NY Next Generation Math NY-8.G.6

Math8th GradeUnderstand and apply the Pythagorean Theorem.

The Standard

Understand a proof of the Pythagorean Theorem and its converse.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students understand a proof of the Pythagorean Theorem and a proof of its converse. They explain how area or rearrangement establishes each relationship.
What Mastery Looks Like: The student connects square areas on a right triangle to a squared plus b squared equals c squared. The student explains why satisfying that equation establishes a right angle.
Common Misconceptions: Students may treat a, b, and c as interchangeable and fail to identify the hypotenuse. They may use numerical examples as a complete proof.
How to Assess It: Give students a rearrangement diagram of four congruent right triangles and a separate triangle whose side lengths satisfy a squared plus b squared equals c squared. Ask them to explain the area proof of the theorem and outline why the second triangle must be right.

Lesson moves

Rearrange four congruent right-triangle cutouts inside two equal squares and compare uncovered areas.
Ask students why c must label the side opposite the right angle in the theorem.
Play Proof Sequence Sort by ordering statements from an area-based demonstration.
Use a carpenter square and three measured lengths to discuss how the converse verifies a right corner.

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