ALGEBRA TILES Dawne Spangler. Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes...
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Transcript of ALGEBRA TILES Dawne Spangler. Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes...
![Page 1: ALGEBRA TILES Dawne Spangler. Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes algebraic logic simpler and easier to comprehend.](https://reader035.fdocuments.net/reader035/viewer/2022062511/55178a575503460e6e8b5750/html5/thumbnails/1.jpg)
ALGEBRA TILESDawne 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 “1”UNIT,
THEN THIS IS 11. 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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EXAMPLES5 – 2 5 + (-2)
3 3
-4 – (-3)
-1 -1
-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 EXPRESSIONSTHE 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.
1x
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Use tiles to express the following:
x + 2
3x
2x -1
EXAMPLES
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COMBINING EXPRESSIONS
3x – 2x
x + 4 + x – 3
2x + 3 – x + 1
= x
= 2x + 1
= x + 4
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MORE ALGEBRAIC EXPRESSIONS
3(x + 2) - 4
(5x - 6) -(3x - 2)
THE TILES MAKE THE CONCEPTS SIMPLE.
3x + 2
2x - 4
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Section 4
Solve one variable equations
OBJECTIVES
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SOLVING EQUATIONSMODEL 2x + 1 = 5
TO SOLVE, SUBTRACT 1 TILE FROM EACH SIDE.
NEW EQUATION 2x = 4ISOLATE x BY DIVIDING INTO TWO GROUPS
=
x = 2
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2x = 4
x = 2
SOLVING EQUATIONS
2x + 3 = 72x + 3 – 3 = 7 – 3
2x = 4 2 2
Subtract 3 from each side of the equationDivide by 2 on each side of the
equation
The operations and the result are exactly the same.
x = 2
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SOLVEx – 4 = 5
x = 9
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Solve3x + 2 = 11
3x = 9
x = 3
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Solve
2(x - 3) = 10
2x - 6 = 10
2x = 16
x = 8