You Will Learn to add and subtract integers using·Pictures (and Diagrams)·Objects (Integer Chips)·Numbers (Yes! Numbers!)

-1 0-2-3-4-5 1 2 3 4 5

Ch 9: Add and Subtract Integers

9.1 - Explore Integer Addition

After this lesson, you will be able to...·Add integers using integer chips

and mean "positive."

and mean "negative."

our chips textbook chips

Key Terms:

zero pair:·a pair of integer chips, with one chip representing +1 and one chip representing -1

·the pair represents zero because (+1) + (-1) = 0

opposite integers:·two integers with the same "numeral", but different signs. For example,

·two integers represented by points that are the same distance in opposite directions from zero on a number line

+2-2

-1 0-2

-3-4-5 1 2 3 4 5

use brackets!

Example 1: Add Integers Using Integer ChipsAdd using integer chips. Complete the addition statement in each case. Cross out or circle zero pairs where applicable.

a) (+1) + (+2) = ___ b) (-3) + (-2) = ___c) (+5) + (-4) = ___ d) (-6) + (+2) = ___

+

Try "Show You Know" on p. 312

Example 2: Apply Integer Addition

Ray spent $5 on bus fares to visit his aunt. During the visit, she gave Ray $12 for doing some yard work. How much money did Ray gain from the visit?

+

Key Terms:

zero pair:·a pair of integer chips, with one chip representing +1 and one chip representing -1

·the pair represents zero because (+1) + (-1) = 0

opposite integers:·two integers with the same "numeral", but different signs. For example,

·two integers represented by points that are the same distance in opposite directions from zero on a number line

+2-2

-1 0-2

-3-4-5 1 2 3 4 5

use brackets!

Assignment:9.1 Explore Integer Additionp. 313, #1–4 (as a class), 5, 7, 9, 11, 13Still Good? # 12, 14-16Pro Star? # 17-20

9.2 - Add IntegersAfter this lesson, you will be able to...·add integers using a number line

You can use an arrow on a horizontal or vertical number line to represent an integer. The direction of the arrow shows the sign of the integer. The length of the arrow shows the value of the numeral of the integer.

-1 0-2

-3-4-5 1 2 3 4 5

-1 0-2

-3-4-5 1 2 3 4 5

+3

-5 -10

- 2-3

-4-5

12

34

5

-10

- 2-3

-4-5

12

34

5

-2

+4

You can also use a horizontal or vertical number line to represent integer addition.

-1 0-2-3-4-5 1 2 3 4 5

Start at "0" and go from there...

What is the addition statement represented by the number line?

Example 1: Add Integers Using a Number Line

a) (+4) + (+2) = ___ b) (-5) + (-3) = ___c) (+2) + (-4) = ___ d) (-6) + (+6) = ___

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Try "Show You Know" on p. 318

Example 2: Apply Integer Addition

The temperature in Yellowknife, NWT, one

morning in October was -4˚C. The temperature

increased by 9˚C to reach the high

temperature for that day. What was the high

temperature?

-10

- 2-3

-4-5

12

34

5

You can use an arrow on a horizontal or vertical number line to represent an integer. The direction of the arrow shows the sign of the integer. The length of the arrow shows the value of the numeral of the integer.

-1 0-2

-3-4-5 1 2 3 4 5

-1 0-2

-3-4-5 1 2 3 4 5

+3

-5

-10

- 2-3

-4-5

12

34

5

-10

- 2-3

-4-5

12

34

5

-2

+4

Key Ideas

Assignment:9.2 Add Integersp. 319, #1-4 (as a class), 5, 7, 9, 10, Math LinkStill Good? #6, 8, 13–15, 17–19Pro Star? #20–23

9.3 - Explore Integer Subtraction

After this lesson, you will be able to...·Subtract integers using integer chips

and mean "positive."

and mean "negative."

our chips textbook chips

Key Terms:

zero pair:·a pair of integer chips, with one chip representing +1 and one chip representing -1

·the pair represents zero because (+1) + (-1) = 0

opposite integers:·two integers with the same "numeral", but different signs. For example,

·two integers represented by points that are the same distance in opposite directions from zero on a number line

+2-2

-1 0-2

-3-4-5 1 2 3 4 5

use brackets!

