LESSO Lesson 8 OVERVIEW Multiply Decimals · Lesson 8 Multiply Decimals Lesson Objectives...

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LESSON OVERVIEW

Lesson 8 Multiply Decimals

Prerequisite SkillsLesson Objectives

Learning Progression

their previous conceptual understanding of multiplication by using decimal grids and area models to multiply tenths and hundredths decimals. Students also use the partial product method to multiply decimals. Before multiplying, students estimate the product and use their estimate to check whether the product they calculate is reasonable.

In the next lesson students will learn to divide decimals. In Grade 6, students will continue to multiply and divide decimals.

In Grade 4 students built a conceptual understanding of multi-digit multiplication by multiplying with area models and finding partial products. Previously in Grade 5, students learned the standard multiplication algorithm and used it to multiply multi-digit whole numbers.

In this lesson students multiply decimals through hundredths. They use place-value understanding to make connections between patterns in decimal multiplication and whole-number multiplication. They expand

There is no new vocabulary. Review the following key terms.

• decimal a number containing a decimal point that separates a whole from fractional place values (tenths, hundredths, thousandths, and so on)

• product the result of multiplication

• factor a number that is multiplied

• place value the value assigned to a digit based on its position in a number; for example, the 2 in 3.52 is in the hundredths place and has a value of 2 hundredths or 0.02.

• to estimate to give an approximate number or answer based on mathematical thinking.

Lesson Vocabulary

• Understand place value.

• Know properties of operations.

• Recall basic multiplication facts.

• Multiply whole numbers of up to four digits by one-digit whole numbers.

• Multiply a two-digit number by a two-digit number.

• Use equations, rectangular arrays, and area models to illustrate and explain calculations.

Content Objectives• Multiply decimals to hundredths.

• Explain how to multiply decimals to hundredths.

Language Objectives• Draw an area model to multiply

decimals and explain the model’s relationship to the factors and the product.

• Estimate the product of decimals and justify using place value reasoning.

• Predict the relationship between an estimated product and a calculated product.

DomainNumber and Operations in Base Ten

ClusterB. Perform operations with multi-digit

whole numbers and with decimals to hundredths.

Standards5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Standards for Mathematical Practice (SMP)1 Make sense of problems and persevere

in solving them.

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

5 Use appropriate tools strategically.

7 Look for and make use of structure.

CCSS Focus

Lesson Pacing Guide

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Teacher-Toolbox.com

Whole Class Instruction

Lesson 8

Small Group Differentiation

Personalized Learning

ReteachReady Prerequisite Lessons 45–90 min

Grade 4 • Lesson 11 Multiply Whole Numbers

Student-led ActivitiesMath Center Activities 30–40 min

Grade 4 (Lesson 11)• 4.23 Multiplying by One-Digit Numbers• 4.24 Multiplying by Two-Digit Numbers

Grade 5 (Lesson 8)• 5.2 Represent Decimal Products

Independenti-Ready Lessons* 10–20 min

Grade 4 (Lesson 11)• Multiplying Two-Digit Numbers by

One-Digit Numbers• Multiply Whole Numbers

i-Ready.com

Day 145–60 minutes

Toolbox: Interactive Tutorial*Multiply Decimals

Practice and Problem SolvingAssign pages 65–66.

Introduction

• Use What You Know 15 min• Find Out More 15 min• Reflect 5 min

Modeled and Guided Instruction

Learn About Multiplying Decimals by Whole Numbers• Picture It/Model It 20 min• Connect It 15 min• Try It 10 min

Learn About Multiplying Decimals with an Area Model• Picture It/Model It 15 min • Connect It 20 min• Try It 10 min

Guided Practice

Practice Multiplying Decimals• Example 5 min• Problems 17–19 15 min• Pair/Share 15 min• Solutions 10 min

Independent Practice

Practice Multiplying Decimals• Problems 1–6 20 min• Quick Check and Remediation 10 min• Hands-On or Challenge Activity 15 min

Toolbox: Lesson QuizLesson 8 Quiz

Teacher-led Activities Tools for Instruction 15–20 min

Grade 4 (Lesson 11) • Multiply Three-Digit Numbers by

One-Digit Numbers• Multiply by One-Digit Numbers

Grade 5 (Lesson 8)• Multiply Decimals

* We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson.

