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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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Algebra tiles
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
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


algebra 1

chapter two

2-3: Jumbled Piles

What is the best description for this collection of tiles?

Algebra 1: Chapter 2 Notes


algebra 1

chapter two

2-4: Jumbled Piles

What is the best description for this collection of tiles?

Algebra 1: Chapter 2 Notes



1

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 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?


Variable
Variable

A symbol which represents an unknown.

Examples:

m

x

z

y


Combining like terms
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 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
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
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
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
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
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
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
2-65: Recording Your Work

Left

Right

Explntn

Original

Flip

Remove 0’s

Balance

?

Right Side is Greater


2 75a solving for x
2-75a: Solving for x

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

Balance

Divide

x = 3


2 75 solving for x
2-75: Solving for x

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

TRUE

When is 0 equal to 0?

Infinite Solutions


2 82 a solving for x
2-82 a: Solving for x

Explntn

Original

Flip

Remove 0’s

CLT

=

Balance

Balance

Divide

x = 3


2 83 solving for y
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
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
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 question1
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
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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