CCSS.Math.Content.8.F.A.2
The standard
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Common Core State Standards for Mathematics · Functions
What this standard means
Students need to compare two functions even when they are shown in different forms, such as an equation, graph, table, or word situation. They should identify key features like rate of change, starting value, increasing or decreasing behavior, and specific input-output pairs.
Mastery means students can translate each representation enough to make a fair comparison and explain their reasoning with numbers. Students often get stuck finding slope from a table or graph, confusing initial value with rate of change, or comparing outputs without checking that the inputs match.
Ways to teach it
- Give pairs a graph card and equation card, then have them calculate slope and intercept and decide which function grows faster.
- Ask students to write: How can you compare two functions when one is a table and one is a story?
- Show a table and a graph on the board, then ask students to write which has the greater rate of change and one reason.
- Compare two phone plans, one shown by an equation and one by a fee table, and decide which costs more after different months.
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Related standards
- CCSS.Math.Content.HSF-IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- 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 ...
- CCSS.Math.Content.HSF-IF.C.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- CCSS.Math.Content.8.F.A
Define, evaluate, and compare functions.