8.7 Square Roots, Irrational Numbers, and Pythagorean Theorem

Beginning Lesson

Aws4 request&x amz signedheaders=host&x amz signature=7c00cb4747b2323e9cbc062a2256965bf1af99b79ca31629f5c9257dd487e685

Square Dancing

What do squares reveal about the universe? Students learn about the Pythagoreans and explore how to square numbers and find square roots, confront the weirdness of irrational numbers, and discover what happens when people’s most fundamental beliefs are thrown into doubt.

Topic: Expressions and Equations (EE), Number System (NS)

Middle Lessons

Aws4 request&x amz signedheaders=host&x amz signature=5dac8196578859f7c7409b17aad070b7809d908e2785644d25b81486e27f99a9

51-Foot Ladder

How high can a ladder safely reach? Students combine the federal guideline for ladder safety with the Pythagorean Theorem (middle school) or trigonometric ratios (high school) to explore how high you can really climb.

Topic: Geometry (G), Similarity, Right Triangles, and Trigonometry (SRT)
Aws4 request&x amz signedheaders=host&x amz signature=8692d939aac5a513ca66857872efe4980cbec2408c3c9cea2ae9f3f522bf41d8

It's a Trap!

How accurate are police speed guns? Students use rates and the Pythagorean Theorem to examine the accuracy of LiDAR guns used to catch speeding drivers.

Topic: Expressions and Equations (EE), Geometry (G), Ratios and Proportional Relationships (RP)

End Lesson

Aws4 request&x amz signedheaders=host&x amz signature=2bfa2757a13efcbd6017c5565e7bb9108de9c26ba6de0964dd539e774525ce05

Viewmongous

When you buy a bigger TV, how much more do you really get? Students use the Pythagorean Theorem and proportional reasoning to investigate the relationship between the diagonal length, aspect ratio, and screen area of a TV.

Topic: Geometry (G), Similarity, Right Triangles, and Trigonometry (SRT)