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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

694 Unit 9 Measurement

Advance PreparationDraw a 2 ft × 3 ft rectangle on posterboard or on the board prior to the beginning of the Lesson.

Teacher’s Reference Manual, Grades 1– 3 pp. 158, 159

AreaObjectives To provide experiences with the concept of area,

distinguishing between area and perimeter, and finding areas

of rectangular figures by partitioning and counting squares.

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Key Concepts and Skills• Count square centimeters. 

[Number and Numeration Goal 1]

• Partition rectangles and count unit squares

to find the areas. 

[Measurement and Reference Frames Goal 2]

• Make rectangles. 

[Geometry Goal 2]

Key ActivitiesChildren discuss the concept of area. They

compare area and perimeter, including

units used for each measure. They identify

rectangles with the same area but

different perimeters.

Ongoing Assessment: Informing Instruction See page 696.

Key Vocabularysurface

MaterialsMath Journal 2, pp. 222A and 222B

Home Link 9 �6

My Reference Book, pp. 68, 69, 69A, and

69B

per group: 3 copies of Math Masters, p. 434

or 3 sheets of centimeter grid paper �

straightedge � ruler � half-sheet of paper �

checkerboard (optional) � centimeter cubes

(optional)

Playing the Equivalent Fractions Game or Fraction Top-ItMath Journal 2, pp. 198, 199, 203,

and 204

Fraction Cards (2 sets cut from Math

Journal 2, Activity Sheets 5 and 6) �

counters (optional)

Children identify equivalent fractions

and compare pairs of fractions.

Math Boxes 9 �7Math Journal 2, p. 223

Children practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Operations and Computation Goal 4]

Home Link 9 �7Math Masters, p. 283

Children practice and maintain skills

through Home Link activities.

READINESS

Finding the Areas of Geoboard Rectanglesgeoboard � rubber bands � pennies or

counters (optional)

Children create rectangles on a geoboard

and then find the areas of those rectangles.

ENRICHMENTFinding the PerimeterMath Masters, p. 434

centimeter grid paper (optional)

Children draw as many different

rectangles and squares as possible that

have a perimeter of 12 centimeters.

EXTRA PRACTICE

Finding the Areas of Block LettersMath Masters, p. 284

checkerboard (optional)

Children find the areas of block letters

by counting centimeter squares.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 142

Children add the term area to their Math

Word Banks.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

694_EMCS_T_TLG2_G2_U09_L07_57685X.indd 694694_EMCS_T_TLG2_G2_U09_L07_57685X.indd 694 3/9/11 2:39 PM3/9/11 2:39 PM

Lesson 9�7 695

Links to the FutureThis is a beginning exposure to finding area.

Children practice partitioning rectangles

and counting square units to find the area.

Partitioning rectangles and counting unit

squares to find the area of rectangular

shapes is a Grade 2 Goal. Describing and

using strategies to estimate and calculate

area is a Grade 4 Goal. Using a formula to

calculate area is a Grade 5 Goal.

Count the squares to find the area.

Try It TogetherDraw a shape that has a perimeter of 10 inches.Compare your shape with a partner’s shape.

The area of the shape is 15 square centimeters.

Measurement

Sometimes you want to know the amount ofsurface inside a shape. This amount of surfaceinside a shape is the area of the shape.

Note

Use square units for thearea of a shape.

1514131210986531

24

711

Each square is 1 square centimeter.

My Reference Book, p. 69

Student Page

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Ask children to share their solution strategies. Some possibilities: Make an 8-by-8 array; count by 8s; find 8 × 8 from memory, by using a facts table, or by using a calculator.

� Developing the Concept of Area WHOLE-CLASSDISCUSSION

(My Reference Book, pp. 69 and 69A)

Begin an informal discussion about surfaces. To support English language learners, record the key ideas on the board. Ask: What is a surface? The top or outside of an object What are some examples of a surface? A tabletop, the floor, a checkerboard, the cover of a book, the top of a lake, and so on

Most surfaces have boundaries, or borders. Boundaries give a surface its shape. Use the examples from the question above to help children understand boundaries.

