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ALGEBRA TILES Dawne Spangler

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Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes algebraic logic simpler and easier to comprehend.

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Section 1 Use rectangular arrays to model numerical values Define value in terms of measurement OBJECTIVES

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MODELING A WHOLE NUMBER The number 9 - 7 8 9 10 11

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RECTANGULAR ARRAYS The area model does not rely upon counting, but it is countable.

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THE VALUE OF THE PIECE IS DETERMINED BY ITS AREA. IF THIS IS 1UNIT, THEN THIS IS 1 1. THE AREA IS 1 SQUARE UNIT, SO THE VALUE OF THE PIECE IS 1. 1 1 SO, WHAT WOULD TWO LOOK LIKE?

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Section 2 Introduce negative models Develop an INATE understanding of the behavior of negative numbers in addition and subtraction problems. OBJECTIVES

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HOW DO WE MODEL A NEGATIVE NUMBER? WE CAN USE DIFFERENT COLORS… OR WE CAN MARK PIECES WITH +/-

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COMBINE THE TILES Find the value of -2 + -1

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SHOW ME ZERO -1 +1 = 0

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FIND -4 + 2 What happens to the zero pairs? = -2

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MODEL THE FOLLOWING EXPRESSIONS, USING TILES 1 + (-3) -5 + 2 -3 + (-4) ADDITION OF INTEGERS = -2 = -3 = -7

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SUBTRACTION OF INTEGERS 3 – 1 -4 – (-2) = 2 = -2

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HOW WOULD YOU MODEL 1 - 3? METHOD 1 -2 There are not enough positive tiles to take away 3. Add zero. There are still not enough. Add another. Now it is possible to subtract.

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ADDING ZEROS Determine the value of each set of tiles. Use the take away model to find 2 – (-3). 2 – (-3) = 5

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EXAMPLES -2-(-3) 3-6 =1 = -3

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HOW WOULD YOU MODEL 1 - 3? METHOD 2, ADD THE OPPOSITE 1 +(-3) -2 Will it always work?

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EXAMPLES 5 – 2 5 + (-2) 3 3 -4 – (-3) -4 + (+3)

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TRY THESE 3 – (-5)3 + (+5) -2 – 4-2 + (-4) 1 – (4)1 + (-4) = 8 = -6 = -3

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Section 3 Introduce variables as rectangles Create algebraic expressions Perform addition and subtraction on algebraic expressions OBJECTIVES

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ALGEBRAIC EXPRESSIONS THE VALUE OF EACH PIECE IS DETERMINED BY ITS AREA. A NEW PIECE IS CREATED BY ESTABLISHING A NEW DIMENSION, x. FOR PRACTICAL REASONS, x IS NOT A MULTIPLE OF THE DIMENSION REPRESENTING ONE. THE VALUE OF THIS PIECE IS x, BECAUSE 1 x = x. 1 x

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Use tiles to express the following: x + 2 3x3x 2 x -1 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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MORE ALGEBRAIC EXPRESSIONS 3( x + 2 ) - 4 (5 x - 6) - (3 x - 2) THE TILES MAKE THE CONCEPTS SIMPLE. 3 x + 2 2 x - 4

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Section 4 Solve one variable equations OBJECTIVES

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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 + 3 – 3 = 7 – 3 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

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SOLVE x – 4 = 5 x = 9

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Solve 3 x + 2 = 11 3 x = 9 x = 3

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

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