(1) Purpose: Provide readiness for finding possible triangle combinations. Practice finding the perimeter of triangles.

Age Level: Grades 3rd through 6th

(2) Overview: Children use three sizes of straws to construct as many different triangles as they can. They find the perimeter of each.

(9) Materials: Students will need 10 of each the following: 4" straws, 6" straws, 8" straws; 30 twist-ties

(11) Directions: Children work in groups of 2 or 3. Before they start, they discuss what strategy to use to solve the problem of making different triangles as they can from straws; they also discuss how to share the work. They straws can be either 4 inches, 6 inches or 8 inches long.

(1) There are 9 possible ways to combine the straws to construct triangles: 4-4-4; 6-6-6; 8-8-8; 4-4-6; 4-6-6; 4-6-8; 4-8-8; 6-6-8; 6-8-8. As children construct each triangle, they record the length and perimeter on a piece of paper.

(4) Children then compare triangles. Bring the class together to share their observations. These might include the following:

• The triangles with equal sides - 4-4-4; 6-6-6; 8-8-8 - have similar shapes but not the same size.

(7) Two pairs of triangles have the same perimeter: 6-6-6 and 4-6-8; 4-8-8 and 6-6-8. The areas of the 6-6-6 and 6-6-8 triangles are greater than those of the 4-6-8 and 4-8-8 triangles, respectively.

(10) Although there is one other way to combine the straws (4-4-8), this combination cannot be used to construct a triangle since the sum of the lengths of the two shorter sides equals the length of the longer side.

(8) Follow - Up

Discuss these questions with others in your group.

• Which triangles have similar shapes?
• Which pairs of triangles have the same perimeter? By looking at your constructions, estimate which pair of triangles has the larger area.
• What happens if you try to make a triangle out of two 4-inch straws and one 8-inch straw?

(13) Extension

• Try this activity using squares.