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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read functions shown as equations, graphs, tables, or written descriptions. They identify comparable properties, then decide how the functions are alike or different.
What Mastery Looks Like
- Students find properties such as rate of change and initial value from equations, graphs, tables, and descriptions. They compare those properties and support the comparison with numbers or clear statements.
Common Misconceptions
- Students may compare table outputs without checking whether the input values match. They may confuse the initial value with the rate of change or misread a graph's scale.
How to Assess It
- Give a graph and a table for two linear functions. Ask, "Which has the greater rate of change, and what evidence proves your answer?"
Lesson moves
Ways to Teach It
Give pairs graph cards, equation cards, table cards, and description cards, then have students match functions with the same rate and initial value.
Ask students to explain which of two differently represented functions grows faster and cite one calculation or graph feature as evidence.
Run a comparison relay where teams calculate rates of change from mixed representations and place greater than, less than, or equal signs.
Compare two phone plans shown as an equation and a table, then decide which starts cheaper and which cost grows faster.
Free download
Printable 8.F.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.F.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.F.A.1
Students must understand inputs, outputs, and graphs as function pairs before comparing function properties across equations, tables, graphs, or descriptions.
- CCSS.Math.Content.7.RP.A.2b
Finding unit rates across tables, graphs, equations, and words supports comparing function rates and features across different representations.
- CCSS.Math.Content.8.EE.B.5
Comparing unit rates and slopes across graphs, tables, and equations supports later comparisons of function properties across representations.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
- 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.
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