Transcript Honors Algebra 1

Honors Algebra 1
Mr. Wells
Day One: September
th
6
Objective: Discuss the syllabus and classroom
procedures. THEN Interpret points and continuous
graphs, understanding that a point conveys two
pieces of information and that a continuous graph
conveys trends.
• Introduction: Books, syllabus, homework sheet
• 1-1 to 1-2 (pgs 3 & 5, RscrcPg)
• Conclusion
Homework: Fill out information sheet, last page of syllabus,
extra credit tissues OR hand sanitizer, and 1-3 to 1-6
(pgs 6-7)
Support
• www.cpm.org
–
–
–
–
Homework help and answers
Resources (including worksheets from class)
Extra support/practice
Parent Guide
• www.hotmath.com
– Pay site
– All the problems from the book
– Homework help and answers
• My Webpage on the HHS website
– Classwork and Homework Assignments
– Worksheets
– Extra Resources
Getting To Know You, Part 1
1.
2.
3.
Find the other students who have the missing pieces
of your graph. Every graph will have sections 1, 2, 3,
and 4.
Locate a group of desks to sit in (Not permanent).
Choose a scenario for your graph from the list below.
Make sure to discuss how the graph fits the scenario.
1.
2.
3.
4.
A Runner in a timed race
Temperature changing over time
Babysitting earnings over time
Label the x- and label the x- and y-axes. (For example
you can use labels such as time, distance, height,
years, months, minutes, water level, meters, yards,
seconds, number of people, distance from the ground,
volume, etc.)
Getting To Know You, Part 2
Area and Perimeter
Perimeter: The distance around the edge of a figure
40 units
Area: The number of square units the figure covers
75 square units
Day Two: September
th
7
Objective: Practice using the Cartesian
coordinate system by labeling and
reading points. Also, begin to identify
linear patterns.
• 1-7 to 1-8 (pgs 8-9)
• Conclusion
Homework: 1-9 to 1-14 (pgs 10-11)
Diamond Problems
Use the pattern we discovered in the
homework to complete the diamonds
below.
15
5
10
3
8
1
ab
10
11
a
b
a+b
Coordinate Plane
Quadrant
y-axis
+
y-axis goes up and down
just like the tail in the letter
Quadrant
I
II
–
Quadrant
x-axis
Quadrant
III
IV
–
+
How to Plot or Name a point
A coordinate point describes a position on the
Cartesian Plane. A point is always listed as:
Alphabetical
(x,y)
The first number tells how
far left (-) or right (+)
Example: Plot (-4,3)
4 left since it
is negative
3 up since it is
positive
The second number tells far
down (-) or up (+)
Day Three: September
th
9
Objective: Introduce X-Y tables and scatter plots as tools
for organizing data and making predictions. Also the
scaling of axes of a graph and the concept of
dependent and independent measures. THEN How to
extend a tile pattern and how to generalize the
geometric description of the pattern.
•
•
•
•
•
Homework Check
1-15 to 1-19 (pgs 12-14)
Wells Time
1-31 to 1-32 (pg 18)
Conclusion
Homework: 1-21 to 1-30 (pgs 16-17) AND 1-34 to 1-39
(pgs 20-21)
Average
The number that is found by dividing the sum of
data by the number of items in the data set.
Example: Ted is 4.1 feet tall, Greg is 5.3 feet
tall, and Ally is 4.3 feet tall. Find their
average height.
4.1 5.3  4.3 = 13.7
3
3
=4.56
Feet
1-31: Growing, Growing, Growing
Fig. 1
Fig. 2
Fig #
Tiles
Fig. 3
0
1
Fig. 4
Fig. 5
2
3
4
8
15
24
Generalize Pattern/Find a Rule:
5
100
1-31: Find a Convenient Shape
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig #
0
1
2
3
4
5
100
Tiles
0
3
8
15
24
35
10200
Generalize Pattern/Find a Rule:
1-31: Make a Convenient Shape
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig #
0
1
2
3
4
5
100
Tiles
0
3
8
15
24
35
10200
Generalize Pattern/Find a Rule:
1-32: New Tile Patern
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig #
0
1
2
3
4
5
19
Tiles
3
7
11
15
19
24
79
Generalize Pattern/Find a Rule:
Fig. 2
Fig #
Tiles
Fig. 3
0
1
1
3
+2
+2
Fig. 4
2
3
4
5
7
9
+2
+2
5
11
+2
6
13
+2
LINEAR
How is the pattern changing?
The growth rate is consistent. From one figure to the next,
2 tiles are always added.
Rule?
# OF TILES = Fig # *2, +1
Fig. 2
Fig #
Tiles
Fig. 3
0
1
1
4
+3
+3
Fig. 4
2
3
4
7
10
13
How is the pattern changing?
+3
+3
+3
5
6
16 19
+3
LINEAR
The growth rate is consistent. From one figure to the next,
3 tiles are always added.
Rule?
# OF TILES = Fig # *3, +1
Day 4: September
th
12
Objective: Solve a complex problem and develop a new
problem-solving strategy called “Guess and Check.”