Introduction

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Students use their understanding of multiplication to develop a model for multiplying decimals. They use a picture of tiles to multiply a decimal by a whole number. Then they express the product in tenths and as a decimal. Then students investigate the place-value patterns involved in multiplying by 0.1 and 0.01. They apply knowledge of place value to the problem of multiplying decimals.

• Work through Use What You Know as a class.

• Tell students that this page models a way to think about multiplying decimals.

• Have students read the problem at the top of the page.

• Ensure that students understand the relationship between the estimate and the actual product.

Mathematical Discourse 1 and 2

• Ask students to explain their answers for the last question.

SMP TIP Model with Mathematics Help students connect the visual model of six 0.8-inch tiles with the mathematical model “8 tenths 3 6.” Students can count the tiles to see that there are 6. They can read the problem and see in the illustration that each tile is 0.8 inch wide. Have a student explain what “length of tile 3 number of tiles” means. [It represents the total length of the row made from six 0.8-inch tiles.] (SMP 4)

Concept Extension

At A Glance

Step By Step

Mathematical Discourse

1 Why do you estimate the product?

Estimating the product helps you know about how much the actual product should be.

2 Look at your estimate and look at the product you found. Does your answer make sense? How can you tell?

The product 4.8 inches makes sense because it is close to the estimate of 6. It is a little less because we rounded up for the estimate. The greatest place value of the estimate is ones—not tenths or tens—and the greatest place value of the actual product is also in the ones.

Concept ExtensionRepresent the total length in many forms.

• Write “48 tenths” on the board.

• Challenge students to come up with as many representations for “48 tenths” as they can.

• Possible answers include: 48 ··

, 4 8 ··

, 480 ···

4.8, 4.80, 4 1 0.8, “4 and 8 tenths,”

8 ··

3 60 ··

, 0.8 1 0.8 1 0.8 1 0.8 1 0.8 1

0.8, 8 ··

1 8 ··

, etc.

Introduction

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Use What You Know

Lesson 8Multiply Decimals

a. First, estimate the length of the side of each tile to the nearest inch.

b. Estimate the length of the row of 6 tiles using your answer.

c. Will the actual length be more or less than your estimate?

d. Why?

e. The length of the side of each tile is tenths of an inch. There are tiles in the row.

f. How many tenths of an inch long is the row of tiles? tenths of an inch

g. Write the decimal equivalent:

The length of the row is inches.

h. Is your answer reasonable? Explain your thinking.

i. Use your own words to explain how you could find the length of the row of tiles.

Margo has 6 square tiles of equal size. Each side of each tile is 0.8 inch long.

If Margo places all the tiles in a row with sides touching, how long is the row?

You know how to multiply whole numbers by other whole numbers and by fractions. Now you’ll learn how to multiply whole numbers by decimals. Take a look at this problem.

5.NBT.B.7

1 inch

6 inches

I rounded up for the estimate.

Possible answer: You multiply the length of each tile in the row by the

number of tiles.

Possible answer: Yes, 4.8 is less than and close to 6 inches.

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Lesson 8

©Curriculum Associates, LLC Copying is not permitted. 61Lesson 8 Multiply Decimals

Find Out More

On the previous page you saw that 6 3 0.8 5 4.8. How is this related to 6 3 8 5 48?

Notice that the digits of 6 3 0.8 are the same as the digits of 6 3 8. The digits of their products are also the same. Why is this?

In earlier lessons, you learned that dividing a number by 10 shifts the decimal point to the left so the value of the number decreases by a factor of 10. Dividing a number by 10 has the same result as multiplying the number by one tenth, or 0.1.

Look at the table below to see patterns when you multiply numbers by 0.1 and 0.01.

ExpressionEquivalent

ExpressionsProduct

6 3 86 3 8 3 1.0

48 3 1.048.0

6 3 0.86 3 8 3 0.1

48 3 0.14.8

6 3 0.08

6 3 8 3 0.016 3 8 3 0.1 3 0.1

48 3 0.0148 3 0.1 3 0.1

Notice that the decimal point moves one place to the left each time you multiply by 0.1.

