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Modeling Review

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Zero Pairs One of the first concepts students need to understand when using Algebra Tiles is “zero pairs” You can always add and take away “zero pairs” when needed This concepts is key for all other concepts You can tie in the Additive Inverse and Identity Properties here

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Zero Principle 1+ (-1) = 0 2 + (-2) = 0

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**Adding Integers Example 1: 3 + 5 = 8**

Model 3 Model 5 Combine the tiles and read the answer

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**Adding Integers Example 2: 2 + (-4) = ?**

-2 Model 2 Model -4 Combine the tiles and remove any zero pairs read the answer

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**Subtracting Integers 6-2 = ?**

4 Remove 2 yellow tiles and read the answer Model 6

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**Subtracting Integers -5 – (-3) = ?**

-2 Remove 3 red tiles and read the answer Model -5

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**Subtracting Integers 4 – (-3) = ?**

7 Remove 3 red tiles and read the answer Add 3 zero pairs Model 4

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**Subtracting Integers -3 – 2 = ?**

-5 Model -3 Add 2 zero pairs Remove 2yellow tiles and read the answer

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**Multiplying Integers Based on whole number representation**

Use counters to represent a number of groups of a quantity of tiles

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**Prerequisites Students must understand whole number multiplication**

That a x b means a groups of b

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**Multiplying Integers 3 x 2 -> 3 groups of 2 yellow tiles**

3 x -2 -> 3 groups of -2 red tiles -3 x 2 -> “the opposite” of 3 groups of 2 yellow tiles -3 x -2 -> “the opposite” of 3 groups of 2 red tiles You can also think of “the opposite” as “to remove”. Making this change forces students to put zero pairs on the mat.

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**Multiplying Integers 2 x 5 = ?**

10 2 groups of 5 yellow tiles

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**Multiplying Integers 2 x -4 = ?**

-8 2 groups of 4 red tiles

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**Multiplying Integers -2 x 6 = ?**

-12 The opposite of 2 groups of 6 yellow tiles

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**Multiplying Integers -2 x -3 = ?**

6 The opposite of 2 groups of 3 red tiles

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**Dividing Integers Same concept as multiplication**

The dividend tells you how many of what color tiles you have. The divisor tells you to make those tiles and make groups If the divisor is negative then you would take the opposite

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Prerequisites Students should know how division works with positive whole numbers. Students should work with multiplication of integers before moving on to division.

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**3 Dividing Integers 6 ÷ 2 You start with 6 yellow tiles**

Split the 6 yellow tiles into two groups How many, of what tiles are in each row?

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**-4 Dividing Integers -8 ÷ 2 You start with 8 red tiles**

Split the 8 red tiles into two groups How many, of what tiles are in each row?

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**-5 Dividing Integers 10 ÷ -2 You start with 10 yellow tiles**

Split the 10 yellow tiles into two groups… then take the opposite How many, of what tiles are in each row?

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**4 Dividing Integers -12 ÷ -3 You start with 12 red tiles**

Split the 12 red tiles into three groups… then take the opposite How many, of what tiles are in each row?

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