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Published byTyler Ramos Modified over 3 years ago

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ALGEBRA TILES Expressions and Equations

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OBJECTIVES Provide a visual model to help students develop conceptual understanding for variables as unknown values. Build conceptual understanding of solving equations. Construct meaning for algebraic solutions of equations.

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The value of each piece is determined by its area. A new piece is created by developing a new dimension, x. for practical reasons, x is not a multiple of the dimension representing 1. The value of this piece is x, because 1 x = x. ALGEBRAIC EXPRESSIONS 1 x

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Use tiles to express the following: x + 2 3x3x 2 x -1 -4 x EXAMPLES

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COMBINING EXPRESSIONS 3 x – 2 x x + 4 + x – 3 2 x + 3 – x + 1 = x = 2 x + 1 = x + 4

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DISTRIBUTION 3( x + 2) - 4 (5 x - 6) -(3 x - 2) Tiles make the concepts simple. 3 x + 2 2 x - 4

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MODEL THE EXPRESSION -2(3 x -1) Begin inside the parenthesis. -6 x + 2 3 x - 1 There are two sets, and their signs are opposite of the originals.

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SOLVING EQUATIONS MODEL 2 x + 1 = 5 To solve, SUBTRACT 1 tile from each side. NEW EQUATION 2 x = 4 Isolate x by DIVIDING into two groups = x = 2

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2 x = 4 x = 2 SOLVING EQUATIONS 2 x + 3 = 7 2 x = 4 Subtract 3 from each side of the equation Divide by 2 on each side of the equation The operations and the result are exactly the same. x = 2 = -3

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SOLVE x – 4 = 5 x = 9 =

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SOLVE 2( x - 3) = 10 2 x = 16 x = 8 = 2 x - 6 = 10

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Demonstrate the behavior of numbers so students can form INNATE conceptual understandings. Reaffirm arithmetic and algebraic concepts using a visual model Reassure and encourage struggling students, allowing them to develop number sense and confidence with signed numbers ALGEBRA TILES

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