Reflect1 What is the product of 6 3 0.008? Explain your reasoning.

Possible answer: 6 3 8 3 0.001 which equals 48 3 0.001. Multiplying a

number by 0.001 moves the decimal point three places to the left.

6 3 0.008 5 0.048.

• Read Find Out More as a class.

English Language Learners

• Have students read and interpret each row of the table. For example: 6 times 8 tenths is equivalent to 6 times 8 times 1 tenth, which equals 48 tenths, or 4 and eight tenths.

• Have students read the products in the table: 48, 4 and 8 tenths or 48 tenths, 48 hundredths. Point out that the digits of the products are the same, but the actual value of the products is different.

• Discuss with students that a tenths decimal such as 0.8 can be broken apart as 8 3 0.1. Similarly, a hundredths decimal such as 0.08 can be broken apart as 8 3 0.01 and then 0.01 can be further broken apart as 0.1 3 0.1.

Visual Model

• Have students extend the pattern shown in the table to complete Reflect on their own. Then discuss.

Real-World Connection

Assign Practice and Problem Solving pages 65–66 after students have completed this section.

Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING

English Language Learners

Explain that a mathematical expression is a way to represent a quantity or a mathematical relationship. Students may be familiar with facial expressions or with verbal expressions (or idioms). In general, an “expression” is a way to communicate something. This is true in math, as well.

Visual ModelUse a place-value chart to represent each product.

• Display a place-value chart that includes hundreds through hundredths.

• Write each product from the table in the place-value chart.

• Have students describe how the place-value chart shows the change in the value of the digits.

Discuss how items are priced using dollars and cents. Remind students that cents are hundredths of a dollar ($0.01). Have students look up prices of various school supplies, such as pencils, notebooks, or erasers. Students may not yet be ready to multiply to find the cost of 2, 4, or 5 notebooks; by the end of this lesson they should be able to compute these prices.

Another approach would be to bring in various kinds of produce and weigh a single tomato, potato, onion, or pepper on a scale with a decimal read-out. Ask students how they could find the weight of 6 or 7 onions or peppers.

62 ©Curriculum Associates, LLC Copying is not permittedLesson 8 Multiply Decimals

Lesson 8 Multiply Decimals Modeled and Guided Instruction

Learn About

Lesson 8

Multiplying Decimals by Whole Numbers

Read the problem below. Then explore different ways to understand multiplying by hundredths.

Padma bought 3 pounds of grapes. Each pound of grapes costs $2.75. How much money did Padma spend on grapes?

Picture It You can use decimal grids to picture multiplying with hundredths.

Think of 3 3 $2.75 as 3 groups of 2.75.

Model It You can use partial products to multiply with hundredths.

2.753 3

3 ones 3 5 hundredths 3 ones 3 7 tenths 5 21 tenths 3 ones 3 2 ones 5 6 ones

hundredths 5 8.25

5 15 hundredths5 210 hundredths5 600 hundredths

Students use decimal grids and partial products to multiply a hundredths decimal by a whole number. Then students revisit this problem and apply knowledge of place value and expanded form to multiply hundredths.

• Read the problem at the top of the page as a class. Invite volunteers to explain their estimate of the solution.

Picture It• Discuss Picture It with students. Have a

volunteer explain how the product of 3 and 2.75 is represented. For example, a student might point out that there are three groups of grids where 2 whole grids and 75 hundredths of a grid are shaded.

Model It• Discuss Model It with students. Have

students identify each partial product.

• Have students look in detail at the sum of partial products. Discuss why each partial product is rewritten in hundredths. [Numbers are added by combining like place values.]

• Have students check the solution against their estimates to see if the solution makes sense.

Concept Extension

At A Glance

Step By Step

Concept ExtensionDeepen students’ understanding of partial products in decimal multiplication.

Materials: play money: dollars, quarters, dimes, and pennies

• Direct students to show $2.75 using just dollars and quarters. Then have students show 3 equivalent groups to model 3 3 2.75.

