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Alge-Tiles

Alge-Tiles. For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus. Variables. x 2. x. 1. -x 2. -x. -1. Example. Represent the following trinomials using alge-tiles:. 1. 2x 2 +3x+5. 2. x 2 -2x-3. Alge-Tile Uses.

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Alge-Tiles

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

  2. Variables x2 x 1 -x2 -x -1

  3. Example Represent the following trinomials using alge-tiles: 1. 2x2+3x+5 2. x2-2x-3

  4. 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

  5. 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

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

  7. Section 3. Adding and Subtracting Trinomials Example 1. 2x2+3x+5 + x2-5x-1

  8. Section 3. Adding and Subtracting Trinomials Example 1. 2x2+3x+5 + x2-5x-1 Answer 3x2-2x+4

  9. Section 3. Adding and Subtracting Trinomials Example 2. 2x2+3x+2 - ( x2-2x+1 ) - A CONCRETE IDEA FOR CHANGING SIGNS.

  10. Section 3. Adding and Subtracting Trinomials Example 2. 2x2+3x+2 - ( x2-2x+1 ) A CONCRETE IDEA FOR CHANGING SIGNS.

  11. Section 3. Adding and Subtracting Trinomials Example 2. 2x2+3x+2 - ( x2-2x+1 ) Answer x2+5x+1 A CONCRETE IDEA FOR CHANGING SIGNS.

  12. Practice • Simplify the following: • 2-8-1 • -5-1-4+1 • x2+2 • x2+5x+x2-2x • 2x2-x+1 - (2x2-2x-5) • x2- 2x2-2x+4 - (x2+2x+3) • 3x2-4x+2 - (x2+2) • x2+x-2 - 2(x2+2x-3) • -4x-3 - (2x2-2x-4) • Simplify the following: • 6-7 • 3-2-4-1 • 5x2+2x • 2x2+4x+2x2-x • 3x2-2x+4+x2-x-2 • x2-3x-2-x2-2x+4 • 2x2-2x-1-3x2-2x-2 • x2+2x+1- 3x2-x • x2-x+3-2x2+2x+x2-2x-5

  13. Multiplying & FactorisingGeneralAim • 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

  14. Section 4. Multiplying in algebra Example 2. Multiply (x-1)(x-3) Answer: x2-4x+3

  15. Practice • Multiply the following: • x(x+3) • 2(x-5) • 3x(x-1) • (x+4)(x+3) • (x-1)(x+2) • (x-4)(x-2) • (3x-1)(x-3) • (x-1)(x-1) • (2x+1)2 • (x-2)2

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

  17. Show (x+1)(x+3) by arranging the tiles in a rectangle. How it works x + 3 Now Arrange them into a Rectangle Remember the little guys go in the bottom right corner x + 1 Rearrangethe tiles to show the expansion: x2 + 4x + 3

  18. Factorise x2 + 6x + 8 Factorise x2+6x+8 x2 + 6x + 8 To factorise this expression form a rectangle with the pieces. x + 4 x + 2 The factors are ( x + 4 )( x + 2 )

  19. Show (x+3)(x-1) by arranging the tiles in a rectangle. - 3 x2 + 3x -1x (x+3)(x-1) x + 3 x - 1 NOTE: REDS ARE NEGATIVE NOW COMPLETE THE RECTANGLE WITH NEGATIVE SQUARES Rearrangethe tiles to show the expansion: = x2 + 2x - 3

  20. Factorise x 2 - 4x + 3 x2 + 3 - 4x Factorise x2-4x+3 x - 3 x - 1 The factors are ( x - 3 )( x - 1 )

  21. Factorise x 2 - x - 12 x2 -12 - x Factorise x2-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.

  22. Factorise x 2 - x - 12 Factorise x2-x-12 x - 4 x + 3 The factors are ? ( x + 3 )( x - 4 )

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

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

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

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

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

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

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

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

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

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

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