Repeated Addition and Multiplication

Est. Class Sessions: 2

Developing the Lesson

Part 1: Multiplication Concepts

Solve Zoo Produce Problem. The amounts of food listed on the Children’s Zoo Produce List Master and the Children’s Zoo Produce pages were taken from actual vendor produce lists furnished by Lincoln Park Zoo in Chicago, Illinois. The zoo animals really eat these fruits, vegetables, and other food items.

Display the Children’s Zoo Produce List Master.

Point out the amount of each food on the list, then present the following situation:

This list shows the daily amount of different foods that the Children’s Zoo uses to feed the animals. There will be one food delivery to cover the animals’ meals for a three-day weekend. The zookeeper needs your help to figuring out how much of each kind of food she will need to order for these three days.

Ask students to help you find the amount of yellow squash the zookeeper needs to order for a three-day weekend.

Ask:

How much yellow squash does the zookeeper order for one day? (14)
How can we find out how much yellow squash is needed for three days?

Discuss students’ methods and strategies for finding the amount of squash needed for three days. Pass out connecting cubes and ask them to model the amount. Once students have modeled the problem with connecting cubes, ask students to explain their strategies for solving the problem. Record the solution on the display. See the Sample Dialog. Work a few more of the problems on the display with the whole class.

The following dialog was adapted from a videotape of student discussions in a second-grade classroom.

Teacher: Now that you have made 3 stacks of 14 cubes, how can you figure out how many you have in all? What did you do, Irma?

Irma: I counted them. It was 40.

Teacher: How did you count them?

Irma: By ones.

Teacher: Did counting like that work all right for you?

Irma: Yes, but it took a long time because I kept getting mixed up.

Teacher: Yes, that is sometimes a problem with counting so many things.

Luis: I just made them into tens and leftovers and then I counted.

Teacher: How did you do that, Luis?

Luis : I took the 14 stack and if you take 4 off it makes ten. I did that with all of them so I had 3 tens. That’s 10, 20, 30.

Teacher: Then what did you do?

Luis : I had 4 and 4 and 4 left over. [shows 3 stacks each with 4 cubes, points to each stack and counts] 31, 32, 33, 34, [pause], 35, 36, 37, 38, [pause], 39, 40, 41, 42.

Teacher: You got a different answer from Irma. What answer did the rest of you get?

Frank: I got 42, too. [Other students also say 42.]

Teacher: Irma, you got 40 for your answer. What do you think the problem might be?

Irma: I probably got mixed up in my counting.

Teacher: That’s what I think, too. It’s easy to do when you are counting a lot of things by ones.

Keenya: I didn’t even count. I just knew 10 + 10 + 10 is 30. I added 4 + 4 + 4 and got 12. That’s another ten so then it was 40. And 2 left over, so 42.

Pay attention to what strategies and tools students are using to solve the problems. Encourage students to model the problems using the connecting cubes. Help them manage their cubes and count efficiently. See the TIMS Tip.

Many students, however, will not need to model every problem with cubes. Encourage them to use cubes for numbers as needed and to use one of the other strategies and tools when appropriate.

Working with as many cubes as are needed for the different problems is cumbersome and may lead to confusion and error. Help students manage the large numbers of cubes by keeping their cubes clearly separated from any extra cubes at their tables. A large piece of construction paper can be used as a work mat. Encourage them to count their cubes by tens and fives rather than by ones to determine the amount needed for the three days.

Develop Repeated Addition Strategies. Instruct student pairs to use their Children’s Zoo Produce pages in the Student Activity Book to find the amount of certain foods needed for three days. Students will record their solutions on order slips for the zookeeper. Encourage them to use a variety of strategies to triple the number of each food listed. See Figure 1 for some tools and techniques students might use to solve these problems.

Upon completion, have students explain their strategies for finding the solutions.

Ask:

What strategy did you use to solve the problem?
Did anyone use a different strategy?
How can you use [student name]’s strategy to solve the next problem?
Did anyone use the answer they found in one problem to help solve a different problem? (Possible response: For 13 stalks of celery, my answer was 39, so I knew that 12 bags of apples would be 3 less. I subtracted 39 − 3 = 36.)

Record students’ strategies on the “Repeated Addition Strategies” chart prepared prior to the lesson. See Materials Preparation. Display the chart throughout the remainder of the unit to allow students to refer to it as needed.

If some student pairs finish early, have them finish the items on the display of the Children’s Zoo Produce List Master if it was not completed earlier in the lesson.

Adventure Book: