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
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
+++
+++
+++
+++
+++
+++
Remove 6 groups of (+3) tiles
+++
+++
+++
+++
+++
+++
(4) x (2)
Answer: total tiles in the bank
Answer: (+8)
Remove 4 groups of (2) tiles
++
+ +
++
++
++
++
++
++
Example B:
Add
Add
Take Away positive 3
Add 5 groups of negative 3Take Away 4 groups of Negative 2
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.
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:
(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:
(+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)
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
12
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