Division in Lizardland

Est. Class Sessions: 2

Developing the Lesson

Discuss Math Practices. Direct students' attention to the Division in Lizardland pages in the Student Guide. They will find the information needed to solve the problems in the pictures of Lizardland.

Each problem can be solved using division. Students will need to find a strategy [MPE2] and show their work [MPE5]. The division problems can be represented with number lines, drawings, rectangular arrays, counters, and number sentences. Encourage students to use a variety of solution strategies including skip counting, repeated addition, repeated subtraction, reasoning from known facts, and their own invented strategies. Display and refer student to the Math Practices page in the Student Guide Reference section.

Share the following problem aloud:

A small bus is taking 24 children to Lizardland. Each seat holds 3 children. How many seats will be needed?
Tell in your own words what question needs to be answered [MPE1]. (Possible response: We need to find out how many seats filled with 3 children there will be if there are 24 children on the bus.)
Show how to use counters to help you solve the problem. (A student counts out 24 counters and then places them in rows of groups of 3 until all of the counters are placed into 8 rows or groups.)
Show this problem with a drawing. (See Figure 1.)
Write a number sentence that matches this solution and include labels [MPE6]. (24 children ÷ 3 children in each seat = 8 seats)
Show how to check this problem using a number line. (See Figure 2.)
Share another way to check this problem. (Possible response: I used repeated subtraction. I started with 24 children and kept subtracting groups of 3 until I got to 0. I subtracted 3 eight times, so 24 ÷ 3 = 8.)
Is there another way to solve this problem?

Encourage students to use the multiplication facts they have been working with to obtain the related division facts. Multiplication facts and their related division facts are often referred to as fact families. Discuss the relationship between multiplication and division.

Point out that a problem such as 24 × 3 can be solved by thinking:

How many 3s are there in 24? (8)
What number times 3 equals 24? This can be represented as × 3 = 24.

Students can use their completed copy of My Multiplication Table for help learning the division facts.

Ask students to focus on Math Practices Expectations 1, 2, 5, and 6 as they solve Questions 1–7. Remind them to show their work and to use labels.

Use Representations and Strategies to Divide. Upon completion, take time to discuss some of the problems and solution strategies. Questions 4 and 5 provide an opportunity to discuss whether there is a turn-around rule for division. In Question 4, Mrs. Moore has three oranges to share among six people: 3 ÷ 6 = 1/2.

Ask:

Draw a picture to solve 3 ÷ 6. (See Figure 3.)

In Question 5, Mrs. Moore shares six cookies among her three children: 6 ÷ 3 = 2.

Ask:

Draw a picture to solve 3 ÷ 6. (See Figure 4.)

Use these examples to point out that changing the order of the terms in a division sentence, unlike a multiplication sentence, does change the answer. There is no turn-around rule for division.

Ask:

What is 2 × 3's turn-around fact? (3 × 2)
2 × 3 equals? 3 × 2 equals? (6)
Does changing the order of the factors in a multiplication sentence change the answer? (no)
Is there a turn-around rule for division? Does 3 ÷ 6 = 6 ÷ 3? Explain. (No, the turn-around rule does not work for division. 3 ÷ 6 = 1/2 and 6 ÷ 3 = 2. Students may refer to their solution drawings as shown in Figures 3 and 4.)
Does changing the order of the numbers in a division sentence matter? Why? (Yes. Possible explanation: The number of things you are dividing up goes first in the division sentence. The next number tells how many equal shares there will be. If you change the order of these numbers, you will get a different answer.)

Division Involving Zero. Questions 6 and 7 provide an opportunity to discuss division involving zero. In Question 6, Mr. Moore has zero cupcakes to share among six people. Each person receives zero cupcakes, so 0 ÷ 6 = 0. In fact, 0 divided by any nonzero number is 0.

In Check-In: Question 7, the ticket taker has 100 game tokens to distribute to the families as they enter the park. Students examine what will happen if he distributes different numbers of tokens to the families. Depending on how many he gives to each family, he runs out after different numbers: Giving 4 game tokens to each family, he runs out after 25 families enter; giving 2 tokens, 50 families; giving 1 token, 100 families. These situations can be represented by these division sentences: 100 ÷ 4 = 25, 100 ÷ 2 = 50, and 100 ÷ 1 = 100. If, however, he gives 0 game tokens to each family as they enter, then more and more families will enter the park, but he will never run out of tokens. Therefore, there is no numerical value for 100 ÷ 0. We say that division by 0 is undefined. See the Mathematics in this Lesson section for a discussion of division by zero.

Use Check-In: Question 7 on the Division in Lizardland pages in the Student Guide with the corresponding Feedback Box in the Teacher Guide to assess students' abilities to represent division problems with number sentences and drawings [E1]; use appropriate and efficient strategies to solve division problems [MPE1, MPE2, E2]; show their work so someone else can understand their thinking [MPE5]; and use labels to show what numbers mean [MPE6].

The Workshop in Lesson 10 provides targeted practice for these expectations.

Use Division Symbols. Display the following division sentences: 24 ÷ 6, 24/6, and .

Ask:

What do these number sentences mean? (They all mean 24 divided by 6.)

Point out to students that they will see these three different symbols for division in Questions 8–13. As you continue to write division number sentences, vary the notation so students will become familiar with all three.

Solve Division Facts with Fact Families. Explain to students that knowing the multiplication facts in a fact family can help them solve division facts within the same family. Questions 14–16 show students number sentences for related fact families.

Ask students to find their Triangle Flash Cards for 4 × 5, 5 × 9, and 6 × 10. Demonstrate how to use a flash card to find all four facts in a fact family using a display of the Large Triangle Flash Card Master.

For 4 × 5, write 4 in the square, 5 in the circle, and 20 in the gray triangle of the Master. First, find the multiplication sentences in the fact family. Cover 20 to show how to use the card to solve 5 × 4 = . Uncover the number so that students can check their answers. Cover 5 to show how to solve 4 × = 20. Record each of the multiplication number sentences, 5 × 4 = 20 and 4 × 5 = 20.

Then, find the division sentences in the fact family. Cover the 4 to show 20 ÷ 5 = and then cover the 5 to show 20 ÷ 4 = . Record each of the division number sentences, 20 ÷ 5 = 4 and 20 ÷ 4 = 5 to complete the fact family.

Ask a student to show each of these number sentences with counters. For example, 5 groups of 4 counters is 20, and 20 counters divided into groups of 4 will result in 5 groups. Or students can make arrays with 20 counters. 20 counters divided into 5 rows of 4, and so on.

Assign Questions 8–16 in the Student Guide.

The Homework section in the Student Guide provides multiplication and division practice with fact families.

Student Guide: 207 208 REF

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