Year 2 Lesson Plan 9 - Pythagorean
Theorem
- (5 min) Mental Math
- Take 20% of 200, then add 50 [90]
- Take 1/5 of 45, then subtract 6 [3]
- Take 30% of 80, then multiply by 2 [48]
- If 100% of 60 is 60, what is 400% of 60? [240]
- What is 2/5 of 100? [40]
- (5 min) Review of selected problems from lesson 8 (no more than 3
problems)
- Handout the Pythagorean theorem handout and use it in the following discussion:
- (10 min) Introduce the Pythagorean theorem
Definitions:
- A right triangle has one 90 degree angle.
- The hypotenuse is the longest side of a right triangle
(the one opposite the 90 degree ("right") angle.
Pythagoras was a famous Greek (about 2200 years ago) who discovered
some interesting math. Pythagoras discovered that if you drew
squares on each side of a right triangle, then the biggest square
had the same area as both of the smaller two squares.
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The easiest Pythagorean triangle to construct is the [3,4,5] triangle.
Draw the squares of the triangle shown (32 and 42)
and add them up. You get 25. What is the side of the square whose area is
25?
42 = 16
32 = 9
9 + 16 = 25
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Here is the general formula for calculating the
hypotenuse:
Use the equation now, and plug in the following numbers:
Notice that the hypotenuse is always the longest side. Most
of the time the numbers do not come out nice. This bothered
the Greeks a lot, and they thought that the [3,4,5] triangle
was magic. By the way, if you are ever building a house and
want to get a right angle, carpenters use the [3,4,5]
triangle to construct a right angle.
What if you are given the hypotenuse and only one leg of the
triangle? How can you find the missing side, such as in this
problem?:
Well, you work the Pythagorean theorem backward, using this
formula:
b2 = c2 -
a2
You find 52 and you subtract 42 to get
32 = 9. then you have to take the square root of
your answer (9) to get 3.
- (Remainder of class) In-class exercise
- Hand out homework as students successfully complete the in-class exercise.
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