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

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Presentation on theme: "ALGEBRA TILES Dawne Spangler. Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes algebraic logic simpler and easier to comprehend."— Presentation transcript:

1 ALGEBRA TILES Dawne Spangler

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

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

4 MODELING A WHOLE NUMBER The number

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

6 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 SO, WHAT WOULD TWO LOOK LIKE?

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

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

9 COMBINE THE TILES Find the value of

10 SHOW ME ZERO = 0

11 FIND What happens to the zero pairs? = -2

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

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

14 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.

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

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

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

18 EXAMPLES 5 – (-2) – (-3) -4 + (+3)

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

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

21 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

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

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

24 MORE ALGEBRAIC EXPRESSIONS 3( x + 2 ) - 4 (5 x - 6) - (3 x - 2) THE TILES MAKE THE CONCEPTS SIMPLE. 3 x x - 4

25 Section 4 Solve one variable equations OBJECTIVES

26 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

27 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

28 SOLVE x – 4 = 5 x = 9

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

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


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