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.
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)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
Additional assessment tools to help you monitor student learning
and identify any skill or knowledge gaps.
Learn how to use these tools with our
Guide to Assessments
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function
input/output
initial value
rate of change
linear function
nonlinear function
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Input/output table of functions |
Example: |
Equation of function |
Example: Degrees Fahrenheit is a function of degrees Celsius $$F=\frac{9}{5}C+32$$ |
Graph of function |
Example: Temperature is a function of time. |
Verbal representation of function | Example: The total distance a runner has traveled is a function of time spent running. |
8.F.A.1
Define and identify functions.
8.F.A.1
Use function language to describe functions. Identify function rules.
8.F.A.1
8.F.A.2
8.F.B.4
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
8.F.A.1
8.F.B.4
Represent functions with equations.
8.F.A.1
Read inputs and outputs in graphs of functions. Determine if graphs are functions.
8.F.A.1
8.F.B.4
Identify properties of functions represented in graphs.
8.F.A.3
Define and graph linear and nonlinear functions.
8.F.A.1
8.F.A.3
Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.
8.F.A.2
Compare functions represented in different ways (Part 1).
8.F.A.2
Compare functions represented in different ways (Part 2).
Key: Major Cluster Supporting Cluster Additional Cluster
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