• Discuss the values of 3 groups of dollar bills and 3 groups of quarters. Invite volunteers to show the value of each currency with an equation: 3 3 $2 5 $6; 3 3 $0.75 5 $2.25.

• Explain to students that using dollars, dimes, and pennies can demonstrate the place value of each digit in a product. Model 2.75 using 2 dollars, 7 dimes, and 5 pennies. Then direct students to make 3 identical groups.

• Discuss the relationship of each group of coins to the partial products shown on the Student Book page.

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Lesson 8

Connect It Use what you know about decimals and place value to solve the problem.

2 To solve the problem, you need to fi nd 3 3 $2.75. Estimate the total cost of

the grapes. Explain your thinking.

3 Look at Picture It. How many full grids can you make?

How many squares would be shaded in the partially fi lled grid?

4 Look at Model It. How is multiplying with decimals like multiplying with

whole numbers?

5 Complete the following:

825 hundredths 5 tenths

825 hundredths 5 ones

6 Both Picture It and Model It show that 3 3 $2.75 5 .

Is the product reasonable? Explain.

7 Explain how to multiply a whole number by a decimal in the hundredths.

Try It Use what you have learned about multiplying by hundredths to solve these problems. Show your work on a separate sheet of paper.

8 Bananas cost $0.65 per pound. Sasha bought 4 pounds of bananas. How much did

she pay for the bananas?

9 Brian creates a chain of 11 paper clips. Each paper clip is 2.48 centimeters long.

How long is the chain of paper clips?

Possible answer: $9. $2.75 is about $3,

3 3 $3 5 $9.

Possible answer: The procedure is the same. You just need to

decide where to place the decimal point in the product.

Possible answer: Yes. $8.25 is close to my

estimate of $9.

Possible answer: Multiply as you would with whole numbers. The product will

be in the hundredths.

27.28 centimeters

Discuss items that are sold by price per pound.

Examples: fruit, vegetables, and deli items such as sliced cheeses or meats

Discuss other situations in which decimals are multiplied.

Example: finding the area of a room in feet or yards

Students may create problems similar to the one on the page and use decimal grids to solve.

Connect It• Read each problem and lead students

through the solutions.

• Discuss problem 2 and how the estimates compare to the actual product. [2.75 is close to 3, so the product will be close to 3 3 3 5 9. The actual product will be less than 9 because we rounded up.]

• Discuss problem 5. Ensure that students

understand that the value of each digit

decreases by a factor of 10 each time they

multiply by 1 ··

• Discuss students’ answers to problem 7.

Try It• Students complete Try It on their own.

SMP TIP Make Sense of ProblemsEncourage students to verbalize their understanding of the Try It problems before they begin to compute. Encourage students to draw pictures or diagrams to help them understand what the problem is asking. Have them estimate solutions prior to solving. (SMP 1)

8 Solution$2.60; Students may multiply 4 3 65 5 260 and then shift the decimal point two places to the left.

9 Solution27.28 cm; Students may multiply 11 3 248 5 2,728 and then shift the decimal point two places to the left.

Error Alert Students who wrote 2.728

may not yet understand how far to shift

the decimal point. Have them write each

factor in expanded form, using “3 0.1” or

“3 1

·· 10 ,” and shift the decimal point

accordingly. Then compare the solution

with their estimate.

Step By Step

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Lesson 8 Multiply Decimals Modeled and Guided Instruction

Learn About

Lesson 8

Multiplying Decimals with an Area Model

Read the problem below. Then explore different ways to multiply tenths by tenths.

Hayden made a sign that is 1.4 meters long and 1.2 meters wide to post on the wall of his store. How many square meters of wall will the sign cover?

Picture It You can use an area model to multiply tenths by tenths.

The rectangle measures 1.4 meters by 1.2 meters.

Each small square is 1 tenth of a meter by 1 tenth of a meter, or 0.1 meter by 0.1 meter.

The area of each small square is 0.1 meter 3 0.1 meter 5 0.01 square meter.

Model It You can also use partial products to multiply tenths by tenths.

