.1, 8.3 Multiplying and Dividing Integers Using...

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Positive Integer = A number greater than zero. Negative Integer = A number less than zero. Opposite Integers = Two integers with a sum of zero. For example, +3 and 3 are opposite integers. Recall from Grade 7 Integer tiles are used to model integers. They combine to form a Zero Pair . + Positive Integer Tile models +1 Negative Integer Tile models 1 + 8.1, 8.3 Multiplying and Dividing Integers Using Models

Transcript of .1, 8.3 Multiplying and Dividing Integers Using...

Page 1: .1, 8.3 Multiplying and Dividing Integers Using Modelsramymelhem.com/uploads/3/4/4/1/34417566/multiplying... · Positive Integer = A number greater than zero. Negative Integer = A

Positive Integer = A number greater than zero.  

Negative Integer = A number less than zero.  

Opposite Integers = Two integers with a sum of zero.For example, +3 and ­3 are opposite integers.

Recall from Grade 7Integer tiles are used to model integers.

They combine to form a Zero Pair.

+ ­Positive Integer Tile models +1 Negative Integer Tile models ­1

+ ­

8.1, 8.3 Multiplying and Dividing Integers Using Models

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When the FIRST Number is Positive (+)

Method 1A:  Multiplication with Integer Tiles

When the FIRST Number is Negative (­)

• ADD tiles to the bank • Remove tiles from the bank• ZERO Pairs

(+3)  x  (+2)3 groups 2+ tiles in

each group

++

++

++

Answer:  total tiles in the bank

Answer:  (+6)

Example A:

Example B:

(+5)  x  (­3)

Answer:  total tiles in the bank

Answer:  (­15)

­­­

­­­

­­­

­­­

­­­

Example A:(­6)  x  (+3)

Answer:  total tiles in the bank

Answer:  (­18)

6 groups of

+++

­­­

+++

­­­

+++

­­­

+++

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+++

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+++

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Remove 6 groups of (+3) tiles

+++

­­­

+++

­­­

+++

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+++

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+++

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+++

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(­4)  x  (­2)

Answer:  total tiles in the bank

Answer:  (+8)

Remove 4 groups of (­2) tiles

++

­­

+ ­+ ­

++­­

++­­

++

­­

++

­­

++

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++

­­

Example B:

Add

Add

Take Away positive 3

Add 5 groups of negative 3Take Away 4 groups of Negative 2

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When the Signs are the SAME• ADD tiles to the bank• Answer is POSITIVE

• Remove tiles from the bank• ZERO Pairs• Answer is NEGATIVE

(+10)    (+2)total tiles in bank

Answer:  total number of groups

Answer:  (+5)

++

++

++

++

++

Count the groups

++

++

++

++

++

1 2 3 4 5

Example A:

Example B:

Example A:

Answer:  total number of groups removed

Answer:  (­3)

total zero pairs in bank

Remove ALL groups of (­2) tiles

(+6)    (­2)

+ ­+ ­

+ ­+ ­

+ ­+ ­

+ ­+ ­

+ ­+ ­

+ ­+ ­

Count how many groups you removed

+ ­+ ­

+ ­+ ­

+ ­+ ­

1 2 3

Example B:

Method 1B:  Division with Integer Tiles

When the Signs are the DIFFERENT

(­12)    (­6)total tiles in bank

6­ tiles ineach group

Answer:  total number of groups

Answer:  (+2)

Count the groups

­­­­­­

­­­­­­

­­­­­­

­­­­­­

1 2

4 zero pairs ineach group

total zero pairs in bank

(­8)    (+4)

Read: Add 2 groups to make +10 Read: Take Away 2 groups to make +6

Read: Add 4 groups to make -8

Ignore Drawing Below. I wasn't able to delete them. Try to solve it though.

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Method 2A:  Multiplication with Number Lines

(+4)  x  (+2)count by 2s on number linewalk forward

Answer:  where you stop walking is the answer

Answer:  (+8)

4 stepsface +

Start at 0Turn and Face (+) and Walk Forward

Example A:

(+5)  x  (­3)count by 3s on number linewalk backward

Answer:  where you stop walking is the answer

Answer:  (­15)

5 stepsface +

Start at 0Turn and Face (+) and Walk Backward

Example B:

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(­2)  x  (+3)count by 3s on number linewalk forward

Answer:  where you stop walking is the answer

Answer:  (­6)

2 stepsface ­

Start at 0Turn and Face (­) and Walk Forward

Example C:

(­7)  x  (­5)count by 5s on number linewalk backward

Answer:  where you stop walking is the answer

Answer:  (+35)

7 stepsface ­

Start at 0Turn and Face (­) and Walk Backward

Example D:

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(+10)    (+2)final number on 

number line

Count how many steps you took

Answer:  (+5)

Start at 0In order to walk forward from 0 to +10, you must face +

Example A:

count by 2s on number linewalk forward

Answer:  the number of steps you took

1 2 3 4 5

The sign is +, because you face +

Method 2B:  Division with Number Lines

(­12)    (­6)final number on 

number line

Count how many steps you took

Answer:  (+2)

Start at 0In order to walk backward from 0 to ­12, you must face +

Example B:

count by 6s on number linewalk backward

Answer:  the number of steps you took

The sign is +, because you face +

2 1

(OPTIONAL)

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Start at 0In order to walk backward from 0 to 6, you must face ­

(+6)    (­2)final number on 

number line

Count how many steps you took

Answer:  (­3)

Example D:

count by 2s on number linewalk backward

Answer:  the number of steps you took

The sign is ­, because you face ­

1 2 3

Start at 0In order to walk forward from 0 to ­8, you must face ­

(­8)    (+4)final number on 

number line

Count how many steps you took

Answer:  (­2)

Example C:

count by 4s on number linewalk forward

Answer:  the number of steps you took

The sign is ­, because you face ­

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