algebra tiles *make sure all tiles are positive side up (negative [red] side down)* 1 1 area = 1 5 1...
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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
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
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