1.23 1.4

4 tenths 3 2 tenths 4 tenths 3 1 one 5 4 tenths 1 one 3 2 tenths 5 2 tenths 1 one 3 1 one 5 1 one

hundredths 5 1.68

5 8 hundredths5 40 hundredths5 20 hundredths5 100 hundredths

Students study two models for multiplying tenths by tenths. The first model is a grid showing the intersection of 1.2 and 1.4. The second model uses partial products. Then students revisit this problem and apply knowledge of place value and expanded form to multiply tenths by tenths.

• Read the problem at the top of the page as a class.

Mathematical Discourse 1

Picture It• Read Picture It. Point out that the width

represents 1 and 2 tenths and the length (or height) represents 1 and 4 tenths. Ask a volunteer to explain why each small square represents 0.01 square meter. [Each side of a small square is 0.1 meter. So the area of a small square is 0.1 3 0.1, or 0.01 square meter.]

Model It• Read Model It with students. Remind

students that multiplying 1 tenth by 1 tenth results in 1 hundredth.

• Explain that partial products are a representation of the distributive property: 1.2 3 1.4 is equivalent to 1.2 3 (1 1 0.4), which is equivalent to (1 1 0.2) 3 1 1 (1 1 0.2) 3 0.4. Then show students how this leads to the 4 partial products shown. Explain that breaking apart a factor can help a student think about simpler multiplication facts.

Mathematical Discourse 2

Visual Model

At A Glance

Step By Step

Mathematical Discourse

1 How can you tell that this is a multiplication problem?

The problem describes a rectangle with a given length and width and asks for the area of the rectangle. The operation that deals with finding the area of a rectangle is multiplication. When you model the problem with a drawing, it shows four rows with two squares in each

row. This is multiplication.

2 How are the area model and the partial products related?

The area model shows 4 sections of area, each in hundredths, which are represented by the 4 partial products written as hundredths.

Visual ModelModel a simpler problem.

• If students struggle with the decimal area model, illustrate the problem as whole-number multiplication.

• Draw a rectangle that is 12 units wide and 14 units tall. Separate the 14 units with a line to show 10 units and 4 units and label the rectangle accordingly.

• Ask students to identify the area of each section and write an equation to show each: 12 3 10 5 120 square units, 12 3 4 5 48 square units.

• Review units of area: 1 tenth unit 3 1 tenth unit 5 1 hundredth square unit. Invite a volunteer to explain the sum of the the areas of whole rectangle: 120 1 48 5 168 hundredths square units.

• Show students: 168 hundredths square units 3 100 5 1.68 square units.

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Lesson 8

Hands-On ActivityUse base-ten blocks to model multiplying decimals.

Materials: base-ten blocks (flats, longs, and cubes)

• For this activity, flats represent ones, longs represent tenths, and cubes represent hundredths.

• Have students model 4 3 2 with flats (8 flats) and write 4 3 2 5 8.

• Tell students to multiply 4 3 2 by one tenth. Students trade their 8 flats for 8 longs.

• Have students write 4 3 2 3 0.1 5 0.8.

• Tell students to multiply 4 3 2 3 0.1 by one tenth. They trade the 8 longs for 8 cubes and write 4 3 2 3 0.1 3 0.1 5 0.08.

Connect It Now you will use the model and properties of operations to solve the problem.

10 To solve the problem, you need to fi nd 1.4 3 1.2. Estimate the area of wall that the

sign will cover. Explain your thinking.

11 Look at Picture It. Complete the area model below to fi nd the area of each of the four sections of the rectangle.

1 3 1 5

0.4 3 1 5

1 3 0.2 5

0.4 3 0.2 5

12 Look at Model It. How do the partial products relate to the area model above?

13 Both Picture It and Model It show that 1.4 3 1.2 5 square meters.

Is the product reasonable? Explain.

14 Explain what you know about the product when you multiply tenths by tenths.

Try It Use what you have learned about multiplying by tenths to solve these problems. Show your work on a separate sheet of paper.

15 Rosa fi lled her car’s tank with 9.8 gallons of gas. Each gallon costs $3.85. How much

did Rosa spend on gas?

16 Harry has 0.5 bottle of water in his game bag. The bottle holds 0.9 liter of water. How

many liters of water does Harry have?

