1. Integers
Objective: To read and write integers; To find the opposite and the absolute value of an integer

2. Integers
An integer is any number from the set {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …} Integers greater than 0 are positive integers. Positive integers usually are written without the + sign, so +5 and 5 are the same. Integers less than 0 are negative integers. Zero is neither positive nor negative.

3. Integers can be represented using counters or a number line.
Method 1: Counters
Method 2: Number Line -3 +2

4. Represent -5 and +1 using counters and a number line

5. Write an integer for each situation.
A loss of 6 yards
A profit of $5
A deposit of $10
76ºF below 0
10 years ago

6. Opposites
Two numbers are opposites of one another if they are represented by points that are the same distance from 0, but on opposite sides of 0. The number line below shows that -4 and +4 are opposites.
4 units left units right

7. Absolute Value
The absolute value of an integer is its distance from 0 on a number line. Distance is always positive.
Absolute value is helpful when adding integers.
The absolute value of n is written |n |. So, |-4| = 4 and |4| = 4.

8. Try These: Tell why –7.5 is not an integer.
Represent -6 using counters and a number line.
Write an integer to describe the year 120 B.C.
Give the opposite of -7.
Give the absolute value of -10.
|-6|=____ |7|= _____

9. Give the integer represented by each point
Give the integer represented by each point. Then find its opposite and its absolute value. 1.
Integer: -2
Opposite: +2
Absolute value: 2
Integer:
Opposite:
Absolute value: 2.
Integer:
Opposite:
Absolute value:

10. Coordinate Plane Objective:
To find, position and reflect pairs of integers and other rational numbers on a coordinate plane.

11. Coordinate Plane
Definition: It is a plane containing two perpendicular axes (x and y) intersecting at a point (0,0) called origin.
QUADRANT II
QUADRANT I
QUADRANT III
QUADRANT IV

12. Ordered Pairs Definition:
A pair of numbers where order is important. These are the horizontal and vertical distances of a point from a specific location called the origin

13. Ordered Pairs
Examples:

14. Try These
Starting at the origin, go three units horizontally to the right and four units vertically down. What is the ordered pair? Plot and label on the coordinate plane. In which quadrant is the point located?
Susan lives six blocks horizontally to the left from the origin and four blocks vertically down from the origin. What is the point where Susan’s house is located? Plot and label on the coordinate plane. In which quadrant is the house located? What is the distance between these two points?

15. Reflection Definition:
An image or shape as it would be seen in a mirror.

16. Reflection over the X-Axis

17. Reflection over the Y-Axis

18. Reflection about the Origin

19. Ordering Integers
Numbers lines are useful for putting integers in order least to greatest.
Least numbers are furthest to the left of zero and the greatest are furthest to the right of zero.
Place these integers in order least to greatest by graphing them on the number line. 3, -2, 0, -9, 1, 5, -3
Rewrite them in least to greatest order.

20. Ordering Rational Numbers
Definition: A rational number is any number that can be made by dividing one integer into another (comes from “ratio”). This includes all fractions and decimals both negative and positive.
Use a number line to help you order rational numbers. Remember the least will be furthest to the left from zero and the greatest will be furthest to the right from zero.
Order the following rational numbers: ¼, -.3, .5, -.75, -2 ¼, 2

21. Online Games http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf

22. Online Games II
Fraction to decimal and percentages

23. Online Games III