ALGEBRA TILESDawne Spangler
Demonstrate Reaffirm Reassure
ALGEBRA TILES
Using Algebra Tiles makes algebraic logic simpler and easier to
comprehend.
Section 1
Use rectangular arrays to model numerical values
Define value in terms of measurement
OBJECTIVES
MODELING A WHOLE NUMBER
The number 9 -
7 8 9 10 11
RECTANGULAR ARRAYS
The area model does not rely upon counting, but it is countable.
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?
Section 2
Introduce negative models Develop an INATE understanding of the behavior of negative numbers in addition and subtraction problems.
OBJECTIVES
HOW DO WE MODEL A NEGATIVE NUMBER?
WE CAN USE DIFFERENT COLORS…
OR WE CAN MARK PIECES WITH +/-
COMBINE THE TILES
Find the value of-2 + -1
SHOW ME ZERO
-1 +1 = 0
FIND -4 + 2
What happens to the zero pairs?
= -2
MODEL THE FOLLOWING EXPRESSIONS, USING TILES
1 + (-3)
-5 + 2
-3 + (-4)
ADDITION OF INTEGERS
= -2
= -3
= -7
SUBTRACTION OF INTEGERS
3 – 1
-4 – (-2)
= 2
= -2
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.
ADDING ZEROS
Determine the value of each set of tiles.
Use the take away model to find 2 – (-3). 2 – (-3) = 5
EXAMPLES
-2-(-3)
3-6
=1
= -3
HOW WOULD YOU MODEL 1 - 3?
METHOD 2, “ADD THE OPPOSITE” 1 +(-3)
-2
Will it always work?
EXAMPLES5 – 2 5 + (-2)
3 3
-4 – (-3)
-1 -1
-4 + (+3)
TRY THESE
3 – (-5)
3 + (+5)
-2 – 4 -2 + (-4)
1 – (4) 1 + (-4)
= 8
= -6
= -3
Section 3
Introduce variables as rectangles Create algebraic expressions Perform addition and subtraction on
algebraic expressions
OBJECTIVES
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
Use tiles to express the following:
x + 2
3x
2x -1
EXAMPLES
COMBINING EXPRESSIONS
3x – 2x
x + 4 + x – 3
2x + 3 – x + 1
= x
= 2x + 1
= x + 4
MORE ALGEBRAIC EXPRESSIONS
3(x + 2) - 4
(5x - 6) -(3x - 2)
THE TILES MAKE THE CONCEPTS SIMPLE.
3x + 2
2x - 4
Section 4
Solve one variable equations
OBJECTIVES
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
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
SOLVEx – 4 = 5
x = 9
Solve3x + 2 = 11
3x = 9
x = 3
Solve
2(x - 3) = 10
2x - 6 = 10
2x = 16
x = 8