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Mathematics · Grade 8

The Pythagorean Theorem

Learners see why a^2^ + b^2^ = c^2^ through an area argument with squares, and use the converse to test whether a triangle has a right angle. They then find missing sides of right triangles in real situations, extend the theorem to the space diagonal of a box, and compute distances between points on the coordinate plane, giving exact square roots or rounded values as asked.

  • 4 lessons
  • About 90 minutes
  • Pythagorean theorem check: 10 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, put in order and sort into groups
See plans Included with Family, Teacher and School plans. Open in PlayOwl

What learners will discover

  • Explain a proof of the Pythagorean theorem using areas of squares, and use its converse to decide whether a triangle is a right triangle.
  • Use the Pythagorean theorem to find unknown side lengths of right triangles in real-world and mathematical problems in two dimensions.
  • Apply the Pythagorean theorem in three dimensions, including the space diagonal of a rectangular box.
  • Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Lessons

  1. Squares on the sides: why a² + b² = c² 9 steps4 practiceabout 24 min
  2. Missing sides in two dimensions 9 steps5 practiceabout 23 min
  3. The theorem in three dimensions 8 steps5 practiceabout 21 min
  4. Distance on the coordinate plane 8 steps5 practiceabout 22 min
  5. Pythagorean theorem check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups