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All courses Math Foundations · MF.GR.4 43 of 60
Distinguish additive change from multiplicative change in tables, graphs, and contexts.

Tell whether the change is additive or multiplicative

Problem
Analyze the consecutive changes in \(5,~9,~13,~17\). Classify the pattern as additive or multiplicative and state the repeated amount or factor.
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Hint

Compare neighboring terms by subtracting: 9−5, 13−9, and 17−13.

Additive patterns have the same difference each step. Multiplicative patterns have the same factor each step.

Solution walkthrough

01

Compute consecutive differences

\[9-5=4;~13-9=4;~17-13=4\]

Every neighboring pair has the same positive difference four.

02

Check the repeated operation

\[5+4=9;~9+4=13;~13+4=17\]

Adding four reproduces each transition in the pattern.

03

Classify the pattern

\[\text{constant}~\text{difference}~⇒~\text{additive}\]

A pattern generated by a repeated addition has additive change.

04

Report classification and amount

\[\text{Additive};~\text{add}~4~\text{each}~\text{time}.\]

The answer names both the change type and its repeated amount.

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Another way

  1. Label each arrow between terms +4 and observe that all arrows agree.

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Common mistake

Do not use 17-5=12 as the repeated amount; compare consecutive terms.

Solution walkthrough video