Alge-Tiles

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Alge-Tiles
For all Alge-Tile work it is essential to
remember that RED means minus And Any other
colour means plus.
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Variables
x2
x
1
-x2
-x
-1
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Example
Represent the following trinomials using
alge-tiles
1. 2x23x5
2. x2-2x-3
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Alge-Tile Uses

• Algebra tiles can be used for (among other
  things)
• Section 1. Identifying like and unlike terms
• Section 2. Adding and Subtracting Integers
• Section 3. Simplifying Expressions
• Section 4. Multiplying in algebra
• Section 5. Factorising trinomials
• Section 6. Doing linear equations

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Section 1. Like Terms
Example 1. 4x5
Can any of these be added ? Explain your answer
Example 2. 4x5x
Can any of these be added ? Explain your answer
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Section 2. Adding and Subtracting Integers
Example 1. 4-7
Example 2. 3-6
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Section 3. Adding and Subtracting Trinomials
Example 1. 2x23x5 x2-5x-1
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Section 3. Adding and Subtracting Trinomials
Example 1. 2x23x5 x2-5x-1
Answer 3x2-2x4
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Section 3. Adding and Subtracting Trinomials
Example 2. 2x23x2 - ( x2-2x1 )
-
A CONCRETE IDEA FOR CHANGING SIGNS.
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Section 3. Adding and Subtracting Trinomials
Example 2. 2x23x2 - ( x2-2x1 )
A CONCRETE IDEA FOR CHANGING SIGNS.
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Section 3. Adding and Subtracting Trinomials
Example 2. 2x23x2 - ( x2-2x1 )
Answer x25x1
A CONCRETE IDEA FOR CHANGING SIGNS.
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Practice

• Simplify the following
• 2-8-1
• -5-1-41
• x22
• x25xx2-2x
• 2x2-x1 - (2x2-2x-5)
• x2- 2x2-2x4 - (x22x3)
• 3x2-4x2 - (x22)
• x2x-2 - 2(x22x-3)
• -4x-3 - (2x2-2x-4)

• Simplify the following
• 6-7
• 3-2-4-1
• 5x22x
• 2x24x2x2-x
• 3x2-2x4x2-x-2
• x2-3x-2-x2-2x4
• 2x2-2x-1-3x2-2x-2
• x22x1- 3x2-x
• x2-x3-2x22xx2-2x-5

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Multiplying FactorisingGeneral Aim

• Whether multiplying or factorising, the general
  aim is to generate a rectangle and have no pieces
  left over.
• Also the small squares always go in the bottom
  right hand corner

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Section 4. Multiplying in algebra
Example 2. Multiply (x-1)(x-3)
Answer x2-4x3
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Practice

• Multiply the following
• x(x3)
• 2(x-5)
• 3x(x-1)
• (x4)(x3)
• (x-1)(x2)
• (x-4)(x-2)
• (3x-1)(x-3)
• (x-1)(x-1)
• (2x1)2
• (x-2)2

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Factors and Area
Section 5. Factorising Quadratic Trinomials
- a geometrical approach Review
Multiplication Again
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How it works
Show (x1)(x3) by arranging the tiles in a
rectangle.
x

3
Now Arrange them into a Rectangle Remember the
little guys go in the bottom right corner
x

1
Rearrange the tiles to show the expansion
x 2 4x
3
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Factorise x26x8
Factorise x 2 6x 8
x 2 6x
8
To factorise this expression form a rectangle
with the pieces.
x

4
x

2
( x 4 )( x 2 )
The factors are
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(x3)(x-1)
Show (x3)(x-1) by arranging the tiles in a
rectangle.
x

3
x
-
1
NOTE REDS ARE NEGATIVE
NOW COMPLETE THE RECTANGLE WITH NEGATIVE SQUARES
Rearrange the tiles to show the expansion
x2 2x - 3
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Factorise x2-4x3
Factorise x 2 - 4x 3
x - 3
x - 1
The factors are
( x - 3 )( x - 1 )
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Factorise x2-x-12
Factorise x 2 - x - 12
?
Clearly there is no way to accommodate the 12
small guys in the bottom right hand corner. What
do you do?
You add in Zero in the form of x and x. And
Keep doing it to complete the rectangle.
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Factorise x2-x-12
Factorise x 2 - x - 12
x - 4
x 3
The factors are ?
( x 3 )( x - 4 )
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Section 6. Doing linear equations
Solve 2x 2 -8

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Section 6. Doing linear equations
Solve 2x 2 -8

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Section 6. Doing linear equations
Solve 2x 2 -8



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Section 6. Doing linear equations
Solve 2x 2 -8
Solution x -5


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Section 6. Doing linear equations
Solve 4x 3 9 x

You can take away the same thing from both sides
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Section 6. Doing linear equations
Solve 4x 3 9 x

You can add the same quantity to both sides
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Section 6. Doing linear equations
Solve 4x 3 9 x

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Section 6. Doing linear equations
Solve 4x 3 9 x



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Section 6. Doing linear equations
Solve 4x 3 9 x



Solution x 4
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Practice

• Solve the following
• x4 7
• x-2 4
• 3x-1 11
• 4x-2 x-8
• 5x1 13-x
• 2(x3) x-1
• 2x-4 5x8