LESSO Lesson 9 OVERVIEW Divide Decimals

[Pages:16]LESSON Lesson 9 OVERVIEW Divide Decimals

CCSS Focus

Domain

Number and Operations in Base Ten

Cluster

B. Perform operations with multi-digit whole numbers and with decimals to hundredths.

Standards

5.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.

Lesson Objectives

Content Objectives

? Divide decimals to hundredths. ? Explain how to divide decimals to

hundredths.

Language Objectives

? Describe orally how use multiplication to understand a division problem.

? Estimate the quotient of decimals and justify using place value reasoning.

? Predict the relationship between an estimated quotient and a calculated quotient.

Prerequisite Skills

? Understand place value. ? Know properties of operations. ? Recall division basic facts. ? Divide three- and four-digit dividends

by two-digit divisors. ? Understand the relationship between

multiplication and division.

Lesson Vocabulary

There is no new vocabulary. Review the following key terms. ? dividend the number that is divided

by another number. ? divisor the number by which another

number is divided. ? quotient the result of division. ? to estimate to give an approximate

number or answer based on mathematical thinking.

Learning Progression

Previously in Grade 5 students divided whole numbers with up to four-digit dividends by two-digit divisors. Students learned to recognize division as a missing factor problem in which the quotient is the unknown factor.

In this lesson students apply their understanding of division to dividing with decimals. They use place-value understanding to identify connections between patterns in decimal division and whole-number division. They use visual models and the relationship between

multiplication and division to divide decimal numbers by whole numbers, tenths decimals, and hundredths decimals. Students use multiplication to check the results of decimal division and explain how to divide decimals using their own words.

Later in Grade 5 students will use their knowledge of decimal division when they convert from larger units of measurement to smaller units. In Grade 6, students will continue to multiply and divide with decimals.

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Lesson 9 Divide Decimals

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Lesson 9

Lesson Pacing Guide

Whole Class Instruction

Day 1

45?60 minutes

Toolbox: Interactive Tutorial* Divide Decimals

Introduction ? Use What You Know 15 min ? Find Out More 15 min ? Reflect 5 min

Practice and Problem Solving Assign pages 75?76.

Day 2

45?60 minutes

Modeled and Guided Instruction

Learn About Dividing a Decimal by a Whole Number ? Picture It/Model It 20 min ? Connect It 15 min ? Try It 10 min

Practice and Problem Solving Assign pages 77?78.

Day 3

45?60 minutes

Modeled and Guided Instruction

Learn About Dividing by Tenths ? Picture It/Model It 10 min ? Connect It 10 min ? Try It 5 min

Modeled and Guided Instruction

Learn About Dividing by Hundredths ? Picture It/Model It 10 min ? Connect It 10 min ? Try It 5 min

Practice and Problem Solving Assign pages 79?82.

Day 4

45?60 minutes

Guided Practice

Practice Dividing Decimals ? Example 5 min ? Problems 17?19 15 min ? Pair/Share 15 min ? Solutions 10 min

Practice and Problem Solving Assign pages 83?84.

Day 5

45?60 minutes

Independent Practice

Practice Dividing Decimals ? Problems 1?6 20 min ? Quick Check and Remediation 10 min ? Hands-On or Challenge Activity 15 min

Toolbox: Lesson Quiz Lesson 9 Quiz

Small Group Differentiation Teacher-

Reteach

Ready Prerequisite Lessons 45?90 min Grade 4

? Lesson 12 Divide Whole Numbers

Teacher-led Activities

Tools for Instruction 15?20 min Grade 4 (Lesson 12)

? Divide by One-Digit Numbers

Student-led Activities

Math Center Activities 30?40 min Grade 4 (Lesson 12)

? 4.25 Dividing by One-Digit Numbers ? 4.26 Division Methods

Personalized Learning i-

Independent

i-Ready Lessons* 10?20 min Grade 4 (Lesson 12)

? Divide Whole Numbers ? Relating Division to Multiplication

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

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Lesson 9 Divide Decimals

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Lesson 9 Divide Decimals

Introduction

Lesson 9 Introduction Divide Decimals

5.NBT.B.7

At A Glance

Students explore dividing a whole number by a decimal. They use a diagram to understand the problem. Then they explore a process of logical reasoning using place value and division concepts. Then students explore the effect of dividing by 0.2 and 0.02 and notice patterns in the quotients.

