
Solve the following equations and identify the number of
solutions:
 3(x+7)=10
1
 2(x - 5)= (4x + 6)
2
 2(x + 3) = 2x + 6
Problem Task
Create equations that would result in one solution, no
solutions, or infinitely many solutions. What is it about the
structure of the original equation that reveals the number of
solutions?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
CORE CONTENT
Cluster Title: Define, evaluate, and compare functions.
Standard 8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a
linear function represented by an algebraic expression, determine which function has the greater rate of change.
Concepts and Skills to Master
 Compare two linear functions each represented a different way and describe similarities and differences in slopes, yintercepts, and values.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Determine slopes and y-intercept.
Academic Vocabulary
slope, intercept, rate of change, function, linear, non-linear
Suggested Instructional Strategies
Resources
 Textbook Correlation
 Given one representation of a function, create the
o Moving Straight Ahead (CMP2)
others.
 Put students in small groups. Give groups scenarios
and ask each group to create a different
representation of the scenario (table, equation,
graph).

Identify attributes (slope, y-intercept, values) of a
function in its equation, graph, or a table.
o
 Investigations 4
Common Core Investigations (CMP2)
 Investigation 2: Function

MARS ConceptAssessmentTaskLesson (MS):
A05: Baseball Jerseys; A17: Linear Graphs, A19: Meal Out

MARS Concept Formative AssessmentLesson (MS):
Interpreting Distance–Time Graphs
Lines and Linear Equation
Modeling Situations With Linear
 Texas Instrument 8.F.2
Lessons:http://education.ti.com/calculators/downloads/US/Activities/Se
arch/Standards
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Sample Formative Assessment Tasks
Skill-based task
Problem Task
Is y=2(x+5) the same as the function described as “twice a Billy argues that the equation y=4x+5 is equivalent to the equation
quantity plus 5”?
of the line that goes through (2, 6) and (3, 10). How did he arrive
at this conclusion? Is he correct? Justify your answer.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
CORE CONTENT
Cluster Title: Use functions to model relationships between quantities.
Standard 8.F.4: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 a linear function in terms of the situation it models, and in
terms of its graph or a table of values.
Concepts and Skills to Master
 Determine and interpret the initial value and rate of change given two points, a graph, a table of values, a geometric
representation, or a story problem (verbal description) of a linear relationship.
 Write the equation of a line given two points, a graph, a table of values, a geometric representation, or a story problem
(verbal description) of a linear relationship.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand the meaning of slope and y-intercept.
 Write an equation as y = mx + bgiven a graph.
Academic Vocabulary
linear relationship, y-intercept, slope
Suggested Instructional Strategies
 Use a real-world application to generate a table of
values. Use the table to construct a function that
models the relationship.