When we measure the amount of surface inside a shape, we are finding the area of the shape. As a class, read about area in My Reference Book, pages 69 and 69A.

Remind children of the different ways in which they have tiled surfaces. (See Exploration E in Lesson 4-7.) They covered surfaces without gaps or overlaps using multiples of identical shapes. Point out that they were finding the areas of the surfaces.

In Exploration B in Lesson 9-6, children measured area using a square grid. Area can be measured in square “standard” units, such as square inches (squares measuring 1 inch on each side), square feet, square centimeters, or square meters.

ELL

Getting Started

Home Link 9�6 Follow-UpAsk volunteers to share their findings. Have children share strategies for one or two of the Practice problems.

Math MessageA checkerboard has 8 rows of squares. There are 8 squares in each row. How many squares does the checkerboard have in all? 64 squares

Write or draw a picture to show your strategy on a half-sheet of paper.

Mental Math and Reflexes Pose problems like the following:Which fraction is greater?

6

_ 10 or

3

_ 10

6

_ 10

1

_ 2 or

3

_ 4 3

_ 4

1

_ 2 or

5

_ 8 5

_ 8

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696 Unit 9 Measurement

Rectangles with an area of 12 square centimeters

Finding Area continuedLESSON

9 �7

Date Time

For each shape, use the tick marks to draw lines to show square units. Then count the squares to find the area.

5.

3 in.

1 in.

1 in.

2 in

.

1 in

.1 in.

2 in.

1 in. 6.

1 cm

2 cm

3 cm

3 cm

3 cm

6 cm

Area = sq in. Area = sq cm

7. Draw tick marks and line segments to make square units. Then count the squares to find the area.

6 cm

4 cm

Area = sq cm

Try This

5 15

24

222A_222B_EMCS_S_SMJ_G2_U09_57640X.indd 222B 3/24/11 3:07 PM

Math Journal 2, p. 222B

Student Page

Finding AreaLESSON

9 �7

Date Time

For each shape, count the square centimeters to find the area.

1. 2.

Area = sq cm Area = sq cm

Use the tick marks to draw lines to show square units. Then count the squares to find the area.

3. 3 in.

2 in

.

4. 3 cm

4 cm

Area = sq in. Area = sq cm

12 18

6 12

222A_222B_EMCS_S_SMJ_G2_U09_57640X.indd 222A 3/24/11 3:07 PM

Math Journal 2, p. 222A

Teaching Master

� Comparing Units Used to WHOLE-CLASSDISCUSSION

Measure Area and Perimeter(My Reference Book, p. 68)

Refer back to the Math Message problem. Remind children that the checkerboard has 64 squares. Explain that the sides of each square on the checkerboard are 1 inch long. Each square is 1 square inch. The area of the checkerboard is 64 square inches.

Read My Reference Book, page 68 to review perimeter. Ask: How would you find the perimeter of the checkerboard? Add the lengths of all the sides How long is each side of the checkerboard? 8 inches What is the perimeter of the checkerboard? 32 inches How did you find the perimeter? Sample answers: I added 8 + 8 + 8 + 8; I multiplied 8 × 4.

Call attention to the difference between the units for area and the units for perimeter.

● Because 32 is half of 64, does it make sense to say that the perimeter of the checkerboard is half its area? No; perimeter and area are measured using different units and cannot be compared in this way.

● How are the units for measuring area different from the units used for measuring perimeter? The units for perimeter measure the distance between points along a line segment; the units for area measure a surface.

� Investigating Perimeter SMALL-GROUP ACTIVITY

and Area(Math Masters, p. 434)

Distribute several copies of Math Masters, page 434 or sheets of centimeter grid paper to each group. Ask children to draw as many different rectangles as they can whose area is 12 square centimeters each. Ask them to find the perimeter of each rectangle.

