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, eighth-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 real-world situations for rates of change and initial values and use these features to construct equations to model the function relationships (MP.4). Students will 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 will make connections between stories and graphs by modeling situations like distance or speed over time.
In sixth and seventh 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 will 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, eighth-grade 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)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 8th Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
Unit Launch
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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
rate of change
linear function
nonlinear function
initial value
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