1. Incredible Integers +9
-10
Lesson 10.1 -4 -1 -1 +3 -7 +5 -2 -8

2. CCS: 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6. a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

3. Objectives Students will be able to:
Locate positive and negative integers on a number line
Identify opposite integers on a number line
Describe real-world situations involving positive and negative integers

4. What is an integer?

5. Integers are the whole numbers and their opposites.

6. Okay…but what does that mean?

7. Two integers are opposites if they are the same distance from 0 in either the positive or negative direction on a number line.

8. This means…
Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, ...
Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5, …
Negative numbers are less than zero.

9. Let’s look at some examples of opposites!
-4 and +4
-2 and +2
-5 and +5

10. Integers can also represent situations

11. Here are some examples:
Sarah went up four steps
The temperature is twelve below zero.
The elevation of the mountain is 52,000 feet +4
-12
+52,000

12. And a few more… The football team lost 8 yards Anne gained 10 pounds
Tara spent $20 of her checking account. -8
+10
-$20

13. You try some!! +212 The stock market showed a gain of 212 points today
-282 -2
The stock market showed a gain of 212 points today
Death Valley, California is 282 feet below sea level
The elevator went down two floors.

14. Now let’s talk about Absolute Value

15. The distance a number is from zero on the number line.
Absolute Value is…
The distance a number is from zero on the number line.

16. So… Absolute value is shown by two bars on either side of an integer.
The absolute value of the number is really just the number without a sign (or neither negative nor positive) 4

17. Unless…
The negative sign is OUTSIDE of the absolute value bars.
= -4

18. Here are some examples!
= 9
Example 1:
Example 2:

19. INTRODUCTION TO INTEGERS
REMEMBER…Integers are positive and negative numbers.
…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …
Each negative number is paired with a positive number the same distance from 0 on a number line. -3 -2 -1 1 2 3

20. INTRODUCTION TO INTEGERS
We can represent integers using red and yellow counters.
Red tiles will represent negative integers, and yellow tiles will represent positive integers.
Negative integer
Positive integer

21. INTRODUCTION TO INTEGERS
The diagrams below show 2 ways to represent -3.
Represent -3 in 2 more ways. -3 -3

22. INTRODUCTION TO INTEGERS
Tell which integer each group of tiles represents. +1 -2 +2

23. INTRODUCTION TO INTEGERS
If there are the same number of red tiles as yellow tiles, what number is represented?
It represents 0.

24. Number Lines -5 5 10
-10
A number line is a line with marks on it that are placed at equal distances apart.
One mark on the number line is usually labeled zero and then each successive mark to the left or to the right of the zero represents a particular unit such as 1 or ½.
On the number line above, each small mark represents ½ unit and the larger marks represent 1 unit.

25. Number Lines -5 5 10 -10 Number lines can be used to represent:10
-10
Number lines can be used to represent:
Whole numbers – the set {0, 1, 2, 3, …}
Positive numbers – any number that is greater than zero
Negative numbers – any number that is less than zero
Integers – the set of numbers represented as
{…, -3, -2, -1, 0, 1, 2, 3, …}
The arrows at the ends of the number line show that the number line continues in both directions without ending.

26. Graphing on Number Lines-5 5 10
-10
A number can be graphed on a number line by placing a point at the appropriate position on the number line.
Example
{4} (blue point)
{integers between –10 and –5} (purple)

27. Graphing on Number Lines-5 5 10
-10
Name the set of numbers that is graphed.
{-8, -4, 1, 5, 8}
{-8, -4, 1, 5, 8}

28. Moving on Number Lines -5 5 10 -1010
-10
Movement to the right on the number line is in the positive direction (increasing). Do this to add a positive #.
Movement to the left on the number line is in the negative direction (decreasing). Do this to add a negative #.
Make the following moves on the number line. Start at 5 and move left 7 integers.
Where did you stop? -2
How can we represent this mathematically?
5 + (-7) = -2

29. Video Time!
Watch this video to help you graph and order numbers on a number line
10.1 Video

30. You Try It!
1) Graph these pairs of numbers on a number line. Write two inequalities comparing the two numbers.
a) -2, 7
b) -9, -4
2) Find each sum using a number line. Place the 1st # on a # line, then move to the right or left. a)
b) (-7) c) d)

31. Problems 1 a & b -5 5 10
-10 a) -5 5 10
-10 b)

32. Problems 2 a & b -5 5 10
-10
Show using the number line.
Start at 3 and move 7 places to the right.
3 + 7 = 10 -5 5 10
-10
Show -1 +(-7) using a number line.
Start at -1 and move 7 places to the left.
-1 + (-7) = -8

33. Problems 2c & d -5 5 10
-10
Show –9 + 5 using the number line.
Start at –9 and move 5 places to the right.
–9 + 5 = –4 -5 5 10
-10
Show using a number line.
Start at -6 and move 6 places to the left.
= 0

34. Classwork:
Homework