Possible answer: about 1 square meter. 1.4 is about 1, and 1.2 is also about 1.

Possible answer: The partial products show the area of each of the four

sections of the area model.

Possible answer: Yes. 1.68 is close to my

estimate of 1. Since I rounded both numbers down to estimate, it makes

sense that the answer is greater than 1.

Possible answer: The product will be in the hundredths.

$37.73

0.45 liter

0.4 0.08

Connect It• Read each problem and lead students

through the solutions.

• Discuss the estimate in problem 10. Ask students to explain if the area will be more or less than 1 square meter. [It will be more because each factor is slightly greater than 1.]

• Discuss the area model shown for problems 11 and 12 and how it relates to the grid and partial products on the Student Book page. Be sure students understand why 0.2 3 0.4 is 0.08 and not 0.8.

• Invite students to share the method for multiplying decimals that helps them better understand the problem.

SMP TIP Use StructureStudents should recognize the place-value

pattern that occurs when multiplying

by 1 ··

. Encourage them to make use of this

pattern or structure when they multiply

decimals. Students should be able to

explain the shift in the values of the digits.

(SMP 7)

Hands-On Activity

Try It15 Solution

$37.73; Students may show partial products for 385 3 98 and then use place-value understanding to rewrite the sum of the partial products as a decimal.

16 Solution0.45 liter; Students may multiply 5 3 9 3 0.1 3 0.1 5 45 3 0.1 3 0.1 5 0.45.

Step By Step

Guided Practice

Teacher Notes

Lesson 8 Multiply Decimals Guided Practice

Practice

Lesson 8

Multiplying Decimals

Example

Pair/ShareSolve the problem without a model.

Pair/ShareWhat is a reasonable estimate for this problem? Explain your thinking.

I multiply tenths by tenths to solve this problem.

The student wrote 1.25 as 1 1 0.2 1 0.05 and used an area model to solve the problem.

17 Gina rides her bike to work at an average of 10.4 miles per hour. She bikes 1.2 hours each day. How many miles does Gina ride each day?

Show your work.

Solution

Liam ate 0.5 of a 1.25-ounce bag of raisins. How many ounces of raisins did Liam eat?

Look at how you could show your work using an area model.

0.5 3 1 5 0.5 0.5 3 0.2 5 0.10 0.5 3 0.05 5 0.025

1 0.2 0.05

Solution

Study the example below. Then solve problems 17–19.

0.5 1 0.10 1 0.025 5 0.625

0.625 ounce

Possible student work:

10.43 1.2

1 1040

12.48 miles

Students study a model for solving a decimal multiplication word problem. Then they solve several decimal multiplication problems.

• Ask students to solve the problems individually. Circulate to monitor and provide support.

• Encourage students to estimate their solutions before they begin computation.

• If students struggle, provide place-value charts and have them write out the expanded form.

• Encourage students to compare solutions to their estimates.

• Pair/Share When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

Example A model is shown as one way to solve the problem. Students could also use partial products to solve.

17 Solution

12.48 miles; See possible work on the Student Book page. Students could solve the problem by using partial products.

At A Glance

Step By Step

Solutions

Teacher Notes

Lesson 8

Pair/ShareDoes Aaron’s answer make sense?

Pair/ShareSolve the problem using an area model.

Will the product be in tenths or hundredths?

18 If a person’s hair grows 1.2 centimeters a month, how much would it grow in 9 months?

Show your work.

Solution

19 What is the product of 1.05 and 0.7? Circle the letter of the correct answer.

A 73.5

B 7.35

C 0.735

D 0.0735

Aaron chose C as the correct answer. How did he get that answer?

Will the product be greater than or less than 1.05?

1.2 5 12 tenths

9 3 12 tenths 5 108 tenths

108 tenths 5 10.8

10.8 centimeters

Possible answer: He correctly multiplied 1.05 and 0.7.

18 Solution

10.8 centimeters; See possible work on the Student Book page. Students could solve the problem by using place-value understanding.

19 Solution

C; Students could solve the problem by using a place-value approach, first multiplying 105 by 7, and then shifting the decimal point 3 places to the left.

