.
Grade 7
. What Is It? Current Page:Tips and Tricks When Students Ask Lesson Ideas
. . .
Tips and Tricks

Pythagorean Theorem

  • It's important when you work with right triangles, to keep the Pythagorean Theorem in mind: Not only is it true that a2 + b2 = c2, it is also true that if a2 + b2 c2, the triangle is not a right triangle. When you're in a hurry to make up a problem for classwork or a test, be careful that what you define as a right triangle can actually be one.

  • Be careful that you don't ask students to assume that a triangle is a right triangle (or a quadrilateral is a square, etc.) just by looking at it. When you present problems to the class, give enough clues so that they can be sure of the characteristics of a figure.
    • Specify the shape of the figure.
    • Mark right angles in figures with the right-angle symbol.
    • Use the perpendicular symbol ().
    • Teach students about using tick marks to indicate same-length segments in a figure.

  • Encourage students to use calculators when they work with right triangles. If you prefer not to use calculators, there are two ways to be sure the computation is not so difficult that students lose the sense of the topic. 1. Always use Pythagorean Triples in problems you present. 2. Teach students to leave their answers in radical form.

  • If you don't use calculators, and prefer a numerical answer: - Provide a table of squares and square roots. - Ask students to show their work and be willing to give partial credit if students demonstrate that they understand the concept but have trouble with the computation.

  • Allow a range of answers to problems whose answers are not integers. All of these answers will be approximations because a root that is not a perfect root is a non-terminating, non-repeating decimal. Different calculators and square-root tables round to different places.
 

Mathematics Center | Math Steps
Education Place | Site Index
Copyright © 1999 Houghton Mifflin Company. All Rights Reserved.
Terms and Conditions of Use | Privacy Policy.