ADDING & SUBTRACTING INTEGERS NS 1.2 and AF 1.3

Integers Whole numbers and their opposites are integers such as 6 and -6. Zero is also a whole number. -6 6 Opposites

Negative Numbers Are Used to Measure Temperature

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

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 $15,000.When counting all their money they add in -$15.000 to show they still owe the bank.

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

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

INTRODUCTION TO INTEGERS Each of the following groups of counters represent -3. You may represent -3 by using 3 red tiles and any number of groups of +1 and -1 tiles

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

INTRODUCTION TO INTEGERS Tell which integer each group of tiles represents. -1 -4 +4

INTRODUCTION TO INTEGERS Tell which integer each group of tiles represents. +5 -4 -3

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

Adding and Subtracting Integers -3 + 4 = -3+4=1

Adding and Subtracting Integers 6 – 10 = 6 – 10 = -4

Adding and Subtracting Integers -6 + -7 = -6 + -7 = -13

Adding and Subtracting Integers 12 + -7 = 12 + -7 = 5

Adding and Subtracting Integers Three Meanings of the Minus Sign Subtract Example: 8 – 5 is read “subtract 5 from 8” Negative Example: 8 – 5 can be read “8 and negative 5” The Opposite Of Example 8 – (-5) can be read “8 and the opposite of (-5)” or 8 + 5

Adding and Subtracting Integers -3 – (-4) = Reads -3 “and the opposite of” -4 What is the opposite of -4?

Adding and Subtracting Integers -3 – (-4) = Reads 3 “and the opposite of” -4 -3 – (-4) = 1

Adding and Subtracting Integers 5 – (-9) = What is the opposite of -9? Reads 5 “and the opposite of” -9

Adding and Subtracting Integers 5 – (-9) = What is the opposite of -9? Reads 5 “and the opposite of” -9 5 – (-9) = 14

Addition with a number line Add 3 + 4 using a number line. Add -4 + (-2) Add 5 + (-7) +4 -2 Using the laminated number lines, students can follow along with their finger, or use dry-erase markers to track each problem. When students use a number line to add integers, they will develop a general understanding that the sum, for example: 12 + (-7), is the number found when moving a total of 7 units from 12 to the left, since 7 is negative. When adding a positive number, we move to the right. When adding a negative number we move to the left. -7 22

Practice with the number line -2 + (-2) 3 + (-3) -4 + (-6) -8 + (-1) 10 + (-4) -9 + 4 Have students practice using the number line to add integers. When adding, we move right for positive and left for negative. You can add more problems for students to practice with. 23

Subtraction on a number line -3 – 2 -6 – (-2) 3 – (-6) -2 -(-2) Using the laminated number lines, students can follow along with their finger, or use dry-erase markers to track each problem. Students will see that subtraction is the same thing as adding the opposite. -(-6) 24

Practice with the number line 5 – 9 3 – 10 -5 – 4 -7 – 9 5 – (-6) -8 – (-8) Have students practice using the number line to subtract integers. You can add more problems for students to practice with. 25

On your own -4 + 4 = -6 – 15 = -6 + 13 = -21 2 + -13 = -4 – (-4) = 7 -9 – (-9) = -21 7 -11