Student Guide

Questions 1–6 (SG p. 53)1. 20 inches

2. 21 square inches

3. Answers may vary. Solution range should be6–7 square inches. Students may questionwhether the center square (i.e., the one withthe circle in it) is covered by water or not.

4. Answers will vary. Solution range should be14–15 square inches. See the answer forQuestion 3 above.

5.* Answers will vary. Some possible solutions areshown in Figure 4 in the lesson.

6.* Answers will vary. Possible response: First Itook 8 square-inch tiles because I knew Ineeded an area of 8 square inches. Then Imade a shape that was 2 rows of 4 tiles.

I counted the edge around my shape and it was12 inches. The playground needed to have aperimeter of 14 inches so I changed the shapeby moving 2 tiles. I counted the edge again.

My new perimeter was 14 inches but the areawas still 8 square inches.

1 2 3

41 2 35

4 5 6 7 7

12 11 10 9 8

6

8

14

13

1 2 3 4

1 2 3 4

5 6 7 8

10 9 8 7

5

6

12

11

The perimeter is the edge all around a two-dimensionalshape; it is also the distance all the way around theshape.

Here is a picture of a one-square-inch tile.

Each side of this tile is one inch long.The perimeter of the tile is 4 inches.The area of the tile is one-square inch.

Area is the amount of surface that is needed to cover something. The size of anobject or shape is often measured by counting the number of unit squares thatcan be placed on top of the shape to cover it. This is called the area of the object.

A grid of square-inch tiles has been drawn on the diagram of the fountain. You canuse it to measure the distance the ants walked to travel the perimeter of thefountain. The grid of tiles can also help you measure the square inches needed tocover the area of the fountain.

� 1. Find the perimeter of the fountain.

� 2. Find the area of the fountain.

3. Find the area of the fountain that is covered by water.

4. Find the area of the fountain that is not covered by water.

Use the Perimeter-Area Puzzles pages in the Student Activity Book to practicemeasuring the perimeter and area of different shapes.

Check-In: Questions 5–6

The ants of Antopolis want to build a playground with an area of 8 square inches.They have ordered enough material to build a 14-inch fence around it.

5. Draw a design for a playground for the ants which has an area of 8 squareinches and a perimeter of 14 inches. (They want the young ants to be ableto walk from one part of the playground to any other part without goingoutside the perimeter.)

6. Write a paragraph that explains how you chose your playground design.Use expectations on the Math Practices page to help you write yourparagraph. Look in your Student Guide Reference section.

Continue to practice finding area and perimeter using the Measuring Areaand Perimeter pages in the Student Activity Book.

Investigating Perimeter and Area SG • Grade 4 • Unit 2 • Lesson 1 53

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Student Guide - Page 53

*Answers and/or discussion are in the lesson.

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TG • Grade 4 • Unit 2 • Lesson 1 • Answer Key   1

Answer Key • Lesson 1: Investigating Perimeter and Area

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Student Activity Book

Perimeter-Area Puzzles (SAB pp. 11–12)

Shape Perimeter inInches

Area inSq. Inches

A

B

C

D

E

F

G

16

12

16

10

16

12

12

8

6

7

6

7

5

9

Investigating Perimeter and Area SAB • Grade 4 • Unit 2 • Lesson 1 11

Name Date

Perimeter–Area PuzzlesUse square-inch tiles to measure the area for each shape. Use a ruler tomeasure the perimeter. Record your measurements on the data table at thebottom of the next page.

B.

A.

C.

D.

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Student Activity Book - Page 11

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SAB • Grade 4 • Unit 2 • Lesson 1 Investigating Perimeter and Area12

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Shape Perimeter in Inches Area in Square Inches

A

B

C

D

E

F

G

E.

G.F.

Student Activity Book - Page 12

2 TG • Grade 4 • Unit 2 • Lesson 1 • Answer Key

Answer Key • Lesson 1: Investigating Perimeter and Area

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Student Activity Book

Measuring Area and Perimeter

Questions 1–8 (SAB pp. 13–15)1. Perimeter: 12 cm

Area: 8 square cm

2. Perimeter: 18 cmArea: 10 square cm

3. Perimeter: 16 cmArea: 12 square cm

4. Perimeter: 16 cmArea: 12 square cm

5. Area: 8 square inches. Perimeter will vary;largest possible perimeter is 18 inches;smallest possible is 12 inches.

6. Area: 12 square cm

Perimeter: 16 cm

7. Area: 8 square inches. The only possiblerectangles are 8 � 1, perimeter 18 inches; and4 � 2, perimeter 12 inches.

8. The area is the same; the perimeter is different.

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SAB • Grade 4 • Unit 2 • Lesson 1 Investigating Perimeter and Area14

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Check-In: Questions 5–85. Use 8 square-inch tiles to make

and draw a shape that is not arectangle. Put the tiles togetheredge to edge. Find the area andperimeter.