Step By Step

? Work through Use What You Know as a class.

? Tell students that this page models dividing a whole number by a decimal.

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

English Language Learners ? If students say that they know the answer

just from looking at the diagram, point out that you would have to "do the math" to know how many sections to draw in the diagram. ? Ask student pairs or groups to explain their answers for the last question and relate the solution to place value. [2.0 is 10 times 0.2.]

Mathematical Discourse 1?3

SMP TIP Construct Arguments/ Critique Reasoning Students may construct arguments to explain the reasoning for this problem in a variety of ways. Encourage students to provide clear, logical explanations, to make connections between their explanations and others' explanations, and to critique reasoning by evaluating each other's reasoning for reasonableness and correctness. (SMP 3)

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Lesson 9 Divide Decimals

Use What You Know

Now that you know how to multiply with decimals, you'll learn how to divide with decimals. Take a look at this problem.

Mr. Kovich is preparing materials for a craft project. He needs to cut 2 meters of string into pieces that are 0.2 meter long. How many 0.2-meter pieces can he cut from 2 meters of string?

a. You need to find how many lengths of 0.2 meter are in 2 meters. Look at the drawing below.

2 meters

0

1

2

b. How many tenths of a meter are in 1 meter? 10 In 2 meters? 20

c. Circle lengths of 2-tenths meter on the drawing above.

How many lengths of 2-tenths meter are in 1 meter?

5

In 2 meters? 10

d. Explain how you could find how many 0.2-meter pieces can be cut from 2 meters of string.

Possible answer: You could draw a number line to show the problem, divide

the line into tenths, and then count to find how many lengths of two-tenths

are in 2 meters and see that the answer is 10.

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Mathematical Discourse

1 How can you explain the solution?

There are 10 tenths of a meter in 1 whole meter, or 5 two-tenths of a meter in 1 whole meter. 2 meters are twice as large as 1 meter, so there are twice as many two-tenths of a meter, which is 10 two-tenths of a meter in 2 whole meters.

2 How does the quotient compare to the divisor? The quotient is greater than the divisor.

3 Does the answer make sense? Why?

It makes sense because you are

splitting 2 meters into smaller

pieces, so there should be more

pieces. If you divide 2 meters into

1-meter pieces, you get two pieces.

If

you

divide

2

meters

into

1 ?2?

-meter

pieces, you get 4 pieces. And so on.

English Language Learners

To help students understand the problem, have them act it out using a 2-meter length of string and a 0.2-meter length of string.

Real-World Connection

Have students brainstorm situations that involve dividing by a decimal. Examples: Suppose you have $3 and you want to buy bananas. The bananas cost $0.80 per pound. How many pounds of bananas can you buy?

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Find Out More

On the previous page, you saw that 2 4 0.2 5 10. How is that similar to the division fact 2 4 2 5 1? How is it different?

Look at the table below to see some patterns in division.

Expression 2 4 2 2 4 0.2

2 4 0.02

Expression in words How many groups of 2 are in 2? How many groups of 0.2 are in 2? How many groups of 0.02 are in 2?

Quotient 1 10 100

When the divisor is greater than 1, the quotient is less than the dividend.

When the divisor is less than 1, the quotient is greater than the dividend.

dividend

divisor

quotient

2

?

2

=

1

2

?

0.2

=

10

2

?

0.02

=

100

Reflect

1 Look at the table above. What do you think is the quotient of 2 4 0.002? Explain your reasoning.

Possible answer: 2 4 0.002 means how many groups of 0.002 are in 2. Based

on the pattern in the table, there should be 1,000 groups of 0.002 in 2. So

the quotient is 1,000.

