CCSS.Math.Content.8.F.B.5
The standard
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Common Core State Standards for Mathematics · Functions
What this standard means
Students need to read a graph as a story. They should describe where values go up, go down, stay flat, change at a steady rate, or curve. They also need to work the other way, taking a verbal situation and sketching a reasonable graph without needing exact numbers.
Mastery looks like clear matching between the graph and the situation, with correct labels and sensible shapes. Students often get stuck reading left to right, mixing up height with slope, or thinking every graph must be a straight line. They may also add extra details that the description does not support.
Ways to teach it
- Have students walk in front of a motion sensor and match their movement to distance-time graph cards.
- Ask: Describe a graph of your phone battery from morning to bedtime, including flat, increasing, and decreasing parts.
- Show four small graphs and ask students to label each interval as increasing, decreasing, constant, linear, or nonlinear.
- Use a temperature graph from a school day and have students explain what likely happened at each section.
Plan a lesson for CCSS.Math.Content.8.F.B.5
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Related standards
- CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- 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...
- CCSS.Math.Content.HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- 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...