·You can use integer chips to represent integer subtraction.·You can model subtraction by removing integer chips of the appropriate colour.·Add zero pairs if there are not enough chips of one colour to remove.·There are two differences between two different integers. For example, the differences between +1 and -2 are +3 and -3.

(+1) - (-2) = (+3) (-2) - (+1) = (-3)

Key Ideas

Example 1: Subtract Integers Using Integer Chips

Determine each difference using integer chips. Cross out or circle zero pairs where applicable.

a) (-7) - (-3) = ___ b) (+3) - (-4) = ___c) (-6) - (+2) = ___ d) (-2) - (-5) = ___

-

Try "Show You Know" on p. 325

a) (+8) - (+2) = ___ b) (-1) - (+2) = ___c) (+4) - (-5) = ___ d) (+4) - (+6) = ___

Show You Know

Example 2: Apply Integer SubtractionOn a typical April day in Whitehorse, Yukon Territory, the temperature is -5˚C in the morning and +6˚C in the afternoon. Determine and explain the difference between these two temperatures.

Method #1: Higher Minus Lower

Method #2: Lower Minus Higher

Assignment:9.3 Explore Integer Subtraction·p. 327, #1-4 (as a class), 5, 7, 9, 11, 13-15, 18·Still Good? #16-17·Pro Star? #19-21

9.4 - Subtract IntegersAfter this lesson, you will be able to...·use addition to subtract integers (WHAT???)

·You can subtract an integer by adding the opposite.·You can represent integer subtraction by adding the opposite on a vertical or horizontal number line.

-1 0-2

-3-4-5 1 2 3 4 5

-1 0-2

-3-4-5 1 2 3 4 5

+3

-5 -10

- 2-3

-4-5

12

34

5

-10

- 2-3

-4-5

12

34

5

-2

+4

Explore the Math

Copy the table. Use integer chips to help you complete each subtraction statement.

(+4) - (+3) = ___ (+4) + (-3) = ___

(-5) - (-3) = ___ (-5) + (+3) = ___

(-3) - (+1) = ___ (-3) + (-1) = ___

0 - (+2) = ___ 0 + (-2) = ___

(+2) - (-4) = ___ (+2) + (+4) = ___

(-4) - (-5) = ___ (-4) + (+5) = ___

What do you notice about the two columns?

Example 1: Use Addition to Subtract IntegersSubtract (-2) - (-5).

Think: To subtract -5, add the opposite, +5.

So, (-2) - (-5) = (-2) + (+5)

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Try "Show You Know" on p. 331

(+3) - (+6) =(-2) - (+3) =(-4) - (-8) =

Show You Know

Example 2: Calculate and Explain a DifferenceThe elevation of a lake is the height of its surface from sea level. The elevation of the Caspian Sea is 28 m below sea level. The elevation of Lake Winnipeg is 217m above sea level. Calculate and explain the difference between these elevations.

10

23

45

67

89

10

-1- 2

-3-4

-5-6

-7-8

-9-1

0

0

-40

40

80

120

160

200

240

Key Ideas·You can subtract an integer by adding the opposite.·You can represent integer subtraction by adding the opposite on a vertical or horizontal number line.

-1 0-2

-3-4-5 1 2 3 4 5

-1 0-2

-3-4-5 1 2 3 4 5

+3

-5 -10

- 2-3

-4-5

12

34

5

-10

- 2-3

-4-5

12

34

5

-2

+4

Assignment:9.4 Subtract Integers·p. 333, #1-4 (as a class), 5, 7, 9, 11, 13, 15, Math Link·Still Good? #16-22·Pro Star? #23, 24

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