1. ILLUSTRATING INTEGERS Multiplication and Division

2. INTEGERS AND MULTIPLICATION
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3. MULTIPLICATION + + + + + +
Red and blue tiles can be used to model multiplication.
Remember that multiplication can be described as repeated addition.
So 2 x 3 = ? + +
2 groups of 3 tiles = 6 tiles + + + +
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4. MULTIPLICATION – – – – – 2 x -3 means 2 groups of -3 2 x -3 = -6 –
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5. MULTIPLICATION
Since 2 x 3 = 6 and 3 x 2 = 6, does it make sense that -3 x 2 = -6 ?
-3 x 2 = -6 is true.
+2 x -3 = -6 and -3 x +2 = -6 belong to a fact family:
+2 x -3 = -6
-3 x +2 = -6
-6 ÷ +2 = -3
-6 ÷ -3 = +2
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6. MULTIPLICATION + + +2 x +4 = +8 + + + + + +
Use your tiles to model each multiplication problem.
+2 x +4 = ?
2 groups of +4
ANSWER + + +
+2 x +4 = +8 + + + + +
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7. MULTIPLICATION – – – – – – +3 x -3 = -9 – – – +3 x -3 = ?
ANSWER – – –
3 groups of -3 – – –
+3 x -3 = -9 – – –
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8. MULTIPLICATION – – – – -2 x +4 = -8 – – – – -2 x +4 = ? 4 groups of -2
ANSWER
4 groups of -2 – – – –
-2 x +4 = -8 – – – –
Use the Commutative Property
-2 x +4 = ?  We can’t show -2 groups of +4
+4 x -2 = ? we can show 4 groups of -2
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9. MULTIPLICATION
To model -2 x -3, think “the opposite” of 2 groups of -3, which would be 2 groups of positive 3.
-2 x -3 = +6
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10. MULTIPLICATION + + + + + + -3 x -4 = +12 + + + + + +
Use tiles to illustrate -3 x -4 =?
ANSWER + + +
The “opposite” of 3 groups of -4 + + +
-3 x -4 = +12 + + + + + +
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11. INTEGERS AND DIVISION
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12. Divide 12 red tiles into 3 equal groups
DIVISION
Use tiles to model +12 ÷ +3 = ?
4 red tiles in each group.
Divide 12 red tiles into 3 equal groups + + + + +
+12 ÷ +3 = +4 + + + + + + +
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13. Divide -15 into 5 equal groups
DIVISION
Use tiles to model -15 ÷ +5 =? –
Divide -15 into 5 equal groups – – –
-15 ÷ +5 = -3 – – – – – – – – – – –
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14. DIVISION Write the fact family -4 x +2 = -8 Compare your answer.
-8 ÷ +2 = -4
-8 ÷ -4 = +2
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15. DIVISION
Three equivalent ways to write a division expression as a fraction: 12 ÷ 3 = .
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16. Mixed Practice
Now try these! Use red and yellow tiles to find each answer.
1) ) +3 x -4
2) ) -5 x -2
3) ) -12 ÷ +6
4) ) -8 ÷ +2
ANSWER
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