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

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.

Integers can be represented using counters or a number line. Method 1: Counters Method 2: Number Line -3 +2 -5 -4 -3 -2 -1 0 +1 +2 +3 +4

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

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

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 4 units right -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +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.

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|= _____

Give the integer represented by each point Give the integer represented by each point. Then find its opposite and its absolute value. 1. -3 -2 -1 0 1 2 3 -9 -8 -7 -6 -5 -4 -3 Integer: -2 Opposite: +2 Absolute value: 2 Integer: Opposite: Absolute value: 2. -1 0 1 2 3 4 5 Integer: Opposite: Absolute value:

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

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

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

Ordered Pairs Examples:

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?

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

Reflection over the X-Axis

Reflection over the Y-Axis

Reflection about the Origin

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.

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

Online Games http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf http://www.crctlessons.com/coordinate-plane-game.html http://www.kidsmathgamesonline.com/geometry/grids.html

Online Games II http://www.math-play.com/Comparing-Rational-Numbers/comparing-rational-numbers.html http://www.quia.com/rr/168625.html http://www.softschools.com/math/rational_numbers/rational_numbers_on_the_number_line/ Fraction to decimal and percentages http://www.math-play.com/Fractions-Decimals-Percents-Jeopardy/fractions-decimals-percents-jeopardy.html

Online Games III http://www.arcademics.com/games/orbit-integers/orbit-integers.html http://www.mathplayground.com/ASB_IntegerWarp.html https://www.sheppardsoftware.com/mathgames/integers/FS_Integer_addition.htm https://www.sheppardsoftware.com/mathgames/integers/FS_Integer_subtraction.htm http://www.mathgoodies.com/games/integer_game/football.html