Students learn how to represent, interpret, and analyze functions in various forms, leading to understanding features such as rates of change, initial values, and intervals of increase and decrease.
Math
Unit 4
8th Grade
In Unit 4, 8th grade students are introduced to the concept of a function that relates inputs and outputs. They begin by investigating all types of relationships between sets, such as students and their number of siblings, coins and the number of minutes of parking at a meter, distance and time spent running, etc. They learn how to represent and interpret functions in various forms, including tables, equations, graphs, and verbal descriptions (MP.2). As students progress through the unit, they analyze functions to better understand features such as rates of change, initial values, and intervals of increase or decrease, which in turn enables students to make comparisons across functions even when they are not represented in the same format. Students analyze realworld situations for rates of change and initial values and use these features to construct equations to model the function relationships (MP.4). Students also spend time comparing linear functions to nonlinear functions, building an understanding of the underlying structure of a function that makes it linear (MP.7), setting them up for Unit 5. Lastly, students make connections between stories and graphs by modeling situations like distance or speed over time.
In 6th grade and 7th grade, students studied rate and constant of proportionality in proportional relationships. They developed an understanding of how one quantity changes in relationship to another. Students draw on that knowledge as they investigate how quantities are related in tables, equations, and graphs, and as they investigate linear vs. nonlinear relationships.
Immediately following this unit, students will begin a unit on linear relationships. In that unit, they will revisit and extend on many of the topics introduced in this Functions unit. Students will interpret rate of change as slope and initial value as the $$y$$intercept of a linear equation $$y=mx+b$$. In high school, the study of functions extends across multiple topics and fields of study, including quadratic, exponential, and trigonometric functions.
Pacing: 16 instructional days (12 lessons, 3 flex days, 1 assessment day)
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The following assessments accompany Unit 4.
Have students complete the PreUnit Assessment and PreUnit Student SelfAssessment before starting the unit. Use the PreUnit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the MidUnit Assessment.
Use the resources below to assess student understanding of the unit content and action plan for future units.
Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.
Model  Example 
Input/output table of functions 

Equation of function 
Degrees Fahrenheit is a function of degrees Celsius $$F=\frac{9}{5}C+32$$ 
Graph of function 
Temperature is a function of time.

Verbal representation of function  The total distance a runner has traveled is a function of time spent running. 
To see all the materials needed for this course, view our 8th Grade Course Material Overview.
function
input/output
initial value
linear function
nonlinear function
rate of change
To see all the vocabulary for Unit 4, view our 8th Grade Vocabulary Glossary.
Topic A: Defining Functions
Topic B: Representing and Interpreting Functions
Topic C: Comparing Functions
Topic D: Describing and Drawing Graphs of Functions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 3
Transformations and Angle Relationships
Unit 5
Linear Relationships
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