Integers and Absolute Value

Objectives Define and identify integers Write the opposites of integers and other numbers. Use integers to represent real-world data. Graph integers on a number line. Compare and order integers. Find the absolute value of a number. Represent integer values with counters.

Integers Integers are all of the positive and negative whole numbers. There are no fractions or decimals that are integers. ….. -3, -2, -1, 0, 1, 2, 3 … Negative DirectionPositive Direction

Circle the integers

Graphing Integers on a number line 1)Draw a number line 2)Graph an Integer by drawing a dot at the point that represents the integer. Example: -6, -2, and

Your turn : Graph the number on the number line 1)Graph -7, 0, and 5 2)Graph -4, -1, and

Order Integers from Least to Greatest You need to know which numbers are bigger or smaller than others, so we need to order them from least to greatest. Example: Order the integers -4, 0, 5, -2, 3, -3 from least to greatest. The order is -4, -3, -2, 0, 3,

Your turn: Order Integers from least to greatest 1)Order the integers 4,-2,-5,0,2,-1 from least to greatest. 2)Order the integers 3,4,-2,-5,1,-7 from least to greatest

Absolute Value Absolute value of a number is the DISTANCE to ZERO. Absolute value of a number is the DISTANCE to ZERO. Distance cannot be negative, so the absolute value cannot be negative

Absolute Value Evaluate the absolute value: Ask yourself, how far is the number from zero? 1)| -4 | = 2)| 3 | = 3)| -9 | = 4)| |

Absolute Value Evaluate the absolute value: Ask yourself, how far is the number from zero? 1)| 12 ÷ -4 | = 2)| 3 ● 15 | = 3)| | - │1 + 2│ = 4)| | + │ │=

Opposites Two numbers that have the same ABSOLUTE VALUE, but different signs are called opposites. Example -6 and 6 are opposites because both are 6 units away from zero. | -6 | = 6 and | 6 | =

What is the opposite? 1)-10 _____ 2)-35 _____ 3)12 _____ 4)100 _____ 5)1 ____ 6)x _____ 7)-1.5 _____

Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.

Negative Numbers Are Used to Measure Temperature Negative Numbers Are Used to Measure Under Sea Level

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.

Using Positive and Negative Words Negative Withdrawal Loss Fall Less than Less Below Spend Decrease Debt Positive Deposit Above Higher Rise Increase Gain More than Save Surplus

Write an integer for each phrase 1.Seven degrees below zero ______ 2.Going up 4 floors on the elevator ____ 3.Owing $50 ____ meters above sea level ____ 5.Move back 4 spaces ____ 6.5 shots under par ____ 7.Loss of 5 yards in football ___ 8.Depositing $20 ____ 9.Loss of 3 Class Dojo points ____

Comparing Numbers 1.) 5 ___ -1 2.) -3 ___ -5 3.) -5 ___ 2 4.) -4 ___ -2 5.) -2___ -2 6.) 0 ___ -2 7.) -8 ___7 8.) 4 ___ 4.0

INTRODUCTION TO INTEGERS 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

Counter chips 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

Zero Pairs If there are the same number of red tiles as yellow tiles, what number is represented? It represents 0.

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

INTRODUCTION TO INTEGERS Tell which integer each group of tiles represents

Draw 3 ways to represent -6

Ticket Out Name __________________ Period __