8.7 Square Roots, Irrational Numbers, and Pythagorean Theorem

Beginning Lesson


Square Dancing

What secrets are hidden in squares? Students use concrete models to explore square numbers and square roots and confront the philosophical and moral questions posed by the existence of irrational numbers.

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

Middle Lessons

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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)
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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



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)