T fa lb e Co t tn n seo

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Format of Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Suggestions for Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Additional Materials for Review . . . . . . . . . . . . . . . . . . . . . . 9

Annotated Answer Key and Extension Activities . . . . . . . . . 10

Reproducible Bonus Lessons . . . . . . . . . . . . . . . . . . . . . . . 84

Bonus Lessons Answer Key . . . . . . . . . . . . . . . . . . . . . . . . 94

Reproducible Tool Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

ISBN 978-0-8454-7643-7

Copyright © 2013 The Continental Press, Inc.

Excepting the designated reproducible blackline masters, no part of this publication may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All rights reserved. Printed in the United States of America.

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Pages 105 and 106Lesson 22 Area and Perimeter

ObjectiveTo review finding the area and perimeter of rectangles and using them to solve problems

FOcus LessOnThe Focus Lesson question leads students to find the unknown width of a rectangle, given the area and the length. Students should know the formula for the area of a rectangle. Guide them to recognize that they need to use the information they know, the area and the length, to solve the equation for the missing width.

Guided PracticeStudents will find the perimeter of a rectangle given the lengths. Students should recognize two ways to find the perimeter of the porch and understand how to use the information in the problem to find the answer.

Vocabularyarea: the amount of space inside a figure, measured in square unitsPerimeter: the distance around a figure

Common Core Learning Standard4.Md.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

3

18 sq ft

18 5 6 3 w

division

Area 5 length 3 width

Divide 18 by 6.

6 ft

10 ft5 ft

P 5 2 3 length 1 2 3 width

P 5 2 3 10 1 2 3 5

30

4.Md.3

4.Md.3

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Pages 107 and 108Lesson 22 independent Practice

answer ratiOnaLe1 All of the rectangles have perimeters of 20 feet, so the

gardener can use the 20 feet of fencing. Multiplying the length and width gives the area of each rectangle: 5 3 5 5 25 square feet, 6 3 4 5 24 square feet, 7 3 3 5 21 square feet, 8 3 2 5 16 square feet, and 9 3 1 5 9 square feet. Only options A and C have areas greater than 22 square feet.

2 Multiplying the length and width gives the area of each rectangle. The rectangles are 3 cm by 8 cm, 4 cm by 6 cm, 1 cm by 24 cm, and 2 cm by 12 cm. Students who chose 3 cm by 9 cm, 4 cm by 8 cm, 2 cm by 10 cm, and 1 cm by 11 cm are calculating the perimeter instead of area.

3 The perimeter of a rectangle is found by adding all four sides together. Rectangle A has a width of 2 m: 5 m 1 2 m 1 5 m 1 2 m 5 14 m. Rectangle B has a width of 1 m: 7 m 1 1 m 1 7 m 1 1 m 5 16 m. Rectangle C has a width of 3 m: 8 m 1 3 m 1 8 m 1 3 m 5 22 m. Rectangle D has a width of 4 m: 6 m 1 4 m 1 6 m 1 4 m 5 20 m.

4 The possible lengths are 13 feet, 14 feet, and 15 feet. With these lengths, the perimeter of the poster could be 10 1 13 1 10 1 13 5 46 feet, or 10 1 14 1 10 1 14 5 48 feet, or 10 1 15 1 10 1 15 5 50 feet. With a length of 11 feet, the perimeter would be 10 1 11 1 10 1 11 5 42 feet. With a length of 12 feet, the pe-rimeter would be 10 1 12 1 10 1 12 5 44 feet. These perimeters are too small. With a length of 16 feet, the perimeter would be 10 1 16 1 10 1 16 5 52 feet, which is too large.

4.Md.3dOK: 2

4.Md.3dOK: 2

4.Md.3dOK: 2

4.Md.3dOK: 2

8 cm 6 cm

24 cm

12 cm

2 m1 m3 m4 m

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Page 109Lesson 22 independent Practice

5 The rectangles are 1 inch by 40 inches, 2 inches by 20 inches, 4 inches by 10 inches, and 5 inches by 8 inches. Since each rectangle has an area of 40 square inches, the length and width of each must be a factor pair of 40.

6 Nathan is not correct. Students should recognize that Nathan used the perimeter formula instead of the area formula, and then wrote the perimeter using square units. Students who say that Nathan is correct are confusing perimeter with area.

Hands-On Extension Activity Give students geoboards and some rubber bands. Ask the students to make a rectangle with a pe-rimeter of 24 units and to determine its area. Then have them make as many rectangles as possible

with a perimeter of 24 units and note the area of each. Have them make as many rectangles as possible with the area of the first rectangle and to note their perimeters.

4.Md.3dOK: 2

4.Md.3dOK: 2

Nathan is not correct. He used the perimeter formula and found the perimeter of the figure. Then he wrote the perimeter in square feet. The area of the figure is actually 12 3 7 5 84 square feet.

40 inches

10 inches20 inches

8 inches

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