Wyoming Math 8.G.7
The Standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems.
2023 Wyoming Mathematics Content and Performance Standards · Understand and apply the Pythagorean Theorem.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the side opposite the right angle as the longest side. They square the known side lengths, add or subtract, then take a square root to find the missing length.
What Mastery Looks Like
- Given legs of 6 cm and 8 cm, a student finds a 10 cm diagonal. Given a 13 cm diagonal and a 5 cm leg, they find the other leg is 12 cm and explain why they subtracted.
Common Misconceptions
- Students may add side lengths instead of their squares. Some subtract when finding the longest side, or forget the square root and report 100 instead of 10.
How to Assess It
- Exit ticket: A 13-foot ladder reaches 12 feet up a wall. How far is its base from the wall? Show the equation and include units.
Lesson moves
Ways to Teach It
Pairs draw a 3-by-4 right triangle on grid paper, draw squares on its sides, and count whole and half cells.
Ask, 'A rectangle measures 6 by 8 inches. Why is its diagonal not 14 inches?' Have partners explain.
Give pairs right-triangle cards labeled 6, 8, 10 and 5, 12, 13; they cover one length, solve, and check each other.
Mark points 3 and 4 feet from a room corner along each wall; students calculate the straight-line distance between them.
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