LESSO Lesson 6 OVERVIEW Divide Whole Numbers

LESSON Lesson 6 OVERVIEW Divide Whole Numbers

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.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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 three- and four-digit dividends by two-digit divisors.

? Use the relationship between multiplication and division to estimate quotients.

? Divide whole numbers using area models and strategies such as placevalue understanding, properties of operations, estimating quotients, and finding partial quotients.

Language Objectives

? Explain the relationship between multiplication and division.

? Define partial products and use the term in a discussion with a partner.

? Draw an area model to represent a multi-digit division problem and discuss the model's relationship to the partial quotients and quotient.

? Construct arguments using objects, diagrams, and models.

Prerequisite Skills

? Understand place value. ? Know the properties of operations. ? Recall basic multiplication and division

facts. ? Divide four-digit dividends by

one-digit divisors. ? Know that multiplication and division

are inverse operations.

Lesson Vocabulary

There is no new vocabulary. Review the following key terms. ? division an operation used to

separate a number of items into equal-sized groups ? divisor the number by which another number is divided ? dividend the number that is divided by another number ? quotient the result of division ? partial quotient a strategy used to divide multi-digit numbers; the quotients you get in each step are called "partial quotients". For example, the partial quotients for 2124 4 4 are 2000 4 4 or 500, 100 4 4 or 25, and 24 4 4 or 6.

Learning Progression

In Grade 4 students divided three- and four-digit dividends by one-digit divisors. They used area models, applied the idea of subtracting partial products, and learned how to find partial quotients to divide. Students solved division problems with remainders and interpreted the remainder in the context of a problem.

In this lesson students divide dividends of up to four digits by two-digit divisors. They see division

problems as missing factor problems in which the quotient is the unknown factor. They use estimation as a strategy to begin finding a quotient when dividing. Students apply place-value understanding to find partial quotients and record the quotient as the sum of the partial quotients.

Later in this grade students will divide decimals using the same strategies that they use with whole-number division.

42a

Lesson 6 Divide Whole Numbers

?Curriculum Associates, LLC Copying is not permitted

Lesson Pacing Guide

Whole Class Instruction

Day 1

45?60 minutes

Toolbox: Interactive Tutorial* Division of Whole Numbers

Introduction ? Use What You Know 10 min ? Find Out More 10 min ? Reflect 5 min

Modeled and Guided Instruction Learn About Dividing by Two-Digit Numbers ? Model It/Model It 10 min ? Connect It 10 min ? Try It 5 min

Practice and Problem Solving Assign pages 47?50.

Day 2

45?60 minutes

Guided Practice

Practice Dividing Whole Numbers ? Example 5 min ? Problems 9?11 15 min ? Pair/Share 15 min ? Solutions 10 min

Practice and Problem Solving Assign pages 51?52.

Day 3

45?60 minutes

Independent Practice

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

Toolbox: Lesson Quiz Lesson 6 Quiz

Lesson 6

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 Grade 5 (Lesson 6) ? 5.17 Division with Area Models ? 5.18 Solve Area Problems with Division

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.

?Curriculum Associates, LLC Copying is not permitted

Lesson 6 Divide Whole Numbers

42b

Lesson 6 Divide Whole Numbers

Introduction

Lesson 6 Introduction

5.NBT.B.6

Divide Whole Numbers

At A Glance

Students explore a division problem involving the quotient of a three-digit dividend and a two-digit divisor. They use multiples of 10, the distributive property, and the relationship between multiplication and division. Then students investigate an area model as another approach for solving this problem.

Step By Step

? Work through Use What You Know as a class.

? Tell students that this page models one way to solve a division problem with a two-digit divisor. Have students read the problem at the top of the page.

? Have students explain how they estimated the quotient to be between 20 and 30. [Think of 345 4 15 5 ? as 15 3 ? 5 345. 345 is between 15 3 20 and 15 3 30.]

? Discuss why 300 is subtracted from 345 when trying to find the quotient. Students might recognize that 345 can be broken apart into 300 1 45 and that they can divide each addend by 15. They get the same result as dividing 345 by 15.

? Demonstrate the advantages of breaking apart 345 into 300 1 45 (e.g., 300 is easy to work with and 45 is a multiple of 15). Show students how the division problem 345 4 15 5 ? can be written as (300 1 45) 4 15 5 ?

