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Math on the Spot Video Tutor Online Assessment

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Soar to Success Math Online Intervention

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Digital ManagementCenter organizes program resources by TEKS!

Interactive Student Edition provides students

with an interactive learning environment!

Resources

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16.2 Use Area Models Why can you multiply to find the area of a rectangle?Essential Question?

Texas Essential Knowledge and Skills

Geometry and Measurement—3.6.C Determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

MATHEMATICAL PROCESSES3.1.A Apply mathematics to problems 3.1.D Communicate mathematical ideas and reasoning3.1.E Create and use representations

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 16.2 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabulary

Go to Multimedia eGlossary at thinkcentral.com

Lesson OpenerMaking ConnectionsInvite students to tell you what they know about painting a space.

Ask students if they have ever helped paint an area or room. For students who answer yes, ask what they painted and about how much paint they used.

Using the Digital LessonIt may help to draw the parking space as a rectangle for students to understand the concepts of length and width. Label the length and width with the stated dimensions from the problem.

Learning TaskWhat is the problem the students are trying to solve? Connect the story to the problem.

• How long is the parking space? (7 meters)

• How wide is the parking space? (3 meters)

• What is the problem asking you to find? (The area of the parking space)

Literacy and MathematicsChoose one or more of the following activities.

• Point out to students that equa- in equation is similar to the word equal. Have students explain how the words equal and equation are related.

• Have students evaluate whether or not they think the problem provides enough information to be solved, explaining why.

Why can you multiply to f ind the area of a

rectangle?

Lesson 16.2 519A

Unlock the ProblemUnlock the Problem

21 3

54 6

RememberA unit square can be different sizes: 1 square meter, 1 square foot, 1 square centimeter, and so on.

Essential Question?

Geometry and Measurement—3.6.C

MATHEMATICAL PROCESSES3.1.A, 3.1.D, 3.1.E

Name

Use Area Models16.2

Melissa has a garden that is shaped like the

rectangle below. Each unit square represents

1 square meter. What is the area of her garden?

You can count the number of square units to find the

area of a figure. This rectangle has an area of 6 square

units. You can also use multiplication.

Why can you multiply to find the area of a rectangle?

One Way Use repeated addition.

Count the number of rows.

Count the number of unit squares

in each row.

_ rows of _ = ■

Write an addition equation.

So, the area is _ square meters.

Another Way Use multiplication.

Count the number of rows. Count the

number of unit squares in each row.

_ rows of _ = ■

This figure is like an array. How do you find

the total number of squares in an array?

Write a multiplication equation.

So, the area is _ square meters.

_ unit squares

_ unit squares

_ unit squares

_ + _ + _ = _

_ rows

_ unit squares in each row

_ × _ = _

Mathematical ProcessesMath Talk

Explain when you can use different methods to

find the same area.

Possible explanation: if the fi gure is shaped like a rectangle,

you can count the number of unit squares in all or multiply the

number of unit squares in each row by the number of rows.

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3

6

6

6

6

6

6 6 6 18

18

3

3

6

6

18

18

You can multiply the number in each row by the number of rows.

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Module 16 519

English Language Learners Language SupportELLLeveled Activities ELPS

Beginning: Activity 44 1.D, 2.C.4, 4.C.1

Intermediate: Activity 3 2.D.2, 2.E.3, 3.F.2

Advanced: Activity 46 1.F, 2.I.4, 4.G.2

Advanced High: Activity 35 1.B.1, 1.F, 3.C.4, 3.G.2

thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: DrawMaterials: 1-Centimeter Grid Paper (see eTeacher Resources)

• Have students draw a rectangle on a sheet of centimeter grid paper. What is the area of 1 unit square? 1 square centimeter

• Have students count rows. You may point to the rows in the drawing to illustrate the word row. Ask how many rows students have. Answers will vary.

• Have students shade unit squares in each row, one by one. Slide your finger along a row if necessary. Ask how many unit squares there are in each row. Answers will vary.

• Have students find the area of their rectangles. Ask how they found the area. Answers will vary.

ELPS 2.C.3, 2.D.1, 2.I.5

Interpersonal / SocialSmall Group

Unlock the Problem Students have learned to find the area of figures by counting unit squares. Tell them there is an easier way, using multiplication. Relate the multiplication strategies students have previously learned to the area problems on this page.

One Way• What do you notice about the number of unit

squares in each row of Melissa’s garden? The same number of unit squares are in each row.

• How can you use addition to find a total amount for a problem involving equal groups? I can use repeated addition to add equal groups.

Another Way• How is this figure like an array? The figure has rows

with the same number of unit squares in each row.

