1. Investigation 1: Review
Rational Numbers
Integers
Positive Integers
1, 5, 9, 10, 27
Negative Integers
-1, -5, -9, -10, -27
Fractions
Positive Fractions
½, ⅓, ⅚, ⅜
Negative Fractions
-½, -⅓, -⅚, -⅜
Opposites
Opposites

2. The distance from 0 on a number line. 2 = 2 -2 = 2
Absolute Value
The distance from 0 on a number line. 2 = 2 -2 = 2

3. Investigation 2.1 Introducing Addition of Integers
Ms. Lyons
Connected Math 2

4. Objectives: SWBAT develop algorithms for adding integers.
SWBAT model addition of integers using distance/direction on a number line and using a chip model.
SWBAT observe that the Commutative Property holds for addition of rational numbers.

5. Vocabulary
Algorithm- A plan, or series of steps, for doing a computation.
Commutative Property- The order of the addition or multiplication of two numbers does not change the result.
Example: = 5 and = 5
(-2) + 3 = 1 and 3 + (-2) = 1
1 × 6 = 6 and 6 × 1 =6
( -1) × 6 = -6 and (-6) × 1 = -6

6. The sum of two positive integers is a positive integer.
John has 8 video games and his friend has 5. Together they have = 13 games + = +5
The sum of two positive integers is a positive integer.

7. George owes his friend Jeanne $3
George owes his friend Jeanne $3. If he borrows another $6, how much will he owe her altogether?
Owing $3 can be represented by -3 and owing $6 can be represented by -6.
( -3 ) + ( -6) = -9
Look at the number line below. If we start at -3 then move to the left 6 spaces, we end up at -9.

8. The sum of two negative integers is a negative integer.
( -3 ) + ( -6) = -9 + =
The sum of two negative integers is a negative integer.

9. If you start with $7 and you spend $4, then you end up with $3
If you start with $4 and you spend $7, then you end up owing $3. (+4) + (-7) = - 3
When numbers have different signs, subtract the larger number from the smaller number and keep the sign of the larger number.

10.   (7) + (- 4) = 3 + =
When numbers have different signs, subtract the smaller number from the larger number and keep the sign of the larger number.

11. Subtract and take the sign of the higher (larger) number
Integer Rules
Addition
(+)
LIKE signs
Add and take the sign
-2 + (-4) = -6
4 + 6 = 10
DIFFERENT signs
Subtract and take the sign of the higher (larger) number
= 4
6 + (-12) = -6

12. Integer Song Same sign add and keep Different sign subtract
Keep the sign of the higher number
Then it will be exact!