? Ask students to explain their answers for problem f.

SMP TIP Construct Arguments and Critique Reasoning Help students present clear reasoning and critique the reasoning of other students. When students present explanations, encourage them to build arguments step by step in a logical fashion so others can follow their reasoning. Have students build on each other's ideas. (SMP 3)

Mathematical Discourse 1 and 2

Use What You Know

In the last lesson, you learned how to find products of two- and three-digit factors. Now you will learn how to divide with two-digit divisors.

There are 345 fifth graders enrolled at Wilson Middle School and 15 fifth-grade classrooms. How many students are in each class if each class has the same number of students?

a. What multiplication equation can you use to solve 345 4 15? 15 3 ? 5 345

b. Multiply 15 by multiples of 10. Fill in the blanks.

15 3 10 5 150

15 3 20 5 300

15 3 30 5 450

c. Now estimate the quotient. The quotient will be between which two tens? 20 and 30

d. If 15 3 20 5 300, what number is left after you subtract this product from 345? 45

e. Divide what is left by 15. 45 4 15 5 3

f. Use the information above to find 345 4 15. Explain your thinking.

Possible answer: 15 3 20 5 300, 15 3 3 5 45, and 300 1 45 5 345.

Using the distributive property, 15 3 (20 + 3) 5 345. So, 15 3 23 5 345 and

345 4 15 5 23.

42

42

Mathematical Discourse

1 What is the benefit of breaking apart dividends into a sum of numbers? We can use multiples of ten and easy basic multiplication facts to find a quotient.

2 How does multiplication help us divide? Multiplication and division are inverse operations. This means they "undo" each other. Multiplying shows the number of groups and the number of items in each group. The product is the total number of items. In division, the dividend is the total number of items. The divisor and quotient are the number of groups or the number of items in each group. In this problem, the divisor is the number of groups and the quotient is the number of people (items) in each group.

42

Lesson 6 Divide Whole Numbers

?Curriculum Associates, LLC Copying is not permitted

Find Out More

On the previous page, you used the relationship between multiplication and division along with properties of operations to divide.

You can also use an area model to show division. It is similar to an area model for multiplication. You can think of division as finding a missing factor. The dividend is the product, the divisor is the known factor, and the quotient is the unknown factor.

The area model shows 345 4 15. ?

15

345

20

1

3

(15 3 20 5 300)

15

345

2 300

45

(15 3 3 5 45)

45 2 45

0

5 23

Start with the greatest place and find the quotient place by place. On the previous page, you estimated the quotient to be between 20 and 30. So, 20 is the greatest ten that can be in the quotient.

? Start by multiplying 15 by 20. ? Subtract the product from the dividend, 345. ? Write the difference, 45, in the next section of the model. ? Think: 15 3 ? 5 45. Multiply 15 by 3 and subtract this product from 45. ? The difference is 0, so there is nothing left to divide.

Reflect

1 How is dividing with an area model similar to multiplying with an area model? How is it different?

Possible answer: The same three numbers are used in related multiplication

and division area models. With multiplication, you use the model to find the

product. With division, you use the product to find the unknown factor.

43

43

English Language Learners

Help students learn and distinguish between the words dividend and divisor. The dividend is the quantity that will be divided. The divisor tells what number to use to divide the dividend. Do not tell students that the dividend is the greater number because later they will learn how to divide numbers that result in a fractional quotient.

Real-World Connection

Encourage students to think about everyday situations where people might need to divide whole numbers. Have volunteers share their ideas.

Examples: splitting up into even kickball teams, sharing toys equally, dividing pages in a book to read over several nights

Lesson 6

Step By Step

? Read Find Out More as a class. Have students point out the dividend, divisor, and quotient in the area model.

English Language Learners ? Have students explain why the area model is

broken into two sections: 300 and 45. [These numbers are easier to work with than 345, so it is easier to divide.] ? Discuss the importance of first estimating a quotient to help break apart a dividend into easy to work with numbers and for checking the answer. Point out to students that the estimated quotients of 20 and 30 would result in dividends of 300 and 450 because 20 3 15 5 300 and 30 3 15 5 450. Since the actual dividend, 345, is closer to 300 than 450, use the estimated quotient of 20 rather than 30. Ask: Which estimated quotient, 20 or 30, is the actual quotient closer to? [23 is closer to 20.] ? Students complete Reflect on their own. Then discuss as a group.