• How can you use multiplication to find the total number of unit squares in an array? I can multiply the number of unit squares in each row by the number of rows.

It is important for students to understand that they can use multiplication in this example because the shape is a rectangle. Rectangles are like arrays and involve rows with the same number of unit squares in each row.

Math Talk Use Math Talk to deepen students’ understandings that each method gives the same result and why they can use the methods to find the area of rectangles.

Mathematical Processes

519 Module 16

Share and ShowShare and Show

1. Find the area of the rectangle in two ways.

_ rows of _ = ■

Add. _ + _ + _ = _

Multiply. _ × _ = _

What is the area of the rectangle?

_ square units

Find the area of the rectangle. Each unit square is 1 square foot.

2.

3.

Find the area of the rectangle. Each unit square is 1 square meter.

4.

5.

6.

7.

Mathematical ProcessesMath Talk

Which method do you prefer using? Explain.

14 square feet 15 square feet

27 square meters32 square meters

Possible explanation: I prefer using multiplication because it is quicker than counting or using repeated addition.

3

3

4

4

4 4 4 12

12

12

40 square meters 25 square meters

520

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Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

Materials: ruler or measuring tape

• Have students estimate the area of several objects in the classroom using two different units of measurement. Suggest the following: computer screen: square inches, square centimeters doorway: square feet, square meters

• Have students measure the object to the nearest whole unit using a ruler or measuring tape. Then have students find the area using multiplication.

• Have students repeat the activity using an object of their own.

Visual / SpatialIndividuals

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 76

COMMON ERRORSError Students use the incorrect unit when writing the area.

Example Students write “square units” or “square feet” when the measurement should be square meters.

Springboard to Learning Tell students that they should circle the unit given in the problem.

CE

If students are having difficulty solving with one method, suggest that they try using a different method.

Math Talk Use Math Talk to continue the discussion about which methods students prefer.

Mathematical Processes

Lesson 16.2 520

Problem SolvingProblem Solving

Name

8. Write MathWrite Math Use Math Language

Multi-Step Compare the areas of the two

rugs at the right. Each unit square represents

1 square foot. Which rug has the greater

area? Explain.

10. Draw and shade three different rectangles

with an area of 24 square units. Then write an addition or

multiplication equation for each area.

9. Pose a Problem A tile company tiled a wall

using square tiles. A mural is

painted in the center. The

drawing shows the design.

The area of each tile used is

1 square foot.

Write a problem that can be solved by using

the drawing. Then solve your problem.

Areas are the same. Possible explanation: the green rug has 4 rows of 3 or 4 × 3 = 12

square feet; the purple rug has 3 rows of 4 or 3 × 4 = 12 square feet.

Possible problem: A wall is tiled using yellow tiles and hand-painted tiles. How many more

square feet of yellow tiles were used than square feet of hand-painted tiles?; 2 more square feet

Possible equations: 12 + 12 = 24 square units; 3 × 8 = 24 square units;

4 × 6 = 24 square units

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Module 16 • Lesson 2 521

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1 2 3 4 5 6 7 8 9 10

3.6.C

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Name

Use multiplication to find the area of the rectangle. Each unit square is 1 square meter.

Step 1 Count the number of rows.There are 6 rows.

Step 2 Count the number of unit squares in each row. There are 10 unit squares.

Step 3 Multiply the number in each row by the number of rows to find the area. number of rows × number in each row = area

6 × 10 = 60

So, the area of the rectangle is 60 square meters.

Find the area of the rectangle. Each unit square is 1 square meter.

1.

2.

Use Area ModelsOBJECTIVE Relate area to addition and multiplication by using area models.

LESSON 76

27 square meters 35 square meters

Geometry and Measurement 151 Enrich© Houghton Mifflin Harcourt Publishing Company

E75

Name Enrich 75

Area Riddles

Use the clues to solve the riddle.

You may use grid paper to draw the fi gure.

1. My sides are all the same length.My area is 9 square meters. What is the length of one of my sides?

2. I am a square. One of my sides is 9 feet long. What is my area?

3. I am a rectangle. One of my sides is 8 centimeters long. Another side is 6 centimeters long. What is my area?

4. I am a rectangle. Two of my sides are each 7 inches long. My area is 28 square inches. What is the length of each of my other two sides?

5. I am a rectangle. Each of my shorter sides measure 5 meters. My area is 45 square meters. What is the length of each of my longer sides?

6. I am a square. My area is 64 square feet. What is the length of one of my sides?

7. How did you find the answer in Exercise 4?

8. Stretch Your Thinking Suppose you know that a figure is a rectangle and its area is 8 square meters. What are all the different whole-number side lengths the rectangle could have?

