M&M Pythagorean Theorem. By: Nicole Havrilla. Level: Middle school, grades 6-8 Goal: Students will explore and analyze the Pythagorean Theorem. *This will allow students to better visual the formula Materials:
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By: Nicole Havrilla
**Experimental based (Empirical) - one of the best ways for students to learn (based on research)
Over 2000 years ago there was an amazing discovery about triangles:
When the triangle has a right angle (90 degrees) the squares are made of each of the three sides, and the biggest square has the exact same area as the other two squares added together!!
This is called Pythagorean Theorem
This is what the students will show through this activity.
Leg- two shorter sides of a triangle
Hypotenuse - longest side of the triangle
In a right triangle the square of the hypotenuse is equal to the sum of the squares of the two legs.
Scalene right triangle
Isosceles right triangle
Counter example: non-right triangle
** numbers in each square represent the number of M&M’s counted during each trial**
triangle they are looking at
Why is this useful?
If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right triangles!)
Has to be a right triangle…
-See if students can work backwards in the equation
(Have students fill the square formed on the hypotenuse and then use those M&M’s to fill the smaller two squares. Does it still work? )
-Use the same procedure however explore the relationship between areas when other similar shapes are constructed on the sides of a right triangle, such as semicircles, triangle, and quarter circles.
An equilateral triangle is along each side
A quarter circle is along each side