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Concept Extension

Model decimal division as repeated subtraction.

? Act out the problem given. Start with a 2-meter piece of string. Measure and cut off 0.2 meter. Write on the board, "2 2 0.2 5 1.8." Explain that after cutting off the first 0.2 meter, you have 1.8 meters left.

? Ask students if you have enough left to cut another 0.2 meter. [yes] ? Measure and cut off 0.2 meter. Under the previous equation, write "1.8 2 0.2 5 1.6."

Say that after cutting off another 0.2 meter, you have 1.6 meters left. ? Ask students if you have enough left to cut another 0.2 meter. [yes] ? Continue cutting of 0.2 meter and subtracting. Consider inviting students to cut or

write the equations. ? When there is no more string left and the last equation, "0.2 2 0.2 5 0," has been

written, count the number of pieces of string that were cut. [10] Have a student count the number of times that 0.2 was subtracted in the equations. [10]

Lesson 9

Step By Step

? Read Find Out More as a class. ? Ask students to describe the patterns they

see in the table for dividing a whole number by a decimal. [Each time the decimal decreases by a factor of 10, the quotient increases by a factor of 10. Dividing by a tenths decimal results in a quotient in the tens. Dividing by a hundredths decimal results in a quotient in the hundreds.] ? Point out to students that the quotient is greater than the divisor. Ask students why this makes sense. [The quotient is greater than the divisor because you are finding how many groups less than 1 are in the whole number.] ? Students complete Reflect on their own. Then discuss as a class.

Concept Extension

Real-World Connection

Mathematics PRACTICE AND PROBLEM SOLVING

Assign Practice and Problem Solving pages 75?76 after students have completed this section.

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Lesson 9 Divide Decimals

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Lesson 9 Divide Decimals

Modeled and Guided Instruction

At A Glance

Students use a bar model and the relationship between multiplication and division to divide a decimal by a whole number. Then students revisit this problem and develop an understanding of how to divide by tenths.

Step By Step

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

? Point out that in this problem, the number of sections, or groups, is known and students need to find the size of each section, or group.

Picture It

? Read Picture It as a class. Point out that the bar represents the length of the race path divided into 9 equal sections. Point out that the question mark represents the size of each section, or group.

Model It

? Discuss the multiplication equation shown in Model It. Ask students to think about what basic multiplication fact they can use to find 9 3 ? 5 27. [9 3 3 5 27]

Mathematical Discourse 1?3

SMP TIP Look for Structure/Use Structure Encourage students to look for structure in place-value patterns and discuss the connections between dividing tenths and dividing whole numbers. Have students discuss the patterns they see and make use of structure to understand problems. (SMP 7)

Hands-On Activity

Lesson 9 Modeled and Guided Instruction

Learn About Dividing a Decimal by a Whole Number

Read the problem below. Then explore different ways to understand dividing a decimal by a whole number.

Coach Ann is setting up a 2.7-kilometer race. She uses flags to mark off 9 equal sections of the race. How far apart should she space the flags to mark off the sections?

Picture It You can draw a bar model to represent the problem.

You know the number of kilometers to be divided into equal groups. You know the number of equal groups.

2.7 kilometers

? You do not know the number of kilometers in each group.

Model It You can use the relationship between multiplication and division to

understand the problem. To find 2.7 4 9, think 9 3 ? 5 2.7.

2.7 5 27 tenths Use words:

9 3 ? tenths = 27 tenths

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Mathematical Discourse

1 Why can you picture a division problem using multiplication? Because division and multiplication are opposite operations. The quotient and divisor in division are the factors in multiplication. The dividend is the product.

2 What basic division fact is related to this problem? 27 4 9 5 3

3 How is this problem related to 27 4 9 5 3? 27 is ten times as much as 2.7, and 3 is ten times as much as 0.3. If you divide both sides of the equation by 10, than you get the equation 2.7 4 9 5 0.3.

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Lesson 9 Divide Decimals

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