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Algebra Tiles

1

1

x

x

x2 Tile

Area = 1

5

y

y

x

1

Unit Tile

Area = x2

Area = x

1

x Tile

5 Piece

Area = 5

y

1

Area = y2

Area = y

y2 Tile

xyTile

x

y Tile

*Make sure all tiles are positive side up (negative [red] side down)*

y

Area = xy

Algebra Tiles: Perimeter

y

1

1

1

1

x

1

1

1

x

x

x

x

P =

4

5

5

y

y

y

y

x

1

P =

4x

P =

2x + 2

1

P =

12

y

y

1

y + y + y + y

P =

P =

2y + 2

= 4y

x

x

*Make sure all tiles are positive side up (negative [red] side down)*

y

P =

2x +2y

chapter two

2-3: Jumbled Piles

What is the best description for this collection of tiles?

Algebra 1: Chapter 2 Notes

chapter two

2-4: Jumbled Piles

What is the best description for this collection of tiles?

Algebra 1: Chapter 2 Notes

1

1

1

x2

x

x

x

x

y2

y

y

y

y

xy

algebra 1

chapter two

2-13: Find perimeter / area

Algebra 1: Chapter 2 Notes

Commutative Properties

Commutative Property of Addition: When adding two or more numbers together, order is not important

Commutative Property of Multiplication: When multiplying two or more numbers together, order is not important

Are two the expressions equivalent?

Are there Commutative Properties for Subtraction and Division?

Combining like Terms

Ex: Simplify the expression below:

6x2 + 4x + 5 + 2x2 + 3x + 6

The x2 Tile

The x Tile

5

6

x

x

x2

x2

8x2 + 7x + 11

Unit Tiles

Terms: Variable expressions separated by a plus or minus sign.

Like terms: Terms with the same variable(s) raised to the same power.

Combine Like Terms: Add the numbers the liked terms are being multiplied by.

6+2

4+3

5+6

Substitution and Evaluation

Substitution: Replace each variable with its indicated value.

Evaluation: Simplify the expression with proper order of operations.

Example: Evaluate the expression below if x = 3 and y = -2.

P

E

MD

AS

Square Notation

Evaluate the following:

Square -5

The opposite of 5 squared

Evaluate the following if x = -3:

Square -3

The opposite of -3 squared

Legal Mat Move: Flipping

To move a tile between the positive and opposite regions, it must be placed on the opposite side.

Algebra

Rules for Showing Work with Mats

- In order to receive credit for a tile and mat problem…
- Copy at least the original mat and tiles
- Circle zeros, use arrows to show flipping, etc.
- It must be organized and clear. Draw a second table if necessary.
- Do NOT make a Picasso!

L.M.M. – Removing Zeros in Same Region

To remove two tiles in the same region, the tiles must be of opposite signs (one positive and the other negative).

Algebra

L.M.M. – Removing Zeros in Different Regions

To remove two tiles in different regions, the tiles must be the same sign (both positive or both negative).

Algebra

Legal Mat Move – Balancing

Adding (or subtracting) like tiles to (or from) the same region of both sides of the mat is allowed.

Algebra

?

2-65: Recording Your Work

Left

Right

Explntn

Original

Flip

Remove 0’s

Balance

?

Right Side is Greater

2-75: Solving for x

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

TRUE

When is 0 equal to 0?

Infinite Solutions

2-83 : Solving for y

Explntn

Original

Flip

Remove 0’s

Balance

=

FALSE

When is 2 equal to -2?

No solution

Solving for x and Checking the Answer

Explntn

Original

Balance

Divide

=

The left side must equal the right side.

Check:

Using a Table to solve a Proportion Question

Toby uses seven tubes of toothpaste every ten months. How many tubes would he use in 5 years?

5 years = 5x12 = 60 months

10

7

x6

x6

60

?

42

42 Tubes

Using a Table to solve a Proportion Question

Toby uses seven tubes of toothpaste every ten months. How long would it take him to use 100 tubes?

10

7

x14.286

x14.286

?

142.86

100

142.86 Months

Using a Diagram to solve a Proportion Question

One more way to organize your work for 2-99

÷ 1.8

15

x 1.8

0x

7.83 =

6

y

= 27

20

14.1

10.8

36

x 1.8

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