1. 7.NS.1 Positive and Negative Numbers

2. Definition
Positive number – a number greater than zero. 1 2 3 4 5 6

3. Definition
Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

4. Definition
Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

5. Definitions
Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero.

6. Opposites - numbers that are the same distance from zero on the number line, but in opposite directions. They are also called Additive Inverses! 7
opposite -7

7. Opposites combine to make zero!
The yellow tile is positive one and the red tile is negative one.

8. Absolute Value – the distance a number is from zero on the number line in either direction. Absolute Value is ALWAYS positive! Example: |-7| = 7 and |7| = 7, Therefore, |-7| = |7|

9. Negative Numbers Are Used to Measure Temperature

10. Negative Numbers Are Used to Measure Under Sea Level30 20 10
-10
-20
-30
-40
-50

11. Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car but
had to get a loan from the bank for $5,000.
When counting all their money they add
in -$5.000 to show they still owe the bank.

12. Positive & Negative Numbers
Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the driving rules.

13. Hint
If you don’t see a negative or positive sign in front of a number it is positive. 9 +

14. One Way to Add Integers Is With a Number Line
When the number is positive count
to the right.
When the number is negative count
to the left. - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

15. One Way to Add Integers Is With a Number Line= -2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

16. One Way to Add Integers Is With a Number Line= +2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

17. One Way to Add Integers Is With a Number Line= -4 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

18. One Way to Add Integers Is With a Number Line= +4 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

19. One Way to Add Integers Is With a Number Line= +4 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

20. One Way to Add Integers Is With a Number Line= +6 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

21. One Way to Add Integers Is With a Number Line= -3 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

22. One Way to Add Integers Is With a Number Line= -6 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

23. One Way to Add Integers Is With a Number Line= -5 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

24. One Way to Add Integers Is With a Number Line= -5 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

25. One Way to Add Integers Is With a Number Line= -5 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -

26. One Way to Add Integers Is With a Number Line
4 + 1 = 5 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

27. One Way to Add Integers Is With a Number Line
3 + 2 = 5 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

28. One Way to Add Integers Is With a Number Line
1 + 5 = 6 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +

29. You can use a Bar Model to understand integer addition ~ the negative numbers are in shaded boxes!25
-18 ? 43

30. Integer Addition Equation Rules
Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.
9 + 5 = 14
= -14

31. Solve the Problems =
4 + 7 =
(+3) + (+4) = =
5 + 9 = = -8 11 7
-13 14
-18

32. Integer Addition Equation Rules
Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the larger one in front of your answer. =
Larger number
Answer = - 4
9 - 5 = 4

33. 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 =
Solve These Problems -2 = =
(+3) + (-4) = = = =
5 – 3 = 2 3
7 – 4 = 3
4 – 3 = 1 -1 1
7 – 6 = 1
9 – 5 = 4 -4
9 – 9 = 0

34. Let’s see what you understand about integers!
Decide if each statement is true for ALL values of x.
Choose yes or no for each of the following:
If the distance from 0 to x on the number line is 7, then –7 + x = 0.
If the distance from 0 to x on the number line is greater than 4, then –4 + x is positive.
If the distance from 0 to x on the number line is greater than 0, then –1 + x is positive.
Yes No
Yes No
Yes No