6. Find the area and the perimeter of the shape below.Draw the lines in if it helps you.

Area:

Perimeter:

1 sq cm 1 cm

edge to edgeedge to edge

not

Area:

Perimeter:

Student Activity Book - Page 14

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Investigating Perimeter and Area SAB • Grade 4 • Unit 2 • Lesson 1 15

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7. Use 8 square-inch tiles to make and draw a rectangular shape. Put the tilestogether edge to edge. Find the area and perimeter.

8. Compare the two shapes you made in Questions 5 and 6. What is thesame? What is different?

Area:

Perimeter:

Measuring Area and PerimeterCheck-In: Questions 5–8

Feedback Box CheckInExpectation Comments

Make shapes with a given area. [Q# 5 and 7]

Find the perimeter:

• of a rectangle. [Q# 7]

• of an irregular shape. [Q# 5 and 6]

Find the area:

• of a rectangle. [Q# 7]

• of an irregular shape. [Q# 5 and 6]

5

6

7

Student Activity Book - Page 15

Measuring Area andPerimeter

Look at the shapes in Questions 1–4. Use the information you are given tofind the perimeter and area of each shape.

1. Perimeter:

Area:

2. Perimeter:

Area:

3. Perimeter:

Area:

4. Perimeter:

Area:

2 cm

5 cm

1 cm

1 cm1 cm

2 cm

2 cm2 cm

6 cm

6 cm

2 cm2 cm

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Investigating Perimeter and Area SAB • Grade 4 • Unit 2 • Lesson 1 13

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Student Activity Book - Page 13

TG • Grade 4 • Unit 2 • Lesson 1 • Answer Key   3

Answer Key • Lesson 1: Investigating Perimeter and Area

Student Activity Book

Homework

Questions 1–5 (SAB pp. 16–18)1–2. A. Perimeter: 14 cm Area: 7 square cm

2 + 2 + 1 + 3 + 1 + 5 = 14 cm

B. Perimeter: 14 cm Area: 6 square cm6 + 6 + 1 + 1 = 14

C. Perimeter: 16 cm Area: 10 square cm1 + 1 + 3 + 2 + 3 + 1 + 1 + 4 = 16

D. Perimeter: 12 cm Area: 8 sq. cm4 + 2 + 4 + 2 = 12

3. Shape X Shape YArea: 9 sq. cm Area: 8 sq. cmPerimter: 12 cm Perimeter: 12 cm

Shapes X and Y have the same perimeter butShape Y has a smaller area.

4. Possible response:

Perimeter: 12 centimeters

5. Possible response:

Area: 20 square inchesPerimeter: 20 inches

Investigating Perimeter and Area SAB • Grade 4 • Unit 2 • Lesson 1 17

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Name Date

3. Find the area and perimeter for Shapes X and Y.

Compare Shape X and Shape Y. What is different and what is the same?

4. Make and draw a shape that is not a rectangle and has an area of 7 square

inches. What is the perimeter of your shape?

Area:

Perimeter:

Area:

Perimeter:

Shape X Shape Y

5. Draw a shape with an area of 20 square inches and a perimeter of at least18 inches.

Student Activity Book - Page 17 Student Activity Book - Page 18

1. Calculate the perimeter of each shape. Write number sentences toshow how you found the perimeters.

2. After you have found the perimeter of each shape, find the area for each.Write the area inside the shape. What label will you use?

A. B.

C. D.

Perimeter:

Perimeter:

Perimeter:

Perimeter:

Dear Family Member:

Your child has been learning to find the perimeter and area of shapes. In thisassignment, help your child find the perimeter by adding the measurementsmarked around the sides of the shape or by using the grid. The area can be foundby counting the number of square centimeters that would fit inside the shape.

Name Date

SAB • Grade 4 • Unit 2 • Lesson 1 Investigating Perimeter and Area16

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Student Activity Book - Page 16

4 TG • Grade 4 • Unit 2 • Lesson 1 • Answer Key

Answer Key • Lesson 1: Investigating Perimeter and Area

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