AlgebraTilesWorking withAlgebraTiles
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Working with Polynomials
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Tiles can be easily (and cheaply) producedusing colored card stock or 3x5 cards.While positive tiles can all be one color, ora variety of colors, negative tiles should bered. Package the tile sets in sandwichbags and create enough sets so that eachstudent in the class has his/her own set.
An "enlarged" tile set with magnets on theback can be prepared for demonstrationsat the blackboard. Magnetic strips can befound in any craft department.
This is my class set of tiles which contains:positive tiles negative tiles
18 unit tiles (yellow) 18 unit tiles8 "x" tiles (pink) 8 "x" tiles4 "x²" tiles (green) 2 "x²" tiles (all red)
Many of the commercial versions of algebra tiles are made from plastic andpossess a "projectile" quality. These homemade tiles are seldom "airborne"since they are aerodynamically deficient. ;-)
Make Your Own TilesMake Your Own Tiles
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Algebra Tile PiecesAlgebra Tile Pieces
From the previous template, you can see the relationshipbetween the sizes of the tiles.
x
x2
1
The x2 tile is a square whosesides measure x by x.
The x tile is a rectangle whose sidesmeasure x by 1. Notice that it isNOT possible to arrange the 1 tilesto create an x tile.
The red pieces are additive inverses for their counterparts.When used together, a “zero pair” is created (they cancel each other out).
+ = 0
+1 -1
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Factors of Integers:Factors of Integers:
6 x 1
1 x 6
2 x 3
3 x 2
Example 2:Represent the number 3.Arrange the pieces to form asmany rectangles as possible.
Example 1:Represent the number 6.Arrange the pieces to form as manyrectangles as possible.
3 x 1
1 x 3
An example of the factorsof prime numbers.
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(+3) – (-2) =
(-4) – (+3) =
(-2) – (+2) =
Signed Numbers: Integer SubtractionSigned Numbers: Integer Subtraction
Subtraction Rule: Change the sign of the number being subtracted and followthe rules for addition. “Adding the opposite”.
-
+
= +5
-
+
= -7
-
+
= -4
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(+3)•(+4) =
(+2)•(-3) =
Signed Numbers: Integer MultiplicationSigned Numbers: Integer Multiplication
We will be using the concept that the “multiplier” will be “counting” for us thenumber of sets we need. If the “multiplier” is positive, we know the number ofrows to draw and we will be done.
= 12
= -6
3 rows ofpositive 4’s
2 rows ofnegative 3’s
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(-3)•(+4) =
(-2)•(-3) =
Signed Numbers: Integer MultiplicationSigned Numbers: Integer Multiplication
If the “multiplier” is negative, after drawing the number of rows, we will have to“take the opposite of” (flip) the answer.
= -12
= 6
3 rows of positive4’s flipped
2 rows of negative3’s flipped
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Signed Numbers: Integer DivisionSigned Numbers: Integer Division
We will again be using the concept of “counting”. The “divisor” will tell us thenumber of rows to draw. If the divisor is positive, draw the rows and you aredone.
= +3
= -2
Divide into 2 rows
Divide into 4 rows
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Using Algebra Tiles forCompleting the SquareUsing Algebra Tiles forCompleting the Square
Algebra tiles can be used to visualize how a perfect
square trinomial can be formed. The tiles can be used
by students (or used by the teacher) as a warm-up to
this concept.
?
What is needed to create aperfect square trinomial for:
Use the algebra tiles to create asquare. What tiles will be neededto complete the square?
4
Help students see a pattern!
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Algebra Tileslet you “feel”mathematics.Algebra Tileslet you “feel”mathematics.
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