## Year 2 Lesson Plan 13 - Evaluating expressions, negative numbers

1. (5 min) Mental Math
1. What is 30% of 90? [27]
2. What is one half of one tenth? [1/20]
3. Take the number of days in a leap year and add four [370]
4. What is 3 cubed divided by 3 squared? [3]
5. Take the number of meters in a kilometer and subtract the number of centimeters in a meter. [900]

2. (5 min) Review order of operations for evaluations and multiplications. Do from left to right
1. If parentheses, do operations within parenthesis first
2. Do exponents and square roots from left to right
3. Multiply and divide from left to right
4. Add and subtract from left to right

Evaluate the following with class help on each step. Go around the room one at a time and ask each student to calculate one step. Stress rewriting at each step.

Demonstrate substitution: for a = 2, b = 4, c = 6; (a b + c)2 = 196

Review multiplication of positive and negative numbers: First do the multiplication, then figure out the sign. If there are an even number of negative signs, then the answer is positive. If there are an odd number of negative signs, then the answer is negative.
What is (- 1)2? What is (- 1)3? What is (- 1)4? What is (- 1)15?

3. (10 min) Adding and subtracting positive and negative numbers
All addition and subtraction starts from zero on a number line. You move right for positive and left for negative. If there is no sign to start with, then you assume it is positive and move right.
```---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
-7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10
<------------------------
--------------->          - 6 + 4 = - 2

```

Here's another way to think about it if the student is good at following rules. This works for some kids.
If the signs are the same, add and use the sign (+ or -) that both numbers have.
If the signs are different, subtract and use the sign of the larger one for the answer.
To subtract a negative number, combine the signs like in multiplying, and then add: 3 - (-4) = + 7

4. (Remainder of class) In-class exercise

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