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Algebra Tiles

Algebra Tiles. 1. 1. x. x. x 2 Tile. Area = 1. 5. y. y. x. 1. Unit Tile. Area = x 2. Area = x. 1. x Tile. 5 Piece. Area = 5. y. 1. Area = y 2. Area = y. y 2 Tile. xy Tile. x. y Tile. *Make sure all tiles are positive side up (negative [red] side down)*. y.

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Algebra Tiles

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  1. Algebra Tiles 1 1 x x x2 Tile Area = 1 5 y y x 1 Unit Tile Area = x2 Area = x 1 x Tile 5 Piece Area = 5 y 1 Area = y2 Area = y y2 Tile xyTile x y Tile *Make sure all tiles are positive side up (negative [red] side down)* y Area = xy

  2. Algebra Tiles: Perimeter y 1 1 1 1 x 1 1 1 x x x x P = 4 5 5 y y y y x 1 P = 4x P = 2x + 2 1 P = 12 y y 1 y + y + y + y P = P = 2y + 2 = 4y x x *Make sure all tiles are positive side up (negative [red] side down)* y P = 2x +2y

  3. algebra 1 chapter two 2-3: Jumbled Piles What is the best description for this collection of tiles? Algebra 1: Chapter 2 Notes

  4. algebra 1 chapter two 2-4: Jumbled Piles What is the best description for this collection of tiles? Algebra 1: Chapter 2 Notes

  5. Answers to 2-4

  6. 1 1 1 1 x2 x x x x y2 y y y y xy algebra 1 chapter two 2-13: Find perimeter / area Algebra 1: Chapter 2 Notes

  7. Answers to 2-13

  8. Commutative Properties Commutative Property of Addition: When adding two or more numbers together, order is not important Commutative Property of Multiplication: When multiplying two or more numbers together, order is not important Are two the expressions equivalent? Are there Commutative Properties for Subtraction and Division?

  9. Variable A symbol which represents an unknown. Examples: m x z y

  10. Combining like Terms Ex: Simplify the expression below: 6x2 + 4x + 5 + 2x2 + 3x + 6 The x2 Tile The x Tile 5 6 x x x2 x2 8x2 + 7x + 11 Unit Tiles Terms: Variable expressions separated by a plus or minus sign. Like terms: Terms with the same variable(s) raised to the same power. Combine Like Terms: Add the numbers the liked terms are being multiplied by. 6+2 4+3 5+6

  11. Substitution and Evaluation Substitution: Replace each variable with its indicated value. Evaluation: Simplify the expression with proper order of operations. Example: Evaluate the expression below if x = 3 and y = -2. P E MD AS

  12. Square Notation Evaluate the following: Square -5 The opposite of 5 squared Evaluate the following if x = -3: Square -3 The opposite of -3 squared

  13. Legal Mat Move: Flipping To move a tile between the positive and opposite regions, it must be placed on the opposite side. Algebra

  14. Rules for Showing Work with Mats • In order to receive credit for a tile and mat problem… • Copy at least the original mat and tiles • Circle zeros, use arrows to show flipping, etc. • It must be organized and clear. Draw a second table if necessary. • Do NOT make a Picasso!

  15. L.M.M. – Removing Zeros in Same Region To remove two tiles in the same region, the tiles must be of opposite signs (one positive and the other negative). Algebra

  16. L.M.M. – Removing Zeros in Different Regions To remove two tiles in different regions, the tiles must be the same sign (both positive or both negative). Algebra

  17. Legal Mat Move – Balancing Adding (or subtracting) like tiles to (or from) the same region of both sides of the mat is allowed. Algebra ?

  18. 2-65: Recording Your Work Left Right Explntn Original Flip Remove 0’s Balance ? Right Side is Greater

  19. 2-75a: Solving for x Explntn Original Flip Remove 0’s CLT = Balance Balance Divide x = 3

  20. 2-75: Solving for x Explntn Original Flip Remove 0’s CLT = Balance TRUE When is 0 equal to 0? Infinite Solutions

  21. 2-82 a: Solving for x Explntn Original Flip Remove 0’s CLT = Balance Balance Divide x = 3

  22. 2-83 : Solving for y Explntn Original Flip Remove 0’s Balance = FALSE When is 2 equal to -2? No solution

  23. Solving for x and Checking the Answer Explntn Original Balance Divide = The left side must equal the right side. Check:

  24. Using a Table to solve a Proportion Question Toby uses seven tubes of toothpaste every ten months. How many tubes would he use in 5 years? 5 years = 5x12 = 60 months 10 7 x6 x6 60 ? 42 42 Tubes

  25. Using a Table to solve a Proportion Question Toby uses seven tubes of toothpaste every ten months. How long would it take him to use 100 tubes? 10 7 x14.286 x14.286 ? 142.86 100 142.86 Months

  26. Using a Diagram to solve a Proportion Question One more way to organize your work for 2-99 ÷ 1.8 15 x 1.8 0x 7.83 = 6 y = 27 20 14.1 10.8 36 x 1.8

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