Wyoming Math F.LE.2

MathGrades 9–12Linear, Quadratic, and Exponential Models

The Standard

Construct linear and exponential functions using a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

2023 Wyoming Mathematics Content and Performance Standards · Construct and compare linear, quadratic, and exponential models and solve problems.

Teacher's field guide

What This Standard Means

What Students Need to Do: Students write linear and exponential equations from graphs, descriptions, and input-output pairs. They find the starting value and either the amount added each step or the multiplier.
What Mastery Looks Like: Given a model type and two points, students write a rule that works for both, even when neither input is zero. They use a table to check for equal differences or equal ratios.
Common Misconceptions: Students may look for a fixed amount added in an exponential table instead of a fixed multiplier. They may use the first output as the starting value even when the first input is not zero.
How to Assess It: Give two tables: A has (0, 3), (1, 6), (2, 9); B has (0, 3), (1, 6), (2, 12). Ask students to name each model and write its equation.

Lesson moves

Ways to Teach It

Plot (0, 3), (1, 6), and (2, 12) on graph paper, then use the points to write an exponential rule.
Ask: Why do the outputs 3, 6, 9 suggest a different rule from 3, 6, 12? Have students explain using differences and ratios.
Give (1, 6), (2, 12) labeled exponential and (1, 6), (2, 9) labeled linear; have pairs race to write both rules.
Compare a $50 account gaining $10 each week with one growing 5% each week; write both balance rules and predict week four.

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