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

1

1

Area = 15

1

Area = 5

x

1

Area = x

x

x

Area = x2

y

1

Area = y

y

y

Area = y2

x

y Area = xy

Unit Tile

5 Piece

x Tile

x2

Tile

y Tile

y2

Tilexy

Tile

Algebra Tiles: Perimeter

*Make sure all tiles are positive side up

(negative [red] side down)*

1

1

45

1

12

x

1

2x + 2

x

x

4x

y

1

2y + 2

y

y

y + y + y + y

x

y 2x +2y

P =

P =

y

y

= 4y

1

5

P =

P = P =

P =

P =

1

x

x

x

1

y

y

x

1

1

chapter two

2-3: Jumbled Piles

Algebra 1: Chapter 2 Notes

What is the best description for this collection of tiles?

chapter two

2-4: Jumbled Piles

Algebra 1: Chapter 2 Notes

What is the best description for this collection of tiles?

Answers to 2-4

2

2

2

a. 4 3 7

b. 3x 3 6

c. can't be simplifed - no like terms

d. y 7 2 4 3

x x y

xy

y xy x

chapter two

2-13: Find perimeter / area

Algebra 1: Chapter 2 Notes

1 yx x1

1

x

1

y2x2

xy

y

x

yy

Answers to 2-13

a. 4x 2y 6

b. 2x 4

c. 2x 4y 2

d. 4x 2y 6

Commutative PropertiesAre two the expressions equivalent?

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

5 1 7 3

1 35 7

a b b aCommutative Property of Multiplication: When multiplying

two or more numbers together, order is not important

ab baAre there Commutative Properties for Subtraction and Division?

5173

1357

Variable

A symbol which represents an unknown.

Examples:

xy

zm

Combining like TermsTerms: 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.

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

The x TileThe x2 Tile

Unit Tiles8x2 + 7x + 11

x2 x 6x2x 5

5+66+2 4+3

Ex: Simplify the expression below:

Substitution and EvaluationSubstitution: 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.

PEMDAS

22 2 3 5 3 2

22 5 5 3 2 2 25 5 3 2 50 15 2

22 5 2y x x

63

Square NotationEvaluate the following:

a. 5 2

b. 52

Evaluate the following if x = -3:

c. x 2

d. x 2

5 5

25

52

25

25

3 2

3 3

9

3 2

9

9

Square -5

The opposite of 5 squared

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

1

x

x 1

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

11

0

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

y y

0

Legal Mat Move – Balancing

+

–

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

Algebra

1 ? 1

0 ? 0

+

–

?

x ? x

2-65: Recording Your Work

+

–

+

–

?

Left Right Explntn

2x 1 3 x 3

2 3 x 2

2x 1 3 x 3

2 3 x 2 Flip

x 5

x 1 Remove 0’s

5

1 Balance

Right Side is Greater

Original

2-75a: Solving for x

+

–

+

–

=

Explntn

x 1 2 2x 1 5 x 1

x 1 2 2x 1 5 x 1 Flip

x 2 2x 4 x Remove 0’s

3x 2 4 x CLT

x = 3

Original

2x 2 4 Balance

2

2

2x 6 Balance

2

2

x 3 Divide

2-75: Solving for x

+

–

+

–

=

Explntn

1 4 4 1 2 4x x

1 4 4 1 2 4x x Flip

3 3 2 4x x Remove 0’s

6 6x x CLT

Infinite Solutions

Original

0 0 Balance

When is 0 equal to 0?

TRUE

2-82 a: Solving for x

+

–

+

–

=

Explntn

x 1 2 2x 1 5 x 1

x 1 2 2x 1 5 x 1 Flip

x 2 2x 4 x Remove 0’s

3x 2 4 x CLT

x = 3

Original

2x 2 4 Balance

2

2

2x 6 Balance

2

2

x 3 Divide

2-83 : Solving for y

+

–

+

–

=

Explntn

2 2 2y y y 2 2 2y y y Flip

2 2y y Remove 0’s

No solution

Original

2 2 Balance

When is 2 equal to -2?

FALSE

Solving for x and Checking the Answer

+

–

+

–

=

Explntn

3 2 8x Original

Balance

2

23 10x

3 3103x

Divide

1033 2 8 10 2 8

8 8

Check:

103x

The left side must equal the right side.

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

Months Tubes

10 7

60 ? x6 x6

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?

Months Tubes

10 7

100? x14.286 x14.286

142.86

142.86 Months

Using a Diagram to solve a Proportion Question

One more way to organize your work for 2-99

0x

20

6

15

10.8

36

14.1

y

x 1.8

x 1.8÷ 1.8

= 27

7.83 =