Problems in mathematics often call for finding all of the different possibilities,
and this month's column of literaturebased activities presents two such
situations based on reallife 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?
Grades:
K–3
Purpose: To explore all possibilities in a problem.
Materials: Stay in Line by Teddy Slater (Scholastic,
1996), counters
Time Needed: two 20minute periods
 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.
 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:
 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.
 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
Grades:
4–6
Purpose: To explore area and perimeter.
Materials: Spaghetti and Meatballs for All! by
Marilyn Burns (Scholastic, 1997), square tiles
Time Needed: 30 minutes
 Read the book
Spaghetti and Meatballs for All! It's a topsyturvy 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.
 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.
 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.
 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?
 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] 2370338).
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 ProblemSolving Lessons, Grades 16 by Marilyn
Burns, distributed by Cuisenaire.
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