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**Introduction to Algebra Tiles**

Created by Nancy McAlinden Numeracy Lead Teacher N.B. District 14

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**Remember how we modeled integers?**

Legend - + ? ?

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What is this worth? (-2) Legend + - ZERO PAIRS

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What is this worth? +2 Legend + -

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**Algebra Tiles work the same way!**

Legend + - +3

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**Algebra Tiles work the same way!**

Legend + - -6

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**Algebra Tiles work the same way!**

Legend + - -2

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**Model this question: (-2) + (+3) =**

Legend + - zero pairs +1

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**Algebra Tiles can show MORE!**

But… Algebra Tiles can show MORE!

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**+ - These tiles help us model the unknown! The variable!**

Legend + - These tiles help us model the unknown! The variable! The mystery number!

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**+ - These tiles represent x! (Or n) (or whatever letter you’re using**

Legend + - These tiles represent x! (Or n) (or whatever letter you’re using for the variable or unknown amount.)

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**+ - One side represents a positive variable;**

Legend + - One side represents a positive variable; the other side represents a negative.

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What does this show? Legend + - 3x

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What does this show? Legend + - -9x

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What does this show? Legend + - -2x

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What does this show? Legend + - 2x + 4

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What does this show? Legend + - x - 6

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What does this show? Legend + - -2x + 5

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What does this show? x + 3

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**But what is x worth? We don’t know until:**

1.) someone tells us the value of x Or 2.) we have some information about the other side of the equation!

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3x = 9 This line represents the = sign, or the middle of the balance scale.

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If 3x = 9, …what is one x worth?

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3x = 9

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3x = 9 x = 3

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Solve for x: x + 2 = 6

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Solve for x: X + 2 = 6 We want a single x alone on one side and its value (the number of units or squares) on the other.

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Solve for x: x + 2 = 6 We can subtract the 2 units (or squares) from the left IF we also subtract 2 units from the right. This keeps the balance.

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Solve for x: x + 2 = 6 x + 2 – 2 = 6 - 2

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Solve for x: x = 4

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Solve for x: 2x + 4 = 8

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Solve for x: 2x + 4 = 8 We want a single x alone on one side and its value (the number of units or squares) on the other.

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Solve for x: 2x + 4 = 8 We can remove the 4 positive units from the left as long as we keep the balance and remove 4 positives from the right too. 2x = 8 - 4

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**2x + 4 = 8 2x = 4 Solve for x: We want one x.**

Now we have 2 x on one side and 4 on the other. 2x = 4 We want one x.

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**2x + 4 = 8 2x = 4 Solve for x: We can’t subtract an x from the left**

because we don’t have an x to subtract from the right, but…

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Solve for x: 2x = 4 We can divide them and share fairly:

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Solve for x: 2x = 4

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Solve for x: ___ = __ 2x = 4

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Solve for x: x = 2

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**What about the big squares?**

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**They represent x2 and (-x2).**

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**We’ll use them in high school!**

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Not all sets of algebra tiles are the same colours as the set we’ve seen here. How can you tell which side is negative?

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**The negative side is the colour that is the same for all sizes of tiles in the set:**

White = negative

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**The negative side is the colour that is the same for all the tiles in the set:**

Black = negative

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