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Algebra Tiles *Make sure all tiles are positive side up (negative [red] side down)* 1 1 x Area = 1 x x2 Tile 5 Unit Tile y 1 x Area = x Area = x2 1 5 Area = 5 Piece x x Tile xy Tile y y 1 y Area = y Area = y2 y Tile Area = xy y2 Tile *Make sure all tiles are positive side up (negative [red] side down)* Algebra Tiles: Perimeter 1 1 1 1 y 1 x 1 1 x P=4 5 x x x 5 y y x 1 P = 4x P = 2x + 2 1 P = 12 y y y y 1 P = 2y + 2 P=y+y+y+y = 4y x x y P = 2x +2y chapter two 2-3: Jumbled Piles What is the best description for this collection of tiles? Algebra 1: Chapter 2 Notes chapter two 2-4: Jumbled Piles What is the best description for this collection of tiles? Algebra 1: Chapter 2 Notes Answers to 2-4 a. 4 x 3 x y 7 2 b. 3x 3 xy 6 c. can't be simplifed - no like terms 2 d. y 7 y 2 xy 4 x 3 2 chapter two 2-13: Find perimeter / area 1 y x x 1 x 1 x2 y y y 1 xy y2 x Algebra 1: Chapter 2 Notes Answers to 2-13 a. 4 x 2y 6 b. 2x 4 c. 2x 4 y 2 d. 4 x 2y 6 Commutative Properties Are two the expressions equivalent? 5 5 1 1 7 7 3 3 1 1 335 5 7 7 Commutative Property of Addition: When adding two or more numbers together, order is not important a b b a Commutative Property of Multiplication: When multiplying two or more numbers together, order is not important a b b a Are there Commutative Properties for Subtraction and Division? Variable A symbol which represents an unknown. Examples: x m z y Combining like Terms 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. Ex: Simplify the expression below: The x2 Tile The x Tile 2 2 x+6 x + 5 + 2x x + 3x x + 4x 6x 2 8x + 7x + 11 6+2 4+3 5+6 Unit Tiles 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. 2 y x 5x 2 2 2 2 3 5 3 2 2 P E MD AS 2 5 5 3 2 2 25 5 3 2 2 50 15 2 63 Square Notation Evaluate the following: a. 5 5 5 25 2 b. 5 5 2 2 Square -5 25 25 Evaluate the following if x = -3: The opposite of 5 squared 2 2 c. x 3 3 3 9 Square -3 2 2 d. x 3 9 9 The opposite of -3 squared Legal Mat Move: Flipping + To move a tile between the positive and opposite regions, it must be placed on the opposite side. Algebra x x – 1 1 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! – 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 – 11 0 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 – y y 0 Legal Mat Move – Balancing + + ? Adding (or subtracting) like tiles to (or from) the same region of both sides of the mat is allowed. Algebra x0 1 ? 10 x – – 2-65: Recording Your Work + Left + Explntn 2x 1 3 x 3 2 3 x 2 Original 2x 1 3 x 3 2 3 x 2 Flip x 5 x 1 Remove 0’s 1 Balance 5 ? Right Right Side is Greater – – 2-75a: Solving for x + Explntn + x 1 2 2x 1 5 x 1 Original x 1 2 2x 1 5 x 1 x 2 2x 4 x 3x 2 4 x = – – Flip Remove 0’s CLT 2x 2 4 2 2 Balance 2x 6 2 2 x3 Balance x=3 Divide 2-75: Solving for x + + 1 4 x 4 1 x 2 4 Original 1 4 x 4 1 x 2 4 Flip 3 x 3 x 2 4 x 6 x 6 00 = TRUE When is 0 equal to 0? – – Explntn Infinite Solutions Remove 0’s CLT Balance 2-82 a: Solving for x + Explntn + x 1 2 2x 1 5 x 1 Original x 1 2 2x 1 5 x 1 x 2 2x 4 x 3x 2 4 x = – – Flip Remove 0’s CLT 2x 2 4 2 2 Balance 2x 6 2 2 x3 Balance x=3 Divide 2-83 : Solving for y + + = 2 y 2 y 2 y 2 y 2 y 2 y Flip Remove 0’s 2 2 Balance FALSE – Original y 2 2 y When is 2 equal to -2? – Explntn No solution Solving for x and Checking the Answer + + = – – 3x 2 8 2 2 3x 10 3 3 10 x 3 Check: 3 103 2 8 10 2 8 88 x 10 3 Explntn Original Balance Divide The left side must equal the right side. 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 x6 Months Tubes 10 7 60 ? 42 42 Tubes x6 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? x14.286 Months Tubes 10 7 ? 142.86 100 142.86 Months x14.286 Using a Diagram to solve a Proportion Question One more way to organize your work for 2-99 15 7.83 = x ÷ 1.8 x 1.8 6 0 y = 27 20 14.1 10.8 x 1.8 36