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Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.

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1 Variables x2x2 -x 2 x -x

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Example Represent the following trinomials using alge-tiles: 1. 2x 2 +3x+5 2. x 2 -2x-3

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Alge-Tile Uses Algebra tiles can be used for (among other things): Section 1. Identifying ‘like’ and ‘unlike’ terms Section 2. Adding and Subtracting Integers Section 3. Simplifying Expressions Section 4. Multiplying in algebra Section 5. Factorising trinomials Section 6. Doing linear equations

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Section 1. Like Terms Example 1. 4x+5 Can any of these be added ? Explain your answer Example 2. 4x+5x Can any of these be added ? Explain your answer

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Section 2. Adding and Subtracting Integers Example 1. 4-7 Example 2. –3-6

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Section 3. Adding and Subtracting Trinomials Example 1. 2x 2 +3x+5 + x 2 -5x-1

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Section 3. Adding and Subtracting Trinomials Example 1. 2x 2 +3x+5 + x 2 -5x-1 Answer 3x 2 -2x+4

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Section 3. Adding and Subtracting Trinomials Example 2. 2x 2 +3x+2 - ( x 2 -2x+1 ) - A CONCRETE IDEA FOR CHANGING SIGNS.

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Section 3. Adding and Subtracting Trinomials Example 2. 2x 2 +3x+2 - ( x 2 -2x+1 ) A CONCRETE IDEA FOR CHANGING SIGNS.

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Section 3. Adding and Subtracting Trinomials Example 2. 2x 2 +3x+2 - ( x 2 -2x+1 ) A CONCRETE IDEA FOR CHANGING SIGNS. Answer x 2 +5x+1

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Practice Simplify the following: 1)6-7 2)3-2-4-1 3)5x 2 +2x 4)2x 2 +4x+2x 2 -x 5)3x 2 -2x+4+x 2 -x-2 6)x 2 -3x-2-x 2 -2x+4 7)2x 2 -2x-1-3x 2 -2x-2 8)x 2 +2x+1- 3x 2 -x 9)x 2 -x+3-2x 2 +2x+x 2 -2x-5 Simplify the following: 10)2-8-1 11)-5-1-4+1 12)x 2 +2 13)x 2 +5x+x 2 -2x 14)2x 2 -x+1 - (2x 2 -2x-5) 15)x 2 - 2x 2 -2x+4 - (x 2 +2x+3) 16)3x 2 -4x+2 - (x 2 +2) 17)x 2 +x-2 - 2(x 2 +2x-3) 18)-4x-3 - (2x 2 -2x-4)

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Multiplying & Factorising General Aim Whether multiplying or factorising, the general aim is to generate a rectangle and have no pieces left over. Also the small squares always go in the bottom right hand corner

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Section 4. Multiplying in algebra Example 2. Multiply (x-1)(x-3) Answer: x 2 -4x+3

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Practice Multiply the following: 1)x(x+3) 2)2(x-5) 3)3x(x-1) 4)(x+4)(x+3) 5)(x-1)(x+2) 6)(x-4)(x-2) 7)(3x-1)(x-3) 8)(x-1)(x-1) 9)(2x+1) 2 10) (x-2) 2

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Factors and Area - a geometrical approach Review Multiplication Again Section 5. Factorising Quadratic Trinomials

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Show (x+1)(x+3) by arranging the tiles in a rectangle. x x 3 1 + + Rearrange the tiles to show the expansion: x 2 + 4x + 3 How it works Now Arrange them into a Rectangle Remember the little guys go in the bottom right corner

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x 2 + 6x + 8 To factorise this expression form a rectangle with the pieces. x +4 x + 2 ( x + 4 )( x + 2 )The factors are Factorise x 2 + 6x + 8

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x+3 x - 1 NOTE: REDS ARE NEGATIVE NOW COMPLETE THE RECTANGLE WITH NEGATIVE SQUARES Show (x+3)(x-1) by arranging the tiles in a rectangle. Rearrange the tiles to show the expansion: x2x2 + 3x-1x - 3 = x 2 + 2x - 3 (x+3)(x-1)

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Factorise x 2 - 4x + 3 x2x2 - 4x + 3 x - 3 x - 1 The factors are( x - 3 )( x - 1 ) Factorise x 2 -4x+3

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Factorise x 2 - x - 12 x2x2 - x -12 Factorise x 2 -x-12 Clearly there is no way to accommodate the 12 small guys in the bottom right hand corner. What do you do? ? You add in Zero in the form of +x and –x. And Keep doing it to complete the rectangle.

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Factorise x 2 - x - 12 The factors are ?( x + 3 )( x - 4 ) x - 4 x + 3

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Section 6. Doing linear equations Solve 2x + 2 = -8 =

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Section 6. Doing linear equations Solve 2x + 2 = -8 =

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Section 6. Doing linear equations Solve 2x + 2 = -8 = = =

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Section 6. Doing linear equations Solve 2x + 2 = -8 = = Solution x = -5

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Section 6. Doing linear equations = Solve 4x – 3 = 9 + x You can take away the same thing from both sides

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Section 6. Doing linear equations = Solve 4x – 3 = 9 + x You can add the same quantity to both sides

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Section 6. Doing linear equations = Solve 4x – 3 = 9 + x

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Section 6. Doing linear equations = Solve 4x – 3 = 9 + x = =

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Section 6. Doing linear equations = Solve 4x – 3 = 9 + x = = Solution x = 4

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Practice Solve the following: 1)x+4 = 7 2)x-2 = 4 3)3x-1 =11 4)4x-2 = x-8 5)5x+1 = 13-x 6)2(x+3) = x-1 7)2x-4 = 5x+8

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