Pythagorean Puzzler

May 22, 2014 | by Albert J. and B. Michael

Primary Market

Education, Secondary Ed

Character Focus

Communication, Cooperation, Teamwork

Items Needed

1 Toobeez set, 1 meter stick, 1 sheet of graph paper per student, 1 pen/pencil per student

The Activity Time

40 - 50 minutes

- Introduce students to the Pythagorean theorem
- Aid students in manipulating and solving Pythagorean equations
- Use predicting skills to determine the lengths of the various sides of right triangles
- Aid students in understanding the mathematical significance of the Pythagorean theorem
- Work cooperatively with others to understand mathematical concepts in a teambuilding style

Character Focus

Teamwork/Cooperation & Communication

The Challenge

Each group will construct right triangles using Toobeez and learn to predict side lengths of triangles using the Pythagorean theorem.

Preparation

**Setup Time: **10 minutes

**Materials**

- 1 Toobeez set
- 1 meter stick
- 1 sheet of graph paper per student
- 1 pen/pencil per student

Activity Plan

**Time:** 40 – 50 minutes

**Instruction:** Whole class, pairs and Individual

**Space:** Medium

1. Have each group build two right angles using the following Toobeez tubes combinations:

a. Two 16” Toobeez tubes

b. Two 24” Toobeez tubes

2. Students should lay their chart paper on the desk so it is visible to the group.

3. Tape a note card to each tube. Label one tube in each triangle “A” and abel the other tube “B.” These will serve as the right angles in the groups’ triangles.

**Helpful Hints**

- Be sure to review these tips prior to beginning the activity, and if necessary, share reminders with the group during the activity.

- The Pythagorean theorem states, in algebraic terms,
*a2 + b2 = c2*where c is the hypotenuse and a and b are the sides of a right triangle - Make sure to remind students to measure the sides of Toobeez triangles using similar points on each vertex (sphere). Failure to do so can result in inconsistent results.
**Hint:**Have students measure from the top center hole of each sphere - Be sure to practice building these triangles in advance of the lesson
- Have students practice measuring with a meter stick

**1. After dividing the students into teams, a mini-lesson should be presented to the class on the Pythagorean theorem. Be sure to review techniques for solving the equation.
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**2. Read aloud the following Activity Challenge Box to the group.
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**Challenge**: Each group will construct right triangles using Toobeez and learn to predict side lengths of triangles using the Pythagorean theorem.

**3. ****Using the meter stick, groups should measure and record the length of the two sides of each angle built during the setup phase of the activity.
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**4. Groups should use the Pythagorean theorem to solve the length of the hypotenuse using the side lengths measured in Step 3.
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**5. As a group, students should use a meter stick and their answer from Step 4 to deduce which tube length is required to build a right triangle from the angle models. A consensus should be reached in the student groups.
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**6. Students should try to then build a right triangle using a tube of the agreed upon length.
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**7. After the activity, circle up the group and ask them the following question: “How can you use the Pythagorean theorem to identify which tube length was required to build a right triangle?
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**8. Finally, move to the “Activity Discussion and Processing” section of the activity.
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- Have students draw right triangles using a protractor and prove the Pythagorean theorem using these models
- Build a right triangle using Toobeez and remove one of the side legs, leaving the hypotenuse and other leg intact. Give this model to student groups and have them solve for the length of the missing leg

*Here are available Training Options!*

To close the lesson, end with a group discussion about what was learned during the activity. Circle up the group and work through the following questions. If possible, record the group’s responses on flip chart paper so all comments are displayed.

- Do all triangles observe the Pythagorean theorem? (Have students draw right and non-right triangles to disprove this assumption)
- Are there relationships in the side lengths of other types of geometric figures
- Why/how could the Pythagorean theorem be useful in everyday life?
- How did using the Pythagorean theorem enhance communication between students?

Here are some additional topics for discussion:

- The mathematical technique for solving the Pythagorean equation
- The relationship between the legs and the hypotenuse
- The team effort in solving the Pythagorean puzzles

**1. A more complex puzzle.
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Students should build an initial right angle using two 36” Toobeez tubes. Have students solve for the hypotenuse and build a right triangle. **Hint:** The hypotenuse required consists of two 24” tubes with a sphere in the center.

**2. Extension/Follow up.
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Have students draw right triangles, collect length and angular measurements, and note any observable relationships between the two sets of variables.