NY Next Generation Math NY-8.F.2

Math8th GradeDefine, evaluate, and compare functions.

The Standard

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students compare properties of two functions even when the functions are shown in different forms. They extract comparable information from equations, graphs, tables, and verbal descriptions.

What Mastery Looks Like

A student finds a rate of change of 3 and an initial value of 2 from a table, then compares them with y = 2x + 5. The student states which function has the greater rate and which starts higher.

Common Misconceptions

Students may compare surface features of the representations instead of the same function property. They may also confuse initial value with rate of change or compare table outputs without accounting for inputs.

How to Assess It

Show Function A as the table (0, 2), (1, 5), (2, 8) and Function B as y = 2x + 5. Ask which has the greater rate and which has the greater initial value.

Lesson moves

Ways to Teach It

  1. Plot a function from a table on transparent grid paper and lay it over a second function’s graph for comparison.

  2. Ask students which information they need before comparing a graphed function with one described in words.

  3. Match equation, graph, table, and description cards, then rank the represented functions by one named property.

  4. Compare two phone plans shown in different formats and decide which has the lower starting cost and usage rate.

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