Use this dialog to guide discussion of Questions 1 and 2 in the Student Guide.
Teacher: How did you find how many people can ride the 8 cars on the roller coaster?
Yolanda: I used hoppers on my number line.
Teacher: Show us how you did that using the class number line.
Yolanda: [She uses a pointer starting at 0 on the class number line and shows hops of 4 each.] Each hop is like filling one car with 4 people. So, 4, 8, 12, 16, 20, 24, 28, 32. So, 32.
Teacher: So that means that you have 32 cars or 32 people?
Yolanda: 32 people.
Teacher: Why did Yolanda hop by 4s? What do the 4s stand for?
Nisha: Each hop is for one car because each car has 4 people, but I don't know why she stopped at 32.
Teacher: Good point, Nisha. How did Yolanda know how many times to hop?
Jason: There were 8 cars, so she made 8 hops.
Teacher: Can you write a multiplication number sentence for this problem and tell me what each number means?
Jason: 8 × 4 = 32. The 8 is for the number of cars, and the 4 is the number of people in the cars. The 32 is for all the people on the roller coaster.
Teacher: Let's look at the display of your solution, Yolanda. Good work! What labels can you add to show what the numbers mean?
Yolanda: I need to add which numbers represent the cars and which numbers represent the people.
Teacher: Yes! [See Figure 1.]
Teacher: Did anyone use a different method?
Julia: I doubled to solve Question 1.
Teacher: What do you mean? What did you double?
Julia: I doubled the cars and the people in the cars.
Teacher: Show us on the board.
Julia: I thought 4 people in a car like in the picture. 4 + 4 = 8. So 8 people in 2 cars. Then I doubled 8. 8 + 8 = 16. 16 people in 4 cars. Then I doubled 16 for 8 cars. 16 + 16 = 32. So 32 people in 8 cars. [See Figure 2.]
Teacher: Are there any questions for Julia about her strategy?
Romesh: How did you know 16 + 16 is 32?
Julia: I added the two 10s to get 20 and then I added the two 6s to get 12. 20 + 12 is 32.
See Figure 3 for other possible strategies to solve Question 1.
Figure 4 shows possible strategies for determining the number of blocks in the entrance wall for Question 2.
Use this dialog to guide discussion of Questions 4 and 5.
Teacher: While you were working together, I noticed that Fern and Roberto made a table to solve Question 4, so I asked them to write it on a display so that they can show it to you. [Figure 5 shows Fern and Roberto's table.] Show us your table and tell how you used it to solve the problem.
Fern: Here it is. The answer is 4 minutes.
Teacher: Do you agree? Do you understand how they used the table? Do you have questions for Fern and Roberto?
Liz: What are the numbers in the first column? There is nothing that tells.
Roberto: They are the number of times it goes around. See, one time around takes 30 seconds and two times around takes one minute. Like that.
Teacher: What can you write in the table to show that?
Roberto: Number of times around? [Writes that at the top of the column.]
Teacher: What is a good heading for the next column of numbers?
Roberto: Time it takes?
Teacher: Okay.
Mark: Look, that table makes it easy to do B. See, 21/2 minutes is 2 minutes and 30 seconds. The table shows that is 5 times around.
See Figure 6 for other strategies to solve time problems about the Lizard-Go-Round in Question 4.
Figure 7 represents possible strategies to solve the ice cream problem in Question 5.
