# 7. Cell Phone Conundrum: Understanding That the Distributive Property Holds for Variable Expressions (C)

teaches Common Core State Standards CCSS.Math.Content.7.EE.A.1 http://corestandards.org/Math/Content/7/EE/A/1
teaches Common Core State Standards CCSS.Math.Content.7.EE.A.2 http://corestandards.org/Math/Content/7/EE/A/2
teaches Common Core State Standards CCSS.Math.Content.7.EE.B.4a http://corestandards.org/Math/Content/7/EE/B/4/a
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4

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Lesson objective:  Students will understand that the distributive property holds for variable expressions as well as numerical expressions.

Students bring prior knowledge of equivalent expressions from 7.EE.A.1. This prior knowledge is extended to distributive property and rational number coefficients as students write expressions to model a cell phone plan. A conceptual challenge students may encounter is thinking that the multiplier is only applied to one number in the sum instead of the entire sum.

The concept is developed through work with an area model, which helps to show that when a number is multiplied by a sum, that number multiplies by each number in the sum.

This work helps students deepen their understanding of equivalence because we can use the distributive property to generate equivalent expressions.

Students engage in Mathematical Practice 4 (Model with mathematics) as they write an expression to model a cell phone plan.

Key vocabulary:

• distributive property
• equivalent expressions
• rational numbers

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