After children complete this task, bring the class together and go over the answers. There are three rectangles whose sides have whole-number lengths. (See margin.) Some children may suggest other rectangles, such as 1 1 _ 2 cm × 8 cm.

� Using Square Units WHOLE-CLASSDISCUSSION

to Find Area(My Reference Book, p. 69B)

As a class, read My Reference Book, page 69B. Draw and label a 2 ft × 3 ft rectangle on the board. First, draw tick marks at each 1 foot measure along the sides of the rectangle. Then, draw lines to connect the tick marks to make square feet. See below.

3 ft

2 ft

3 ft

2 ft

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695-698__EMCS_T_TLG2_G2_U09_L07_57685X.indd 696695-698__EMCS_T_TLG2_G2_U09_L07_57685X.indd 696 3/26/11 2:38 PM3/26/11 2:38 PM

Math BoxesLESSON

9 � 7

1. Draw two ways to show 2 _ 3 .

3. Get 36 counters. Share them equally among 4 children.

How many counters does each child get? counters

How many are left over?

counters

6. In 43,692, the value of

4 is .

3 is .

6 is .

9 is .

2 is .

2. Write 3 even numbers larger than 100.

, ,

Write 3 odd numbers smaller than 100.

, ,

4. I have $2.00. Can I buy 4 bags of chips for $0.55 each?

Unit

5. Solve.

386 - 40 =

= 198 - 60

259 - 40 =

= 243 - 20

114 115

97

10 11

Date Time

102

9no

0

5

110

23

3,000600902

40,000

200

346

219138

223

77

�

Sample answers:Sample answers:

Sample answers:

209_228_EMCS_S_SMJ_G2_U09_57640X.indd 223 2/10/11 9:34 AM

Math Journal 2, p. 223

Student Page

Name Date Time

Find the area of each letter.

1. 2. 3.

Area = sq cm Area = sq cm Area = sq cm

4. What is the perimeter of each letter?

I: cm U: cm J: cm

5. Use a straightedge and the tick marks to draw square units. Count the squares to find the area.

Area = sq cm

283

Today children discussed the concept of finding the area of a surface. Area is measured by finding the number of square units needed to cover the surface inside a shape. Make sure your child understands that, when he or she is finding the perimeter of the letters in Problem 4, he or she is finding the distance around the outside of the letters.

Please return this Home Link to school tomorrow.

Family Note

HOME LINK

9�7 Area and Perimeter

20 24 22

10119

69

9295Practice

6. 67 + 28 = 7. 154 - 62 =

12

252-292_EMCS_B_MM_G2_U09_576949.indd 283 2/9/11 12:55 PM

Math Masters, p. 283

Home Link Master

Lesson 9�7 697

Ask children to count the squares inside the rectangle. 6 Remind children that since all the sides of the squares measure 1 foot, the area of the rectangle is 6 square feet. Write area = 6 square feet under the rectangle. Ask children why the example in My Reference Book is square centimeters. Because each side of each square is 1 centimeter

� Counting and Drawing Square INDEPENDENTACTIVITY

Units to Find Area(Math Journal 2, pp. 222A and 222B)

Children complete journal pages 222A and 222B. When children are partitioning shapes it is not necessary for them to use a ruler or straightedge.

2 Ongoing Learning & Practice

� Playing the Equivalent Fractions PARTNER ACTIVITY

Game or Fraction Top-It(Math Journal 2, pp. 198, 199, 203, and 204)

Children use Fraction Cards to identify equivalent fractions and compare pairs of fractions. See Lessons 8-5 and 8-6.

� Math Boxes 9�7 INDEPENDENTACTIVITY

(Math Journal 2, p. 223)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 9-5 and 9-9. The skill in Problem 6 previews Unit 10 content.

Writing/Reasoning Have children draw, write, or verbalize their answer to the following: Explain your answer to Problem 4. Sample answer: $0.50 times 4 is $2. $0.55 is

more than $0.50, so 4 bags of chips will cost more than $2.

