## Year 2 Lesson Plan 8 - Square roots and other roots

1. (5 min) Mental Math
1. Take 50% of 150, then add 10 [85]
2. Take 1/3 of 90, then subtract 5 [25]
3. Take 25% of 40, then multiply by 2 [20]
4. If 100% of 20 is 20, what is 200% of 20? [40]
5. What is 1/5 of 100? [20]
2. (5 min) Review of selected problems from lesson 7 (no more than 3 problems)

3. (5 min) Square roots review
Discuss square roots: A square root of a number is the number which, when multiplied by itself, gives that number. The square root of 9 is 3 because 3 X 3 is 9. If a number has a whole number for a square root it is called a perfect square.

• 1,4,9,16,25 Now write down the square root below each number
• Ask what is the square root of 81?
• What does this mean? Draw a square whose area is 16. what are the lengths of each side? [they are 4].
Discuss roots of numbers that are not perfect squares.

• What do they think is the square root of 20? guess and check on the calculator without using the square root key. Is it larger than 4? Yes, because 4 x 4 = 16. Is it larger than 5? No, because 5 x 5 = 25. So it is between 4 and 5. Try 4.5 x 4.5 (too big). Try 4.4 x 4.4 (too small)
• the square root of 20 is (approximately) 4.47. We will write it: . Sometimes we write it: 201/2

4. (5 min) Other roots -- an introduction
It is possible to have other roots as well. A root is a number which, multiplied by itself one or more times, gives the original number.
The fourth root of 16 is 2, because 2 x 2 x 2 x 2 = 16. We write it: .
The third root of 27 is 3 because 3 x 3 x 3 = 27. We also call it the cube root: .
(At this time we will not be talking about negative roots, because we haven't yet reviewed multiplication of negative numbers.)

5. (Remainder of class) In-class exercise
6. Hand out homework as students successfully complete the in-class exercise.