ALGEBRA TILES

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ALGEBRA TILES
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ALGEBRA TILES

• Rachel Magnuson

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By the end of this Show, youll be able to. . .

• Define and explain algebra tiles
• Be able to use algebra tiles to factor
• Show how algebra tiles can model polynomials
• Be able to add and subtract polynomials using
  algebra tiles

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Why Use Algebra Tiles?

• They are inexpensive and widespread
• They also make it possible to do the activities
  that are needed to introduce and explain the
  distributive law and factoring
• Provide a useful way to introduce operations on
  polynomials
• Work extremely well with all ages

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What are Algebra Tiles?

• How do they work?

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• Algebra Tiles are manipulatives with which you
  can represent polynomials and perform polynomial
  operations, such as adding subtracting,
  multiplying, and dividing.
• Each tile represents a specific monomial.
• Algebra tiles work by the concept that every
  rectangle has a length, width, and area. The
  lengths and the widths are the lengths of the
  sides of the rectangle in some unit. We will be
  working with unit x. The area is how many
  squares of that unit it takes to cover the
  rectangle.

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Nomials

• Monomial A mathematic expression consisting of
  a single term. Examples X, 2Y
• Binomial A mathematic expression consisting of
  2 terms connected by a plus or minus sign.
  Examples 2X4, 4Y-2
• Polynomial A mathematical expression of one or
  more algebraic terms of which consists of a
  constant multiplier by one or more variables
  raise to a non-negative power. Example
  3X24x5
• Trinomial A polynomial of 3 terms. Example
  2X4Y-Z

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Algebra Tiles can be key in understanding
factoring. Lets take a look at factoring.
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Key Points

• You can think of factoring as the reverse of
  First Outside Inside Last (FOIL)
• Factoring is used to break down or factor a
  quadratic or higher order equation
• You can check your factors by using FOIL to
  determine if you get the original equation back

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3 monomials well be working with

• Large Square
• X2

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• Rectangle
• X

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• Small Square
• 1

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The Basics of Algebra Tiles
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Large Squares

• These are the blocks that will be known as x2. 
  These blocks appear as blue when positive and red
  when negative

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Rectangles

• The rectangular blocks that are as long as the
  square blocks but not as tall are known as x. 
  These blocks appear as green when positive and
  red when negative.

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Small Squares

• The very small squares are constant terms.  They
  look like the blocks that you probably used in
  addition and subtraction.  They are numbers like
  5, 7 ,9, etc.  These blocks appear as yellow when
  positive and red when negative.

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Some Area Examples

• 5 4
  
• 7 9
• 7
• 7

(5 x 7) 35
(4 x 9) 36
(7 x 7) 49
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Now, lets change the numbers in the previous
rectangles to algebraic variables.

• A
• Y
• X B
• X
• 
  X

(B x A) AB
(Y x X) XY
(X x X) X2
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Algebra Tiles
Algebra Tiles are a geometric way to factor.
Each size and shape tile has a specific value.
This value is determined by the size of each side
of a rectangle or square. If you recall, the
area of a rectangle is length width, the area
of a square is side side or s2.
1
x
1
1
x
1
1
-1
-1
1
-x
-x
x2
x
-x
-x2
x
x
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Examples of tiles used to represent equations
such as the following
1 x2s 3 xs 2 1s
2 x2s 5 xs 2 1s
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In some cases, you can combine these shapes to
form perfect rectangles or squares. Here
are two examples
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Now lets try factoring these equations that are
formed into rectangles. The first two examples
will be done for you.
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Resources

• Learning about Algebra Tiles
• Examples using Algebra Tiles
• Everything you need to know
• Play with Algebra Tiles online
• Make your own Algebra Tiles