Real-World Connection

SMP TIP Use Tools Reinforce the use of an area model as a tool for multiplying and dividing by two-digit numbers. Remind students that when multiplying by a two-digit number, they used area models that broke apart one factor into tens and ones. Ask students to describe strategies they might use when creating area models for division problems. For example, breaking apart a dividend between the tens place and the hundreds place or breaking apart the dividend by using a large multiple of the divisor. (SMP 5)

Mathematics PRACTICE AND PROBLEM SOLVING

Assign Practice and Problem Solving pages 47?48 after students have completed this section.

?Curriculum Associates, LLC Copying is not permitted

Lesson 6 Divide Whole Numbers

43

Lesson 6 Divide Whole Numbers

Modeled and Guided Instruction

At A Glance

Students use an area model to think through a process for dividing by a two-digit divisor. Then students revisit this problem and work through the problem using partial quotients to find the solution. Then students apply the partial quotients approach to solve word problems.

Step By Step

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

Model It

? Read Model It. Invite a volunteer to give an estimate of the quotient of 624 divided by 12.

Model It

? Have students examine the area model in Model It.

Mathematical Discourse 1, 2, and 3

? Discuss with students how the steps inside the area model help solve the problem.

? Invite a volunteer to explain how to check the result of (50 1 2) 3 12 with the distributive property. [50 3 12 5 600 and 2 3 12 5 24. Then 600 1 24 5 624.]

SMP TIP Persevere in Problem-Solving Checking one's work using a different method is part of the process of persevering in solving a problem. Encourage students to check to see if their answers make sense. Have a student explain why it helps to use a different method. [You are unlikely to make the same mistake.] (SMP 1)

Hands-On Activity

44

Lesson 6 Divide Whole Numbers

Lesson 6 Modeled and Guided Instruction

Learn About Dividing by Two-Digit Numbers

Read the problem below. Then explore different ways to divide by a two-digit divisor.

A grocery store only sells eggs by the dozen. There are 12 eggs in 1 dozen eggs. If there are 624 eggs in stock, how many dozens of eggs are there?

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

estimate the quotient in a division problem with a two-digit divisor. 624 4 12 5 ? and 12 3 ? 5 624

Multiply 12 by multiples of 10. Make a table.

Number of dozens Number of eggs

10 20 30 40 50 60 120 240 360 480 600 720

Since 624 is between 600 and 720, the quotient is between 50 and 60.

Model It You can use an area model to solve a division problem with a

two-digit divisor.

?

12

624

50

1

2

(12 3 50 5 600)

(12 3 2 5 24)

12

624

2 600

24

24 2 24

0

5 52

44

Mathematical Discourse

1 Why is 624 broken into 600 and 24? It is easy to divide 600 by 12. 12 3 5 5 60, so 12 3 50 5 600. It is also easy to divide 24 by 12.

2 What do we learn from the subtraction equation 624 2 600 5 24? After sharing 600 eggs into 50 dozen cartons, we need to find out what's left. So, we subtract the 600 we shared from the original 624 eggs. There are 24 left.

3 What do we learn from the subtraction equation 24 2 24 5 0? After sharing the remaining 24 eggs into 2 dozens, we want to find out what's left. So, we subtract 24 from the 24 eggs that remained. We have 0 left, so we are finished dividing.

Hands-On Activity

Estimate a quotient using base-ten blocks.

Materials: base-ten longs, prepared area model of 462 4 33 that breaks apart the dividend as 330 1 132

? Give students a problem such as 462 4 33.

? 462 is close to 460, so have students model 462 as 46 tens.

? 33 is close to 3 tens. Ask students: How many groups of 3 tens can you make with 46 tens?

? Students make 15 groups of 3 tens. Connect the 15 groups to an estimated quotient of 15.

? Show students the area model. Demonstrate that 33 3 10 5 330 and 33 3 4 5 132, so the quotient is 10 1 4, or 14.

? Have students compare the actual quotient to the estimate.

?Curriculum Associates, LLC Copying is not permitted

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download