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1 Section 2.2 introduction an exploration into: Equations with Algebra Tiles Section 2.2 introduction an exploration into: Equations with Algebra Tiles

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2 You can use red and blue tiles to represent math equations. Equations show that two things are balanced, and youre not allowed to do anything that might make them unbalanced. Exploration 2.2 Equations with Algebra Tiles This means you can add or remove tiles, as long as you do the same to both sides. =

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3 You can use tiles to represent equations. These tiles show that x + 2 = 5. If you can get x by itself, you can find its value. Here, x = 3. Exploration 2.2 Equations with Algebra Tiles = When you have an equation, you can add or remove tiles as long as you add or remove exactly the same tiles on both sides. = Remove 2 squares from both sides.

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4 Example Show the expression x + 3 = 5 with algebra tiles, and then find the value of x. Solution follows… Solution The equation x + 3 = 5 looks like the picture on the right. Remove 3 squares from both sides to get x by itself. Exploration 2.2 Equations with Algebra Tiles This tells you that x = 2. = = Remove 3 squares from both sides.

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5 For some equations, you need to use zero pairs before you can get x by itself. Exploration 2.2 Equations with Algebra Tiles Remember, a zero pair is one blue tile and one red tile that together have a total value of zero. 1 + (–1) = 0

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6 Example Show x – 4 = 7 with tiles, and find the value of x. Solution follows… Solution The equation x – 4 = 7 looks like this. Add 4 tiles to both sides, Exploration 2.2 Equations with Algebra Tiles = and then remove zero pairs. This leaves x on one side of the equation, and 11 blue tiles on the other side. So x = 11.

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7 Example Show 3 x = –15 with tiles, and find the value of x. Solution follows… Solution 3 x = –15 looks like the picture on the right. Put the x s in a line, and then put the same number of tiles next to every x. For every x, there are 5 red tiles. This tells you that x = –5. Exploration 2.2 Equations with Algebra Tiles =

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8 = x = 5 x = –7 = = = Add 2 reds to both sides Remove zero pairs = x = –4 = = = x = 3 Remove 6 tiles from both sides = Add 3 blues to both sides = Remove zero pairs = x = 11 Exercises Solution follows… 1. Use algebra tiles to model each of these equations, and then find the value of x : a. x + 6 = 9 b. x – 3 = 8 c. x + 2 = –5 d. 2 x = 10 e. 3 x = –12 a.b.c.d.e. Exploration 2.2 Equations with Algebra Tiles

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9 Exercises Solution follows… Exploration 2.2 Equations with Algebra Tiles = This is x – 4 = –5 = = Remove 4 tiles from each side x = –1 2. Write the equation that is represented by these tiles. Then solve the equation to find the value of x.

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10 Round Up Keeping equations balanced by doing the same to both sides is one of the most important things youll ever learn in math. There will be a lot more about this in the next section. Exploration 2.2 Equations with Algebra Tiles

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