Http:// Learn Alberta Let’s Review Integers (Unit 9)

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Let’s Review Integers Let’s Review Integers (Unit 9)(Unit 9)

1. Combine 2 red chips and 2 blue chips…what is their sum?

2. Make the above into an addition statement …use brackets.

Add & Subtract Integers Add & Subtract Integers (Unit 9)(Unit 9)

Red Chips = +1 Blue Chips = -1

Are integers with the same numeral, but different signs (+ or -)

…they are the same distance from zero, in opposite directions.

OppositeOpposite Integers IntegersStudent Outcome: I will learn what opposite integers are.

For example:

a. (+1) and (-1) are opposite integers

b. (-3) and ( ) are opposite integers

c. (+14) and ( ) are opposite integers

d. (-659) and ( ) are opposite integers

Zero Pair: combining (+1) with (-1) (+1) + (-1) = 0

ZeroZero Pairs PairsStudent Outcome: I learn about zero pairs.

We can combine numerous zero pairs to solve problems:

For example:

a. (+1) + (-1) =

b. (-3) + (+3) =

c. (+11) + (-11) =

Grouping: combining “positives with positives” “positives with negatives” or “negatives with negatives” to allow us

to solve

Adding Adding IntegersIntegersStudent Outcome: I will be able to add integers using integer chips.

Addition Statements:

(+1) + (+2) = ______ (+5) + (- 4) = ______

Your turn…apply “integer addition”

1. Draw the model for (-3) + (+ 4)

2. Draw the model for (+11) + (-3)

- Using Tiles to group + and – to find the answer….(great site!)

http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html

2. Using addition equations (small to large #’s) to find the answer.

http://www.berghuis.co.nz/abiator/maths/sa/saintegeradd2.htmL

VARIETY of GAMES:A. http://classroom.jc-schools.net/basic/math-integ.html

Adding Adding Integers Integers GAMESGAMES

Student Outcome: I will be able to add integers using integer chips.

SOLVE

FindFind The Addition The Addition StatementStatement

Student Outcome: I will be able to add integers using integer chips.

Model

Expression

Equation

Answer

- Model the scenario and create an addition statement to find your answer…

FindFind The Addition The Addition StatementStatement

Student Outcome: I will be able to add integers using integer chips.

Ray spent $5 on bus fares to visit his Aunt. Duringthe visit, her Aunt gave him $12 for doing some yardwork. How much money did Ray gain from the visit?

ApplyingApplying Integer Addition Integer Addition

Page 313- 315

12, 17af, 19abd, 20ab

11 6, 9, 14b, 17

1, 2, 5, 8ab, 9

Show Me What You Know Show Me What You Know #1#1

On the front

On the back

Using aUsing a Number LineNumber Line to Add to Add IntegersIntegers

Student Outcome: I will be able to add integers using a number line.

Start at zero and move the direction of the first number…then move the direction of the second number!

Directions:

Positive (+) and Negative (-)

Move the DOTDOT to it’s correct place using the addition statements below…

1. (+4) + (+3) 2. (-2) + (+5) 3. (+5) + (-11)

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

The addition statement below is…

(+4) + (+3)

1. What do the colors of the arrows represent?

2. What do the length of the arrows represent?

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

The addition statement below is…

(+4) + (+3)

1. What do the colors of the arrows represent?

2. What do the length of the arrows represent?

3. What is the total?

What are the “Addition Statements?”

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

What are the “Addition Statements?”

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

Create your own…come on up and test your classmates?

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

Addition Statement…

What are the “Addition Statements?”

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

What are the “Addition Statements?”

What is the What is the “addition “addition statement?”statement?”

Student Outcome: I will be able to add integers using a number line.

Finding TemperaturesFinding Temperatures using a using a Number LineNumber Line

Number lines can also be vertical (grids).

•Top of the “y” axis is positive and bottom is negative.

•Right side of “x” axis is positive and left side is negative.

What are the 2 different addition statements?

Create your own…

Addition Statement…

What is the What is the “addition “addition statement?”statement?”

The temperature in Yellowknife,

Northwest Territories, on 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?

ApplyApply Integer AdditionInteger Addition

0°C

5°C

- 5°C

This morning it was ______°C

and the temperature has gone up

12°C.

What is the high temperature

going to be today?

ApplyApply Integer AdditionInteger Addition

0°C

5°C

- 5°C

ApplyingApplying Integer Addition Integer Addition

Page 320-322:

4,20ab,21ef,22,23

11 4,5,8ab,13,14,18

1,4,5,7ab,9,10

Show Me What You Show Me What You Know#2Know#2

On the front

On the back

Explore Integer Explore Integer SubtractionSubtractionStudent Outcome: I will be able to subtract integers using integer

chips.

Subtract integers using integer chips…

1.What is the subtraction expression for the model above?

1.Take away 4 red chips from the original 6 red chips…what do you have left?

Explore Integer Explore Integer SubtractionSubtractionStudent Outcome: I will be able to subtract integers using integer

chips.