Ongoing Assessment: Math Boxes

Problem 3 �Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess children’s understanding of equal shares.

Children are making adequate progress if they are able to complete the box

accurately using counters or drawings.

[Operations and Computation Goal 4]

� Home Link 9�7 INDEPENDENTACTIVITY

(Math Masters, p. 283)

Home Connection Children find the areas and perimeters of letters.

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698 Unit 9 Measurement

Name Date Time

LESSON

9�7 Letter Areas

Find the area of each letter.

Area = sq cm Area = sq cm Area = sq cm

Area = sq cm Area = sq cm Area = sq cm7 11 7

10 8 11

Try This

An 8-by-8 checkerboard has 64 squares. Some squares on a checkerboard are white. Some are black. Squares of the same color are never next to each other.

7. How many white squares 8. If the square in one corner is

are in each row? black, what color is the square

How many black squares? in the diagonal corner? black44

3.2.1.

6.5.4.

252-292_EMCS_B_MM_G2_U09_576949.indd 284 2/9/11 12:37 PM

Math Masters, p. 284

Teaching Master

Finding the area of a geoboard rectangle

with 5 rows and 4 columns

ENRICHMENT INDEPENDENTACTIVITY

� Finding the Perimeter 5–15 Min

(Math Masters, p. 434)

To apply children’s knowledge of perimeter, have them draw on grid paper as many different rectangles and squares as they can that have a perimeter of 12 centimeters (rather than an area of 12 square centimeters). When they have finished, ask children to describe how they know they have found all the rectangles. Encourage them to use vocabulary from this unit.

Discuss whether the areas are the same in all the shapes. Discuss which shape has the largest area.

EXTRA PRACTICE INDEPENDENTACTIVITY

� Finding the Areas of 5–15 Min

Block Letters(Math Masters, p. 284)

Children find the areas of block letters. Have children work on the Try This problems at the bottom of the page. You might want to display a checkerboard or model one on the board.

ELL SUPPORT SMALL-GROUPACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 142)

To provide language support for measurement, have children use the Word Bank template found on Differentiation Handbook,page 142. Ask children to write the term area, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.

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3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Finding the Areas of 5–15 Min

Geoboard RectanglesTo explore the concept of area as measuring a surface with square units, have children make rectangles on a geoboard and count the squares to find the area. Children can place a penny or counter in each of the square units. (See margin.)

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Planning AheadTo do the demonstration in Lesson 9-8, you

will need labeled containers, such as milk

cartons and beverage bottles, with these

capacities: half-pint, pint, quart, half-gallon,

gallon, and liter. Write the capacity on each

container or circle the capacity if it is printed

on the container. Use a colored marker or a

hole in the container to show the fill level of

each container. You will also need a funnel,

a tray, and at least 1 gallon of a pourable

substance, such as water, sand, or rice.

In Lesson 9-9, children will weigh pennies

on a spring scale. Attach a paper or plastic

cup to the spring scale to hold the pennies.

Each group will need about 40 pennies in a

container.

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Name Date Time

Find the area of each letter.

1. 2. 3.

Area = sq cm Area = sq cm Area = sq cm

4. What is the perimeter of each letter?

I: cm U: cm J: cm

5. Use a straightedge and the tick marks to draw square units. Count the squares to find the area.

Area = sq cm

283

Today children discussed the concept of finding the area of a surface. Area is measured by finding the number of square units needed to cover the surface inside a shape. Make sure your child understands that, when he or she is finding the perimeter of the letters in Problem 4, he or she is finding the distance around the outside of the letters.

Please return this Home Link to school tomorrow.

Family Note

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

HOME LINK

9�7 Area and Perimeter

69

Practice

6. 67 + 28 = 7. 154 - 62 =

252-292_EMCS_B_MM_G2_U09_576949.indd 283252-292_EMCS_B_MM_G2_U09_576949.indd 283 2/9/11 12:55 PM2/9/11 12:55 PM