Area

Lesson 13

Math

Unit 4

3rd Grade

Lesson 13 of 14

Objective


Recognize area as additive. Find the area of a composite figure when not all dimensions are given.

Common Core Standards


Core Standards

  • 3.MD.C.7.D — Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Criteria for Success


  1. Find missing side lengths of rectangles by using the idea that opposite sides of a rectangle are equal and that length is additive. 
  2. Find the area of a composite figure that can be decomposed into two rectangles with some missing side lengths by breaking it into two rectangles, finding any missing side lengths, finding the area of each rectangle given their respective side lengths, and adding those areas together (MP.5).

Tips for Teachers


Similar to Lesson 12, students might suggest covering a composite figure with a larger rectangle and subtracting the voided area, e.g. by computing $$(6\times9)-(3\times5)$$ for Anchor Task #2. This is certainly a valid strategy but not one that all students must show success with. Thus, discuss it in this lesson if students seem ready to talk about it or many students naturally gravitate toward it, or wait until a later lesson (if at all) to introduce it.

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Anchor Tasks

25-30 minutes


Problem 1

Jakayla is trying to label all of the sides of the shape below. Help her figure out what the length of the sides labeled A and B are.

Guiding Questions

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Student Response

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References

Achievement First Grade 3, Unit 7, Lesson 11 (2017-2018)Pose the Problem

Grade 3, Unit 7, Lesson 11 (2017-2018) 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. 3, 2019, noon.

Modified by Fishtank Learning, Inc.

Problem 2

Find the area of the following figure:

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • How were the two problems in #3 different? 
  • What are the two ways you decomposed Antonio’s garden in #4? Did both methods result in the same total area? 
  • Was anyone able to solve #5 without needing to find an unknown side length? How? 
  • What decomposition does Sami’s equation represent in #6? What about Razina’s? Lukas’s?

Target Task

5-10 minutes


A model of a patio is shown.

Find the area, in square meters, of the patio. Explain your answer using an equation or equations.

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Recognize area as additive. Find the area of a complex composite figure.

Lesson 14
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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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