## Year 2 Lesson Plan 9 - Pythagorean Theorem

1. (5 min) Mental Math
1. Take 20% of 200, then add 50 [90]
2. Take 1/5 of 45, then subtract 6 [3]
3. Take 30% of 80, then multiply by 2 [48]
4. If 100% of 60 is 60, what is 400% of 60? [240]
5. What is 2/5 of 100? [40]
2. (5 min) Review of selected problems from lesson 8 (no more than 3 problems)

3. (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.
 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
Here is the general formula for calculating the hypotenuse:

Hand out the formulas worksheet, instructing students to put it in their notebook for reference when they do their homework.
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.

4. (Remainder of class) In-class exercise

5. Hand out homework as students successfully complete the in-class exercise.