Explain to students why the other three answer choices are not correct:

A is not correct because an estimate places the product closer to 1.

B is not correct because the answer should be less than 1.05.

D is not correct because the place value of the digits is not correct.

Solutions

Quick Check and Remediation

If the error is . . . Students may . . . To remediate . . .

have ignored the decimal points and multiplied as if the factors were whole numbers.

Use a grid model to represent the product. Then use expanded form to multiply.

101.4, or 1.014, or 0.1014

have incorrectly placed the decimal point.

Review the process for writing the product in expanded form. Use a place-value chart to help students see how multiplying by 1 ·· 10 3 1 ·· 10 shifts the values of the digits.

a product with incorrect digits

have made a basic fact multiplication error or made an error when recording or adding the partial products.

Use flash cards to practice basic multiplication facts. Have students draw an area model of the partial products and use expanded notation to find each product. Then have students use a place-value chart to line up the partial products and add them.

• Ask students to multiply 2.6 3 3.9. [10.14]

• For students who are struggling, use the chart to guide remediation.

• After providing remediation, check students’ understanding. Ask students to multiply 0.4 3 1.53. [0.612]

• If a student is still having difficulty, use Ready Instruction, Grade 4, Lesson 11.

Practice

Lesson 8

Multiplying Decimals

Solve the problems.

1 Which of the following has a product of 25.16?

A 3.7 3 680

B 3.7 3 68

C 3.7 3 6.8

D 3.7 3 0.68

2 Willa downloads 5 songs. Three of the song fi les are each 2.75 MB. Two song fi les are each 3.8 MB. How much space does Willa need for the songs she downloads?

A 5.55 MB

B 11.55 MB

C 15.85 MB

D 27.75 MB

3 Choose ALL the expressions that have the same value as the product of 0.11 and 4.5.

A 0.495 3 0.01

B 0.495 3 0.001

C 49.5 3 0.01

D 495 3 0.01

E 495 3 0.001

4 The area model below can be used to represent the product of 2.8 and 1.3. Complete the model by writing each of the following numbers in the correct part of the model.

0.6 2 0.24 0.8

Students multiply decimals to solve word problems that might appear on a mathematics test.

1 Solution

C; 3.7 3 6.8 is about 4 3 7 5 28. DOK 1

2 Solution C; Multiply: 2.75 3 3 5 8.25 and multiply 3.8 3 2 5 7.6. Add: 8.25 1 7.6 5 15.85. DOK 2

3 SolutionC; 0.11 3 4.5 5 0.495. The expression 49.5 3 0.01 5 0.495. E; The expression 495 3 0.001 5 0.495. DOK 2

4 SolutionSee completed table on the Student Book page. Each cell has the product of the number left of the row and the number above the column. DOK 1

At A Glance

Solutions

Lesson 8

Self Check

Go back and see what you can check off on the Self Check on page 1.

5 Tyrone said that 2.35 3 5 equals 1.175 because there is only one digit before the decimal point in 2.35, so there must be one digit before the decimal point in the product. Use pictures, numbers, or words to explain whether or not Tyrone is correct.

Show your work.

6 Each product below is missing a decimal point.

Part A Place the decimal point in each product so that the equation is correct.

12.53 3 5 5 6 2 6 5

4.28 3 3.6 5 1 5 4 0 8

1.3 3 0.89 5 1 1 5 7

7 3 6.12 5 4 2 8 4

Part B Circle one of the equations. Explain how you decided where to place the decimal point in this equation.

I know that the answer is around 10 because 2.35 is about 2 and 2 3 5 5 10.

5 3 2.35 5 5 3 (2 1 0.3 1 0.05)5 10 1 1.5 1 0.255 11.75

Tyrone is not correct.

15.408

Answers will vary. Students may mention estimating the product to decide where

to place the decimal point.

5 SolutionTyrone is not correct; Students may use an estimate or show partial products. See possible student work on the Student Book page. DOK 3

6 Part A Solution 62.65, 15.408, 1.157, 42.84

Part B SolutionStudents circle one of the equations. Student explanations will vary but may mention using estimation or place-value understanding to determine where to place the decimal point.

Solutions

Hands-On Activity Use a place-value chart to multiply decimals.

