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

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**
- (5 min) Mental Math
- Take 50% of 150, then add 10 [85]
- Take 1/3 of 90, then subtract 5 [25]
- Take 25% of 40, then multiply by 2 [20]
- If 100% of 20 is 20, what is 200% of 20? [40]
- What is 1/5 of 100? [20]

- (5 min) Review of selected problems from lesson 7 (no more than 3
problems)

- (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*.

Start with the first 5 perfect squares:

- 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: 20
^{1/2}

- (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.)

- (Remainder of class) In-class exercise

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