Connect to other standards in the Expressions and
Equations Domain.
Resources

Textbook Correlation
o Moving Straight Ahead (CMP2)
 Investigations 4
 MARS Concept AssessmentTaskLesson (MS):
A17: Linear Graphs;A19: Meal Out
 MARS Concept Formative AssessmentLesson (MS):
Interpreting Distance–Time Graphs
Lines and Linear Equation
Modeling Situations With Linear
 Texas Instrument 8.F.4
Lessons:http://education.ti.com/calculators/downloads/US/Activit
ies/Search/Standards
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Sample Formative Assessment Tasks
Skill-based task
The student council is planning a ski trip to Sundance.
There is a $220 deposit for the lodge and the tickets will
cost $70 per student. Construct a function, build a table,
and graph the data showing how much it will cost for the
students’ trip.
Find the equation of the line that goes through (3,5) and (5,7).
Problem Task
Wally created the table below for a function he knows to be linear.
He thinks something must be wrong with his table because he
can’t find the original function from the table. Find the error and
the original function. Explain your strategy for finding the error.
3.2
17.8
6.4
30.6
9.6
43.4
12.8
56.2
16
66
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
19.2
81.8
22.4
94.6
25.6
107.4
8th Grade Math Unit 1: Moving Straight Ahead
CORE CONTENT
Cluster Title: Understand the connections between proportional relationships, lines, and linear equations.
Standard 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time
equation to determine which of two moving objects has greater speed.
Concepts and Skills to Master
 Graph a proportional relationship given a table, equation or contextual situation.
 Recognize unit rate as slope and interpret the meaning of the slope in context.
 Recognize that proportional relationships include the point (0,0).
 Compare different representations of two proportional relationships represented as contextual situations, graphs, or
equations.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Use an equation to create a table and plot values on the coordinate axes.
 Understand and calculate unit rates.
Academic Vocabulary
slope, unit rate, rate of change, m (slope)
Suggested Instructional Strategies
Resources
 Categorize linear relationships represented in multiple ways
 Textbook Correlation
as either proportional or not proportional.
o Common Core Investigations (CMP2)
 Investigation 2: Function
 Plot relationships generated from real-life proportional
 MARS ConceptAssessmentTaskLesson (MS):
examples (e.g.,shopping) and interpret the slope in the
context of the situation.
A16: Journey; A24 Shelves
 Texas Instrument 8.EE.5 Lessons:
http://education.ti.com/calculators/downloads/US/Activ
ities/Search/Standards
 NCTM 9-12 Activity: Two Terrains
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Sample Formative Assessment Tasks
Skill-based task
This is a graph of Susie’s trip to
John’s cabin. John made the
same trip in 4 hours.Compare
their rates. Who travelled at a
faster rate? How do you know?
Problem Task
Give examples of relationships that are proportional and
relationships that are linear, but not proportional.
CORE CONTENT
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Cluster Title: Understand the connections between proportional relationships, lines, and linear equations.
Standard 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical 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.
Concepts and Skills to Master
• Determine the slope of a line as the ratio of the leg lengths of similar right triangles.
• Explain why the slope is the same between any two distinct points on a line using similar right triangles.
• Write an equation in the form y = mx + b from a graph of a line on the coordinate plane.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Recognize similar triangles and know that they have proportional sides.
Academic Vocabulary
similar triangles, m (slope), b (y-intercept), linear, right triangle, origin, rise, run
Suggested Instructional Strategies
Resources
 Have students draw many right triangles with the
 Textbook Correlation
hypotenuse on the line and compare the ratio of the leg
o Common Core Investigations (CMP2)
lengths.
 Investigation 2: Function
 Discuss the value of choosing easy-to-read points when
determining slope.
 Relate negative slopes to the change in y as x increases.
 NCTM 3-8 Activity: Chairs
 Texas Instrument 8.EE.6 Lessons:
http://education.ti.com/calculators/downloads/US/
Activities/Search/Standards
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
Sample Formative Assessment Tasks
Skill-based task
Points A, D, B, and E are
collinear. Show that ̅̅̅̅
𝐴𝐵
̅̅̅̅ have the same slope.
and𝐷𝐸
Problem Task
How is it possible to have similar triangles that do not yield
the same slope?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
8th Grade Math Unit 1: Moving Straight Ahead
CORE CONTENT
Cluster Title: Define, evaluate, and compare functions.
Standard 8.F.1: 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.
Concepts and Skills to Master
 Understand that functions describe relationships where one variable determines a unique value of the other.
 Recognize a graph of a function as the set of ordered pairs consisting of an input and corresponding output.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Graph ordered pairs on the coordinate plane.
 Evaluate expressions for a given value.
Academic Vocabulary
function, input, output, dependent, independent
Suggested Instructional Strategies
 Explore functions that arise from real-life relationships
where one variable determines a unique value of another.
 Use a variety of representations to have students identify
functions and relations that are not functions.
Resources
 Textbook Correlation
o Common Core Investigations (CMP2)
 Investigation 2: Function
 NCTM 9-12 Activity: Function Matching
 Texas Instrument 8.F.1 Lessons:
http://education.ti.com/calculators/downloads/US/Activiti
es/Search/Standards
Sample Formative Assessment Tasks
Skill-based task
 Could the set of ordered pairs, (2,5), (3,5), (4,6), (2,8), (6,7)
describe the number of seconds since you left home and the
number of meters you’ve walked? Is this a function? Justify
your answers.
 Does the set of students in the classroom and their birthdays
represent a function? Justify your answer.
Problem Task
Find three examples of relationships in the real world that can be
represented by functions and three relationships that are not
functions.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.