## Drawing Straws

### Timothy Mark DillehayLee County School District

#### Description

Students enjoy this engaging activity by investigating possible lengths to sides of a triangle. Students discover the Triangle Inequality Theorem through hands-on activities with straws.

#### Objectives

Uses properties and relationships of geometric shapes to construct formal and informal proofs.

#### Materials

-Ditto 1 (associated file)
-Ditto 2 (associated file)
-Chalk board for listing
-Straw sets for each student

#### Preparations

1. Gather and cut straws for each student (measurements of 2, 3, 4, and 5 inches long)
2. Duplicate Ditto 1 per student.
3. Duplicate Ditto 2 per student.
4. Make a copy of answers.

#### Procedures

1) Begin by reading this question, "A boy scout is going to create a triangular camp fire, using three large logs. The large logs will be able to contain the fire. Would any measurements of logs he finds make a trangle, if placed end-to-end-to-end?" Allow a few minutes for discussion and then tell students that today we are going to investigate this situation.

2) Hand out Ditto 1.

3) Give students 5 straws of lengths 2, 3, 3, 4, and 5 inches.

4) Have students choose any 3 straws.

5) Have students attempt to place the straws end-to-end-to-end to form a triangle.

6) If a triangle cannot be made, have them pause.

7) After a minute write on the board, “Possible Triangles” and “Not Triangles” as on Ditto 1.

8) Have students raise their handd and give 3 straw measurements that they choose while trying to make a triangle.

9) List each 3 measurements together on the side of the board where it belongs.

10) Complete these exercises by telling the students to choose 3 straws with measurements that are not already listed together on the board.

11)List the additional triplets under the “Possible” or “Not” as appropriate.

12)Have students complete the Ditto 1. (5 minutes)

13) Discuss correct and incorrect conclusions that students had written on Ditto 1.

14) Pass out the Ditto 2.

15) Present (read and explain) the triangle inequality: "Triangle Inequality Theorem = states The sum of the lengths of any two sides of a triangle is greater than the length of the third side." Draw any triangle XYZ, now state "XY + YZ > XZ and YZ + XZ > XY and XZ + XY > YZ." Allow time for discussion and then apply this to the examples and nonexamples listed on the board. Make sure all students understand and agree.

16) Have students complete Ditto 2.

#### Assessments

Use completed Ditto 1 and 2 (see Associated File) to formatively assess the student's ability to create a relationship among the sides of triangles.

Criteria:
(1) To have Ditto 1 completed 100% from the class discussion.
(2) To have only one incorrect answer on Ditto 2.

Students who have difficulty will need additional instruction and practice with guiding feedback.

#### Extensions

How many possible triangles can be made from the measurements of 5, 7, 10, 12, and 15 feet?

#### Attached Files

This file includes Ditto 1 and Ditto 2.     File Extension: pdf

This file includes answers.     File Extension: pdf