Transcript Chapter 2 Power Point Notes

Algebra Tiles
*Make sure all tiles are positive side up (negative [red] side down)*
1
1
x
Area = 1
x
x2
Tile
5
Unit
Tile
y
1
x
Area = x
Area = x2
1
5 Area = 5
Piece
x
x
Tile
xy
Tile
y
y
1
y
Area = y
Area = y2
y
Tile
Area = xy
y2
Tile
*Make sure all tiles are
positive side up
(negative [red] side
down)*
Algebra Tiles: Perimeter
1
1
1
1
y
1
x
1
1
x
P=4
5
x x
x
5
y
y
x
1
P = 4x
P = 2x + 2
1
P = 12
y y
y
y
1
P = 2y + 2
P=y+y+y+y
= 4y
x
x
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
Answers to 2-4
a. 4 x  3 x  y  7
2
b. 3x  3 xy  6
2
c. can't be simplifed - no like terms
d. y  7 y  2 xy  4 x  3
2
chapter two
2-13: Find perimeter / area
1
y
x
x
1
x
1
x2
y
y
y
1
xy
y2
x
Algebra 1: Chapter 2 Notes
Answers to 2-13
a.
b.
c.
d.
4 x  2y  6
2x  4
2x  4 y  2
4 x  2y  6

Commutative Properties
Are two the expressions equivalent?
5 5
1
1 7
7 3 3
1
1 335
5 7 7
Commutative Property of Addition: When adding two or
more numbers together, order is not important
a b  b  a

Commutative Property of Multiplication: When multiplying
two or more numbers together, order is not important
a b  b a
Are there Commutative Properties for Subtraction and Division?
Variable
A symbol which represents an unknown.
Examples:
x
m
z
y
Combining like Terms
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.
Ex: Simplify the expression below:
The x2 Tile
The x Tile
2
2
x+6
x + 5 + 2x
x + 3x
x + 4x
6x
2
8x + 7x + 11
6+2
4+3
5+6
Unit Tiles
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.
2  y  x   5x  2
2
2  2  3  5  3  2
2
P
E
MD
AS
2  5   5  3  2
2  25  5  3  2
2
50  15  2
63
Square Notation
Evaluate the following:
a.
5  5 5 25
2
b.  5  5
2
2
Square -5
  25  25
Evaluate the following if x = -3:
The opposite of 5 squared


2
2
c. x  3  3 3  9 Square -3


2
2
d.  x   3  9  9 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
x  x
–
 1  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
–
11
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
x0
1 ? 10 x
–
–
2-65: Recording Your Work
+
Left
+
Explntn
2x 1 3  x  3 2  3  x  2
Original
2x 1  3  x  3
2 3 x 2
Flip
x  
5
x 1
Remove 0’s
1
Balance

5 

?
Right




Right Side is
Greater
–
–
2-75a: Solving for x
+
Explntn
+
x 1 2  2x 1  5  x 1 Original
x 1  2  2x 1  5  x 1
x  2  2x  4  x

3x  2  4  x

=



 
–
–

 

Flip
Remove 0’s
CLT
2x  2  4
2 2
Balance
2x  6
2 2
x3
Balance
x=3
Divide
2-75: Solving for x
+
+
1  4  x   4 1  x  2   4
Original
1 4  x  4 1  x  2  4
Flip
3  x  3  x  2  4
x  6  x  6
00
=
TRUE
When is 0
equal to 0?
–
–
Explntn
Infinite
Solutions
Remove 0’s
CLT
Balance
2-82 a: Solving for x
+
Explntn
+
x 1 2  2x 1  5  x 1 Original
x 1  2  2x 1  5  x 1
x  2  2x  4  x

3x  2  4  x

=



 
–
–

 

Flip
Remove 0’s
CLT
2x  2  4
2 2
Balance
2x  6
2 2
x3
Balance
x=3
Divide
2-83 : Solving for y
+
+
=
2 y   2  y   2    y 
2 y  2  y  2  y
Flip
Remove 0’s
2  2
Balance
FALSE
–
Original
y  2  2  y
When is 2
equal to -2?
–
Explntn
No solution
Solving for x and Checking the
Answer
+
+
=
 
–
–
3x  2  8
2 2
3x  10
3 3
10
x 3
Check:
3  103   2  8
10  2  8
88
x
10
3
Explntn
Original
Balance
Divide
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
x6
Months
Tubes
10
7
60
?
42
42 Tubes
x6
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?
x14.286
Months
Tubes
10
7
?
142.86
100
142.86 Months
x14.286
Using a Diagram to solve a Proportion
Question
One more way to organize your work for 2-99
15
7.83 = x
÷ 1.8
x 1.8
6
0
y = 27
20
14.1
10.8
x 1.8
36