Birthday Party

Est. Class Sessions: 2

Developing the Lesson

Explore Strategies to Divide. Students work in pairs to solve problems on the Birthday Party pages in the Student Guide. Each of the problems focuses on how Kim will divide various items for her birthday party. Although the problems can be solved using division, students may use a variety of strategies to arrive at the answer. See Sample Dialog 1.

Give each pair about thirty counters. Encourage students to use them to solve Questions 1–3 and to provide explanations with words and pictures. If students answer the questions without the counters, ask them to check their solutions using the counters.

Check to see that students understand that Kim will be included in the plans for games and refreshments. That means that Kim will plan for a total of 15 people in Questions 1–3 and 12 people in Questions 4–9. However, for Question 10, the balloons will be shared among 11 guests and the leftovers go to Kim.

As students work, help them describe what they are doing by rephrasing the problem.

For example, Question 1 can be restated as:

If 15 people are divided into three equal groups, how many are on each group?

Question 2 can be restated as:

How many groups of 4 are in 15?

After students have had time to work on Questions 1–3 use prompts similar to those in Sample Dialog 1 discussing Question 1 to help guide a class discussion about the strategies and number sentences students used to solve these problems.

Use the following dialog to help students explore strategies for solving problems involving division that include interpreting remainders.

Teacher: What strategy did you use to solve Question 1?

Josh: We used our counters. First we took 15 counters to represent Kim and her 14 friends. Then we divided the counters into three groups to show the three teams. There were 5 people in each team.

Teacher: Did anyone use a different strategy to solve this problem?

Rosa: We drew a picture to show the 15 people at the party. Then we put them into three groups. Each group had 5 people in it.

Teacher: Can someone show how to use the number line to solve Question 1?

Yolanda: I think it would be like using a constant hopper. The hopper would start at 0 and hop three times. It would end at 15. Each hop would be five spaces, so it would be a +5 hopper.

Levi: We used the number line a different way. Since there were 15 people at the party we started on 15 and then hopped backwards three times until we got to zero. Our hopper was a −5 hopper.

Teacher: When you think about the number line, what does the 5 mean for each of your hoppers?

Yolanda: I think the 5 shows the number of people on each team.

Levi: I agree.

Teacher: Did anyone use a number sentence to show the solution?

Luis: We thought about 5 + 5 + 5 = 15 to show that there were three teams with 5 kids on each team.

Nisha: We wrote 3 × 5 = 15 to show that there are 3 teams with 5 kids on each.

Teacher: You can also use a division number sentence, 15 ÷ 3 = 5, to show that we are dividing the 15 guests into three equal teams. Look at each of the numbers in the number sentence. What does each number represent?

Chris: I think the 15 shows the number of kids at the party, the three tells the number of teams and the 5 is the number of kids on each team.

Division sentences can be written in many ways, each of which provides different information to the reader. During these early experiences with division, we write sentences like the example below on the far left. The next two examples are important in understanding fractions and decimals and will be introduced later in the curriculum.

In Math Trailblazers we use the representation of division below on the far right infrequently in third grade, but students should be aware that others use this notation.

In Question 2 students will need to decide how to use the remainder in their answers. Although 15 ÷ 4 = 3 with 3 left over, it is important that students understand what each of the numbers in this number sentence represents in order to interpret the remainder. A diagram or drawing may help students understand this problem more clearly. See Figure 1.

In this problem the 15 represents the number of people at the party, the 4 tells the number of people who can sit at each table. The first 3 tells the number of full tables you will need and the “leftover” 3 is the number of people who will not have a place to sit. Since it would be impolite for Tina to let three guests stand, she will have to add another table for her guests. The answer should be four tables.

Use Strategies to Divide. Ask students to continue to work with their partner to complete Questions 4–7. Remind students that they can use counters, drawings, number lines, and number sentences to solve each problem.

Question 7A asks students to decide how to share thirty cupcakes equally among the twelve people at the party. Each person can eat two whole cupcakes, but students must decide what to do with the six leftover cupcakes. They can choose to note that there will be six leftover cupcakes or they can divide each of the six cupcakes in half so each person will get 21/2 cupcakes. Either answer is appropriate. In Question 7B students are asked to find a second way to divide the cupcakes among the guests.

Ask students to complete Check-In: Questions 8–10. Students can continue to work with their partners or these questions can be completed independently.

Question 8 deals with fractions when it asks how much pizza each of twelve people can eat if they order six pizzas. Have students draw pictures to represent the problem as they did in Unit 3 Lesson 3 Multiplication Stories. See Figure 2 for sample correct and incorrect solutions.

Use Check-In: Questions 8–10 in the Student Guide to assess students' abilities to represent solution strategies for problems involving division including interpreting remainders using models, drawings, number lines, and number sentences [E5].