Materials: cards showing the digits 0–9, cards showing the fractions 1 ·· 10 , 1 ··· 100 , 1 ····· 1,000 , poster board, markers

Have students create a large place-value chart showing thousands

through thousandths. Give students a problem such as 13.2 3 0.08.

Have students write the product in expanded form:

13.2 3 0.08 5 1 132 3 1 ·· 10 2 3 1 8 3 1 ··· 100 2 5 (132 3 8) 3 1 1 ·· 10 3 1 ·· 10 3 1 ·· 10 2 .Students multiply the whole numbers and place cards in the

place-value chart to represent the product (1,056). Have students set

out cards for the factors of 1 ·· 10 . For each factor, students shift the

product 1,056 one place value to the right, effectively moving the

decimal point one place to the left. [1.056]

Repeat with other problems, including examples where the solutions are in thousandths, hundredths, and tenths.

Challenge Activity Write multiplication word problems.

Have students write multiplication word problems that involve multiplying decimal numbers. Students should use a tenths or hundredths decimal number for one or both factors. One of the factors could also be a money amount given in dollars and cents. Suggest students limit the factors to 3 digits or fewer. Have students exchange their problem with a partner to solve.

Teacher-Toolbox.com

LESSON QUIZ

Copying permitted for classroom use.Grade 5 Lesson 8 Multiply Decimals

Name ___________________________________________________________ Date ____________________

Lesson 8 Quiz continued

4 Mei has 2.5 packages of pretzels. Each full package weighs 5.39 ounces. Mei wants to know how many ounces of pretzels she has.

Part A

Mei draws this area model to fi nd the partial products.

Complete the model by fi lling in the blanks.

5 0.3 0.09

Part B

How many ounces of pretzels does Mei have in all?

Show your work.

Answer: ounces of pretzels

Copying permitted for classroom use.Grade 5 Lesson 8 Multiply Decimals

Name ___________________________________________________________ Date ____________________

Lesson 8 QuizReady® Mathematics

Solve the problems.

1 Which expression has a product of 32.76?

A 4.2 3 0.78

B 4.2 3 7.8

C 4.2 3 78

D 4.2 3 780

2 A stew recipe calls for 3.75 pounds of meat. Jack wants to make 5 batches of stew. How many pounds of meat does he need?

Show your work.

Answer: pounds of meat

3 Lee needs some school supplies. He will buy 3 notebooks for $1.29 each, 2 dozen pencils at $3.45 a dozen and a box of pens for $14.85 a box. Lee estimates that he will spend about $25 on these school supplies.

Is Lee’s estimation reasonable? How much will he spend exactly?

Fill in the blanks to explain.

Estimating each price to the nearest dollar, Lee will spend about

$ on notebooks, $ on pencils, and

$ on pens. Lee will spend about $ in all for these

school supplies. Lee’s estimation of $25 reasonable. He will

spend exactly $ on these school supplies.

Overview

Assign the Lesson 8 Quiz and have students work independently to complete it.

Use the results of the quiz to assess students’ understanding of the content of the lesson and to identify areas for reteaching. See the Lesson Pacing Guide at the beginning of the lesson for suggested instructional resources.

Tested Skills

Assesses 5.NBT.B.7

Problems on this assessment form require students to be able to estimate the product of decimals and use area models and partial products to multiply decimals to hundredths. Students will also need to be familiar with place value, properties of operations, and basic multiplication facts.

Lesson 8

Lesson 8 Quiz Answer Key

Ready® Mathematics

1. BDOK 1

2. 18.75DOK 2

3. 361524is25.62DOK 3

4. Part A:5 0.3 0.09

2 10 0.6 0.18

0.5 2.5 0.15 0.045

Part B:13.475DOK 2

Common Misconceptions and Errors

Errors may result if students:

• place the decimal point incorrectly.

• ignore the decimal points and multiply as if the factors are whole numbers.

• make a basic multiplication error or an error in adding the partial products.

• add instead of multiplying.

LESSO Lesson 8 OVERVIEW Multiply Decimals · Lesson 8 Multiply Decimals Lesson Objectives...

Documents

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