Finding Multiple Ways to Solve a Problem
by Marilyn Burns

Problems in mathematics often call for finding all of the different possibilities, and this month's column of literature-based activities presents two such situations based on real-life experiences. Primary children investigate the different ways that 12 children can line up, while intermediate students explore how to arrange small square tables to seat different numbers of people.

### ACTIVITY 1: How many ways can our class line up?

Purpose: To explore all possibilities in a problem.
Materials: Stay in Line by Teddy Slater (Scholastic, 1996), counters
Time Needed: two 20-minute periods

1. Read aloud Stay in Line, the story of 12 boys and girls who head off on a field trip to the zoo and find multiple ways of staying in line and sticking together. The story helps build children's number sense by exploring the different ways to organize a dozen children.

2. To help children cement the idea that a dozen is made up of 12 objects, have them decide whether the answer for each of the following questions is exactly a dozen, more than a dozen, or fewer than a dozen:

3. Give each child a dozen counters and ask students to follow your directions to arrange them in twos. Count aloud — 2, 4, 6, 8, 10, 12 — and encourage the children to count aloud with you. Do the same for arranging the counters in threes, fours, and sixes. Then try fives and talk about why there are leftover tiles.

4. Ask the class to figure out how many children are present. Then ask if they would each have a partner if they lined up in twos. Have children line up in pairs to check. Do the same for lining up in threes, fours, fives, and sixes.

### ACTIVITY 2: Discovering area and perimeter

Purpose: To explore area and perimeter.
Materials: Spaghetti and Meatballs for All! by Marilyn Burns (Scholastic, 1997), square tiles
Time Needed: 30 minutes

1. Read the book Spaghetti and Meatballs for All! It's a topsy-turvy tale about Mr. and Mrs. Comfort, who are busily cooking a feast and arranging 8 tables and 32 chairs so that everyone will have a seat. As the guests arrive, however, and families ask to sit together, the Comforts rush around to rearrange the tables so they can accommodate everyone. After they've tried six different combinations, they go back to their original setup and the guests happily get their fill of spaghetti and meatballs.

2. Although Mrs. Comfort doesn't use mathematical terms to describe her seating plans, she's talking about area and perimeter. Have students use small square tiles or other manipulatives to construct different ways the Comforts could arrange eight tables to seat guests.

3. Go through the book again with the class, this time drawing or having students draw a picture of each new table arrangement. Figure out how many people could be seated at each. Use the words area and perimeter to talk about the size of each arrangement and the number of people it seats.

4. Have children use the tiles or drawings to investigate the following problems: Suppose there were going to be just 12 people at the family reunion. What different table arrangements are possible? Which arrangement would use the fewest tables? Which arrangement would use the most tables?

5. For additional challenges, try the same problem for 16, 24, 36, or any other number of people.

Editor's Note: This book and an expanded lesson based on it are included in the forthcoming Marilyn Burns Math By All Means Unit, Area and Perimeter by Cheryl Rectanus (Cuisenaire, [800] 237-0338).

Marilyn Burns is the creator of Math Solutions, inservice workshops offered nationwide, and the author of numerous books and articles.
This activity was adapted from 50 Problem-Solving Lessons, Grades 1-6 by Marilyn Burns, distributed by Cuisenaire.