Numerical and Algebraic Expressions

Lesson 9

Math

Unit 5

6th Grade

Lesson 9 of 12

Objective


Write equivalent expressions using the distributive property (Part 1).

Common Core Standards


Core Standards

  • 6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
  • 6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Foundational Standards

  • 4.NBT.B.5

Criteria for Success


  1. Use area models and tape diagrams to write equivalent expressions.
  2. Understand that when a sum is multiplied by a factor, then every term in the sum is multiplied by the factor. 
  3.  Apply the distributive property to write equivalent expressions.
  4. Factor an expression to write it as a product of a number and a sum.

Tips for Teachers


  • In Unit 3 Lesson 17, students rewrote sums of two whole numbers with a common factor as multiples of a sum of two relatively prime numbers. For example, they rewrote $${ 56 + 24}$$ as $${8(7 + 3)}$$. This concept supports the aims of this lesson and could be an appropriate warm-up to this lesson. 
  • Lessons 9 and 10 focus on writing equivalent expressions using the distributive property. Lesson 9 introduces the concept using area and tape diagrams involving sums. Lesson 10 continues the concept with expressions of difference.
  • Students are familiar with the concepts of the distributive property, but have not yet used the formal language. As properties of operations play an increasing role in middle school algebra concepts, having the language to use to describe these properties will beneficial. Use Lessons 9 and 10 as opportunities to introduce and use the term "distributive property".  
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Anchor Problems


Problem 1

Two rectangles were combined to create a larger rectangle, as shown below.

Write as many expressions as you can to represent the area of the larger, outer rectangle.

Guiding Questions

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Problem 2

Four rectangles are shown in the table below. Some include measurements for length and width, others include measurements for the areas of the smaller rectangles. Fill in the table with expressions to represent length and width, and two ways to show the area of each of the larger rectangles. 

Guiding Questions

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Problem 3

The students in Mr. Nolan's class are writing expressions for the perimeter of a rectangle of side length $$l$$ and width $$w$$. After they share their answers, the following expressions are on the board:

Sam:     $$2(l+w)$$

Joanna:     $$ l+w+l+w$$

Kiyo:     $$2l+w$$

Erica:     $$ 2w+2l$$

Which of the expressions are correct and how might the students have been thinking about finding the perimeter of the rectangle?

Guiding Questions

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References

Illustrative Mathematics Rectangle Perimeter 2

Rectangle Perimeter 2, accessed on Dec. 19, 2017, 11:10 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

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Target Task


For each problem, draw a diagram to represent the expression. Then use the diagram to write an equivalent expression.

a.   $${4(2m+n)}$$

b.   $${5x+15}$$

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 8

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Lesson 10

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Numerical Expressions with Exponents

Topic B: Introduction to Algebraic Expressions

Topic C: Equivalent Expressions & Applications

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