Subtract integers using integer chips…

1.What is the subtraction expression for the model above?

2.Take away 3 blue chips from the original 7 blue chips…what do you have left?

Model it… Model it… SubtractionSubtractionStudent Outcome: I will be able to subtract integers using integer

chips.

Model the equations below…

(-5) – (-2) (+8) – (+3)

Model it… Model it… SubtractionSubtractionStudent Outcome: I will be able to subtract integers using integer

chips.

Model the equations below…

(-5) – (-2) (+8) – (+3)

What do you notice about each equation?

Model it… Model it… SubtractionSubtractionModel the equations below…

(-5) – (+2) (+1) – (+4)

CAN THESE BE SOLVED???

Model it… Model it… SubtractionSubtractionStudent Outcome: I will learn different strategies to use addition to

subtract integers..

STRATEGY #1

“Move in – Move out”

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(+ 2) – (+5)

Steps to follow:

1. Model the first integer2. Move in enough to model the second integer

3. Remove the chips asked in the subtraction statement

4. What is left

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(-1) – (-6)

Steps to follow:

1. Model the first integer2. Move in enough to model the second integer

3. Remove the chips asked in the subtraction statement

4. What is left

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(-1) – (+4)

Steps to follow:

1. Model the first integer2. Move in enough to model the second integer

3. Remove the chips asked in the subtraction statement

4. What is left

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(-3) – (-7)

Steps to follow:

1. Model the first integer2. Move in enough to model the second integer

3. Remove the chips asked in the subtraction statement

4. What is left

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(+2) – (-6)

Steps to follow:

1. Model the first integer2. Move in enough to model the second integer

3. Remove the chips asked in the subtraction statement

4. What is left

Step 1 Step 2 Step 3 Step 4

Model it… Model it… SubtractionSubtractionStudent Outcome: I will learn different strategies to use addition to

subtract integers..

STRATEGY #2

“Zero Pairs”

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(+ 2) – (- 4)

Steps to follow:

1. Model what the question is asking2. ZERO PAIRS: 2nd integer reversing the (+) or (-) of number…

3. Remove the chips asked in the subtraction statement

4. Then group the chips left over!

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(- 2) – (- 3)

Steps to follow:

1. Model what the question is asking

2. ZERO PAIRS: 2nd integer reversing the (+) or (-) of number…

3. Remove the chips asked in the subtraction statement

4. Then group the chips left over!

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(+5) – ( -3)

Steps to follow:

1. Model what the question is asking

2. ZERO PAIRS: 2nd integer reversing the (+) or (-) of number…

3. Remove the chips asked in the subtraction statement

4. Then group the chips left over!

Step 1 Step 2 Step 3 Step 4

What if the Integer #’s are What if the Integer #’s are differentdifferent??

Student Outcome: I will learn different strategies to use addition to subtract integers..

(-4) – ( -8)

Steps to follow:

1. Model what the question is asking

2. ZERO PAIRS: 2nd integer reversing the (+) or (-) of number…

3. Remove the chips asked in the subtraction statement

4. Then group the chips left over!

Step 1 Step 2 Step 3 Step 4

Method #1: Finding the “Method #1: Finding the “Higher Minus Higher Minus LowerLower””

Student Outcome: I will learn different strategies to use addition to subtract integers..

( ) – ( )

The morning temperature is - 5°C. This afternoon it will reach a

temperature of +6°C. How much higher is the afternoon

temperature than (difference) the morning temperature?

1. Model it…

2. Use the steps (Zero Pair, Remove, and then Group)

Method #1: Finding the “Method #1: Finding the “Lower Minus Lower Minus HigherHigher””

Student Outcome: I will learn different strategies to use addition to subtract integers..

( ) – ( )

The morning temperature is - 5°C. This afternoon it will reach a

temperature of +6°C. How much lower is the morning

temperature than (difference) the afternoon temperature?

1. Model it…

2. Use the steps (Zero Pair, Remove, and then Group)

ApplyingApplying Integer Integer SubtractionSubtraction

Page 327-329 3,18,19cd,20ab,21

15 3,6,9cd,11,14,18

2,3,5,9cd,13,18

Model it… Model it… SubtractionSubtractionStudent Outcome: I will learn different strategies to use addition to

subtract integers..

STRATEGY #3

“Double Flip”

Subtracting Subtracting IntegersIntegersUse integer chips to find the answer to the subtraction statement below…

(+4) – (+ 2)

What happens when we change the subtraction statement to an addition statement?

(+4) + (- 2)

1.The answers are ____________________.

2.Which of the two methods above are easier?

Zero Pair Remove Group

Zero Pair Remove Group

NOT needed! NOT needed!

Try it again!Try it again!

(- 5) – (- 3)

(- 5) + (+ 3)

1.The answers are ____________________.

2.Which of the two methods above are easier?

3.Do you see a pattern?

Zero Pair Remove Group

Zero Pair Remove Group

NOT needed! NOT needed!