3 meters

9 meters

48 square centimeters

Possible answer: I found

what number, when

multiplied by 7, equals 28:

4

81 square feet

8 feet

4 inches

1 and 8 meters or 2 and

4 meters

1

2

3

RtI Tier 1 Lesson 76 Enrich 75

Problem SolvingProblems

In Problem 9, students write their own problems. Then, students must solve their problems using the content of the lesson. Be sure that students explain the method they used in their solution.

Problem 10 requires students to understand the concept of area in order to draw three different rectangles with the same area, 24 square units. The problem requires students to start with the area to find appropriate side lengths. Since students have not learned multiplication facts for 12 or 24, encourage them to write an addition equation if they draw a rectangle that is 2 units by 12 units or 1 unit by 24 units.

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

521 Module 16

Mathematical Processes

Daily Assessment TaskDaily Assessment Task

TEXAS Test Prep 14. Heather drew this rectangle. Which equation

can be used to find the area of the rectangle?

A 5 × 8 = 40

B 8 × 8 = 64

C 8 + 8 + 8 + 8 = 32

D 5 × 5 = 25

Fill in the bubble for the correct answer choice.

11. Brianna is coloring a bookmark. Each unit square

is 1 square inch. Which multiplication equation

can be used to find the area of the bookmark?

A 7 + 7 = 14 C 2 × 7 = 14

B 7 × 7 = 49 D 2 × 2 = 4

12. Maria is painting a tile design for her porch.

Each square tile is 1 square foot. What is the area

of the design?

A 9 square feet C 16 square feet

B 18 square feet D 20 square feet

13. Multi-Step Tom and Bill are painting a fence.

Tom paints the yellow area. Bill paints the

white area. Each unit square is 1 square foot.

How many more square feet does Bill paint

than Tom?

A 10 square feet C 15 square feet

B 40 square feet D 25 square feet

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THENIF

YES

NO

Daily Assessment Task 1

2

3

Differentiated Centers Kit

ActivitiesHurray for Arrays!Students complete blue Activity Card 15 by using arrays to model multiplication facts.

ActivitiesJump to 9Students complete blue Activity Card 6 by measuring and then adding lengths.

TEXAS Test Prep CoachTest Prep Coach helps teachers to identify common errors that students can make.

In the Test Prep exercise, if students selected:

B They multiplied the number in each row by itself.

C They used an addition equation and counted only 4 rows.

D They multiplied the number of rows by itself.

Essential Question? WriteMathWriteMath

Why can you multiply to find the area of a rectangle? A rectangle is like an array involving rows with an equal number of unit squares, so I can use multiplication to find the area of a rectangle just like I can use an array to solve a multiplication problem.

• Soar to Success MathWarm-Up 48.28

• Enrich 76

• Homework and Practice Lesson 16.2

Can students understand why they multiply to find the area of a rectangle?

Lesson 16.2 522

TEXAS Test PrepLesson CheckLesson Check

6. Nolan draws this diagram for a rug.

Which equation

can be used to

find the area?

A 5 + 8 = 40

B 5 × 5 = 25

C 8 × 5 = 40

D 8 × 8 = 64

7. Marisol puts together a floor puzzle.

Each puzzle piece is 1 square foot.

What is the area of

the puzzle?

A 27 square feet

B 28 square feet

C 32 square feet

D 25 square feet

8. Multi-Step Lu Chen draws this

diagram of his patio. Each square is

1 square meter. He wants to add 12

square meters to the patio. What will

be the size of the new patio?

A 40 square meters

B 36 square meters

C 42 square meters

D 48 square meters

9. Multi-Step Aliki and Deke are covering a

wall with panels. Aliki covers the yellow

area. Deke covers the white area. Each

panel is 1 square foot. How many more

square feet does Aliki cover than Deke?

A 6 square feet C 9 square feet

B 8 square feet D 7 square feet

Fill in the bubble completely to show your answer.

524

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Problem SolvingProblem Solving

Homeworkand Practice

Name

Find the area of the rectangle.Each unit square is 1 square meter.

1. 2.

3. 4.

Use Area Models16.2

Geometry and Measurement—3.6.CMATHEMATICAL PROCESSES 3.1.A, 3.1.D, 3.1.E

5. Shoshauna is using one-inch tiles to cover

a table. She wants to put a green border

around the edge of the table. She wants

to make the center of the table yellow.

How many more yellow tiles does she need

than green tiles? Explain.

21 square meters

36 square meters 35 square meters

8 more yellow tiles; Possible explanation: The area

of the center of the table is 36 square inches; the area of the border is 28 square inches.

36 − 28 = 8

24 square meters

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Module 16 • Lesson 2 523

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Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

523-524 Module 16