CCSS.Math.Content.8.F.B

CCSS.Math.Content.8.F.B is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.8.F.B.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...

• CCSS.Math.Content.8.F.B.5

  Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or ...

01

What Students Need to Do

Students show how two quantities are connected using tables, graphs, equations, and verbal descriptions. They identify rates and starting values in linear situations. They also sketch and interpret graphs that show changing behavior.

02

What Mastery Looks Like

Students can build a table, graph, or equation from a situation and move accurately between those forms. They can explain the rate of change, starting value, and meaning of key graph features in context.

03

Common Misconceptions

Students may swap the input and output quantities or treat slope as the starting value. They often assume every relationship is linear. Some read a graph as a picture rather than a record of change over time.

04

How to Assess It

Give this exit ticket: “A tank starts with 12 liters and drains 2 liters each minute. Make a table, write an equation, and explain the slope and intercept.”

1. 01

   Have pairs stack paper cups, measure each stack, then make a table, graph, and equation relating cup count to height.

2. 02

   Show two graphs of a bathtub filling, pausing, and draining, then ask students to defend which graph matches the story.

3. 03

   Give groups matching cards with situations, tables, graphs, and equations, and award points for complete sets with correct explanations.

4. 04

   Compare two phone plans with monthly fees and data charges, then find when each plan costs less.

• CCSS.Math.Content.7.RP.A.2

  Recognize and represent proportional relationships between quantities.

• CCSS.Math.Content.HSF-BF.A.1

  Write a function that describes a relationship between two quantities

• CCSS.Math.Content.HSF-BF.A

  Build a function that models a relationship between two quantities

• CCSS.Math.Content.HSF-IF.B.4

  For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...