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Tiered Assignments: Pythagorean Theorem

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**1. **Tiered Assignments: Pythagorean Theorem 8th Grade Mathematics / Algebra I
By: Amanda Davidson

**2. **NC Standard Course of Study
3.02 Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems

**3. **Concepts / Generalizations Concept: Relationships
Topic : Pythagorean Theorem
Generalization: The Pythagorean Theorem states that the relationship between the legs and the hypotenuse of a right triangle are always constant .

**4. **Introduction / Setting Up Students are assigned to one of three groups. Each group starts with the same assignment: Create a vocabulary list of terms associated with right triangles and the Pythagorean Theorem.
One leader is chosen from each group and then called to the front and given their assignment on an index card. The teacher explains each assignment to each individual leader one at a time. The leader then goes back to their group to begin the activity.

**5. **Tiered Assignments Group 1:
Students will use Geoboards and rubber bands to create right triangles, proving the relationship between the legs and the hypotenuse (i.e. the Pythagorean Theorem). They will record their data in a table. Students will write a paragraph about their findings.
Group 2:
Students will go to the computer lab to use Geometer’s Sketchpad and work with the concept of “squaring the triangle” (proving that by using the side of each triangle and creating 3 different squares, that the sum of the areas of the squares created by the legs is equal to the area of the square created by the hypotenuse). Students will write a paragraph about their findings and describe the concept of the Pythagorean Theorem.
Group 3:
Students will research Pythagoras, Euclid, and Leonardo Di Vinci and compare their theories on the Pythagorean Theorem. They will each take a different role and create a debate of who should have gotten credit for the theorem by citing research and explaining the theorem.

**6. **Concluding the Activity / RAFT Students must know:
The formula for the Pythagorean Theorem
Who Pythagoras is and his background
The relationship between the legs and the hypotenuse of a right triangle
Students must understand:
How to apply the Pythagorean Theorem
The role Pythagoras had in discovering the Pythagorean Theorem
Why this theorem is only applicable to right triangles
Students must be able to do:
Apply and understand the Pythagorean Theorem
Research Pythagoras and other mathematicians

**7. **RAFT – Pythagorean Theorem