Try it again!Try it again!

(- 12) – (+ 5)

(- 12) + (- 5)

1.The answers are ____________________.

2.Which of the two methods above are easier?

3.Do you see a pattern?

Zero Pair Remove Group

Zero Pair Remove Group

NOT needed! NOT needed!

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will learn different strategies to use addition to

subtract integers..

Use a number line to add & subtract.

Subtract: (- 2) – (- 5) = ( ) + ( )

Solution…change the above statement into an addition statement. Then use the number line below to find your answer.

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will learn different strategies to use addition to

subtract integers..

Use a number line to add & subtract.

Subtract: (+7) – (+3) = ( ) + ( )

Solution…change the above statement into an addition statement. Then use the number line below to find your answer.

Changing subtraction to Changing subtraction to “addition”“addition”

What do you notice about the signs (+ or -) when you change the subtracting statement to an adding statement?

SUBTRACTION STATEMENT

SUBTRACTION CHANGED TO ADDITION

(+4) – (+3) (+4) + (-3)

(+2) – (- 3) (+2) + (+3)

(-3) – (+1)

(-4) + (- 5)

(+6) + (+2)

Changing subtraction to Changing subtraction to “addition”“addition”

Find the difference of the Caspian Sea (+ 217 m) elevation from the elevation of Lake Winnipeg

(- 28 m)?

Steps:

1.Would you use chips or a number line?

2.Change the subtraction statement to an addition statement.

3.Model your answer.

4.You may use a calculator to help find your answer. 0 m

+ 217 m

+ 28 m

+ 245 m

Page 333-335 3,17,21,23,24

16 3,5,9cd,17,20,22

2,3,5,9ab,13,15

Changing subtraction to Changing subtraction to “addition”“addition”

Show Me What You Know Show Me What You Know #3#3

On the front

On the back

Solve

Use the golf score chart below to find the addition or subtraction statements.

Prize…what does the term “albatross” mean in a golf score?

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will decide when to add and subtract integers.

Golf Term # of Strokes

Double Bogey +2

Bogey +1

Par 0

Birdie - 1

Eagle -2

On hole #1 Rosa made an eagle and Samantha made a bogey.

1.How many more strokes did Samantha take than Rosa?

2.Would subtract or add?

3.Find the answer!

Use the golf score chart below to find the addition or subtraction statements.

Prize…what does the term “albatross” mean in a golf score?

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will decide when to add and subtract integers.

Golf Term # of Strokes

Double Bogey +2

Bogey +1

Par 0

Birdie - 1

Eagle -2

Rosa shot the following score…Hole #1 (par), Hole #2 (Bogey), Hole #3 (Eagle), and Hole #4 (Birdie)…

1.What is her score so far?

2.Would subtract or add?

3.Find the answer!

Applying Integer Applying Integer OperationsOperationsGolf Term # of Strokes

Double Bogey +2

Bogey +1

Par 0

Birdie - 1

Eagle -2

Find out…

What was Rosa’s score?

Hole # Par Rosa

1 5 Par

2 4 Bogey

3 4 Eagle

4 3 Birdie

5 5 Par

6 4 Birdie

7 3 Eagle

8 4 Double Bogey

9 4 Bogey

Use the “Wind Chill Chart” on page 337 to answer the question below.

1.If the air temperature is – 20ºC and the wind speed is

10 km/h…then what is the “wind chill” temperature?

2.If the air temperature is - 25ºC…and the wind speed is

50 km/h…then what is the “wind chill” temperature?

3. What are the differences between the air temperature and the “wind chill” temperatures above? (Hint…colder!)

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will decide when to add and subtract integers.

Use a number line to show how you could figure out the temperature as it changes throughout the day.

• The morning air temperature was 0ºC with a 45 km/h wind. • As the day went on the air temperature changed to -5ºC and

the wind settled to 5 km/h.• What is the new temperature?• Write the information above into an addition or subtraction

statement.

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will decide when to add and subtract integers.

Use a number line to show how you could figure out the temperature as it changes throughout the day.

• • • • •

Applying Integer Applying Integer OperationsOperationsStudent Outcome: I will decide when to add and subtract integers.

Applying Integer Applying Integer OperationsOperationsWhat are some words we use to know whether we should add or subtract integers?

SubtractionSubtraction to to AdditionAddition of of IntegersIntegers

Page 339-340:13ab, 16, 17, 18

12 5-7,10,13ab,14

2, 3, 4, 5, 6

Chapter ReviewChapter Review

Page 342: # 1, 3ab, 4cd, 5, 8d, 9, 10

Page 343: # 11ab, 12bc, 13, 14a, 15a,

16, 17a, 18

Show Me What You Show Me What You Know #4Know #4

Wrap it up – Page 345Wrap it up – Page 345

Game – Page 346Game – Page 346

GamesGames

•Golf

•2 Card Flip (adding and subtracting)

•3 Card Flip (adding and subtracting)