Area

Lesson 11

Math

Unit 4

3rd Grade

Lesson 11 of 14

Objective


Apply the distributive property as a strategy to find the total area of a large rectangle. 

Common Core Standards


Core Standards

  • 3.MD.C.7.C — Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Foundational Standards

  • 3.OA.B.5

Criteria for Success


  1. Look for structure to understand that the area of a rectangle with whole-number side lengths $$a$$ and $$b+c$$ is the sum of $$a\times b$$ and $$a\times c$$, writing equations to represent this relationship (MP.7). 
  2. Make use of structure by breaking apart a rectangle into two smaller rectangles, finding the area of those smaller rectangles, then adding those areas together to get the area of the composed rectangle (MP.7).
  3. Use area models to represent the distributive property in mathematical reasoning (MP.3). 
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Anchor Tasks


Problem 1

Andre is finding the area of this rectangle.

Andre writes 6 × 7. He marks the rectangle like this:

He then writes:

 

6 × (5 + 2)
(6 × 5) + (6 × 2)
30 + 12
42

a.   How are the numbers in Andre’s expressions related to his diagram?

b.   How are 6 × 7 and 6 × (5 + 2) related to each other? What about 6 × 7 and (6 × 5) + (6 × 2)?

Guiding Questions

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References

Illustrative Mathematics Introducing the Distributive Property

Introducing the Distributive Property, accessed on Jan. 3, 2019, 11:51 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.

Modified by Fishtank Learning, Inc.
Illustrative Mathematics Grade 3 Unit 4 Lesson 10 Activity 1

Grade 3 Unit 4 Lesson 10 Activity 1, accessed on Oct. 18, 2022, 10:12 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.

Modified by Fishtank Learning, Inc.

Problem 2

Write three expressions that represent the area of the rectangle below.

Guiding Questions

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Problem 3

Draw a rectangle on the grid below that matches the given expression.

Guiding Questions

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References

Achievement First Grade 3, Unit 7, Lesson 8 (2018-2019)Workshop, Question #3

Grade 3, Unit 7, Lesson 8 (2018-2019) is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed Jan. 2, 2019, 3:23 p.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • What three expressions did you write to represent the area model in #4a? How are each of those expressions represented in the area model? 
  • What rectangle did you draw for #5? What other expressions could you write to represent its area? 
  • Why are both Tori and Leo’s expressions correct in #6? What other expression could they have written to represent the area? 
  • How did you find the total area for Mr. Nuccio’s sandwich shop after the new section was added? What made this problem different from the previous ones?

Target Task


Problem 1

Use the rectangle below to answer Parts (a) and (b).

a.   Which equation represents the total​ number of square feet represented by the rectangle above?

  1. a.   4 × (3 + 2) = 4 + 3 + 2

  2. b.   4 × (3 + 2) = 4 × 3 × 2

  3. c.   4 × (3 + 2) = (4 × 3) × (4 × 2)

  4. d.   4 × (3 + 2) = (4 × 3) + (4 × 2)

b.   What is the area of the rectangle above? Show your work.

Student Response

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Problem 2

Draw a rectangle that matches the expression in the grid underneath. Then, explain how the diagram represents the expression. 

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 10

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Lesson 12

Lesson Map

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

Topic A: Understanding Concepts of Area

Topic B: The Distributive Property and Composite Area

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