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# Algebra Tiles - PowerPoint PPT Presentation

Algebra Tiles. 1. 1. x. x. x 2 Tile. Area = 1. 5. y. y. x. 1. Unit Tile. Area = x 2. Area = x. 1. x Tile. 5 Piece. Area = 5. y. 1. Area = y 2. Area = y. y 2 Tile. xy Tile. x. y Tile. *Make sure all tiles are positive side up (negative [red] side down)*. y.

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## PowerPoint Slideshow about ' Algebra Tiles' - bing

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Presentation Transcript

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

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 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?

A symbol which represents an unknown.

Examples:

m

x

z

y

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: 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

Evaluate the following:

Square -5

The opposite of 5 squared

Evaluate the following if x = -3:

Square -3

The opposite of -3 squared

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

Algebra

• 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!

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

Algebra

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

Algebra

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

Algebra

?

Left

Right

Explntn

Original

Flip

Remove 0’s

Balance

?

Right Side is Greater

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

Balance

Divide

x = 3

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

TRUE

When is 0 equal to 0?

Infinite Solutions

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

Balance

Divide

x = 3

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:

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

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

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