Students will organize their guesses into a Guess and
Check table. THEN Continue to develop our Guess
and Check organizational strategies for traditional
word-problems
•
•
•
•
•
Homework Check
1-40 to 1-43 (pgs 22-24, RscrcPg)
Wells Time
1-50 to 1-51 (pgs 26-27)
Conclusion
Homework: 1-44 to 1-49 (pgs 25-26) AND 1-54 to 1-58
(pg 29)
1-50: Bull’s-Eye
Guess:
# of Bullseyes
# of Outer-Ring
Shots
Total Points
Check: (?=160)
10
50 – 10 = 40
7(10) + 2 (40) = 150
 Too low
15
50 – 15 = 35
7(15) + 2(35) = 175
 Too high
12
50 – 12 = 38
7(12) + 2(38) = 160
 Yes, sir!
Jamie hit 12 bulls-eyes and 38 outer-ring shots!
Rules for Guess and Check
In order to receive credit for a guess and
check answer…
• There must be at least two bad guesses
•
There must be organization (I
recommend a a table)
•
The final answer must have units
Day 5: September
th
13
Objective: Continue to develop our Guess and Check
organizational strategies for traditional word-problems.
THEN Assess Chapter 1 in a team setting.
•
•
•
•
•
•
Homework Check
1-59 to 1-63 (pgs 30-31)
Wells Time
Chapter 1 Team Test
2-1 (pg 41)
Conclusion
Homework: 1-65 to 1-69 (pgs 31-32)
Day 6: September
th
14
Objective: Introduction to algebra tiles, which will start
our work with algebraic expressions and equations.
THEN Finding the perimeter of shapes while learning
the difference between the dimensions (length and
width) and area. Also, simplifying expressions by
combining like terms.
•
•
•
•
•
Homework Check
2-1 to 2-5 (pgs 41-42)
Wells Time
2-12 to 2-14, 2-16 (pgs 44-45)
Conclusion
Homework: 2-6 to2-11 (pgs 42-43) AND 2-17 to 2-21
(pgs 45-46)
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
Answers to 2-13
a. 4 x  2y  6
b. 2x  4
c. 2x  4 y  2
d. 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
Day 7: September
th
15
Objective: Introduction to algebra tiles, which will start
our work with algebraic expressions and equations.
THEN Finding the perimeter of shapes while learning
the difference between the dimensions (length and
width) and area. Also, simplifying expressions by
combining like terms.
•
•
•
•
•
Homework Check
2-22 to 2-26, 2-28 (pgs 47-48)
Wells Time
2-34 to 2-40 (pgs 51-52)
Conclusion
Homework: 2-29 to 2-33 (pgs 49-50) AND 2-41 to 2-46
(pgs 53-54)
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 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 vairable 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
2  y  x   5x  2
2
2  2  3  5  3  2
2
2  5   5  3  2
2
2  25  5  3  2
50  15  2
63
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
Day 8: September
th
16
Objective: Understanding different interpretations of
“minus”. Also, simplifying algebraic expressions while
determining whether expressions are the same or
different. THEN Simplify algebraic expressions and
determine which of two expressions is greater.
•
•
•
•
•
Homework Check
2-47 to 2-51 (pgs 55-57, RsrcPg)
Wells Time
2-57 a-d, to 2-58 (pgs 59-60)
Conclusion
Homework: 2-52 to 2-56 (pg 58) AND 2-59 to 2-63 (pgs
61-62)
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
–
–
Day 9: September
th
19
Objective: Learning how to record work while simplifying
algebraic expressions and determining which of two
expressions is greater. THEN Solving equations for x
and strengthening simplification skills.
•
•
•
•
•
Homework Check
2-64 to 2-66, 2-67 a,b,c (pgs 63-64)
Wells Time
2-73 to 2-76 (pgs 67-69)
Conclusion
Homework: 2-68 to 2-72 (pgs 66-67) AND 2-77 to 2-81
(pg 70)
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
–
–
2-75: 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
Day 11: September
st
21
Objective: Solving equations for x and determining
whether there are no solutions, one solution, or infinite
solutions. THEN Assess Chapter 2 in a team setting.
•
•
•
•
•
Homework Check
2-99 (pg 77), 2-109 (pg 81), 2-101 (pg 77)
Wells Time
Chapter 2 Team Test
Conclusion
Homework: 2-102 to 2-107 (pgs 78-79) AND
2-116 (pgs 82-83)
2-112 to
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
Day 11: September
st
21
Objective: How to identify a rule for a pattern and state
it in words. THEN Find rules for patterns and write
rules algebraically using symbolic notation.
•
•
•
•
•
Homework Check
3-1 to 3-3 (pgs 93-95)
Wells Time
3-9 to 3-12 (pgs 97 to 98)
Conclusion
Homework: 3-4 to 3-8 (pgs 95-96) AND 3-13 to 3-17 (pg
99)
3-2: Finding Rules from Tables
Hard
A
Dark
Heptagon
D
Quadrilateral
S
Right
Decagon
3-2: Finding Rules from Tables
3
-3
3
4
144
60
36
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
-6
Out
(y) -22
2
2
½
10
-2
-2.5 26 -10
1
5
-1
11
0
-1.5
x
-4 -8.5 3x-4
RULE: Multiply the x by 3 and then subtract 4
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
9
-1
0
4
0.5
Out
(y) 24
4
6
14
7
20
-5
7
46 -4
20
3
x
12 2x+6
RULE: Multiply the x by 2 and then add 6
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
2
11
-3
-½
Out
(y)
1
-17
11
6
6
100 -8
5
0
-7 -195 21
-5
5 -2x+5
RULE: Multiply the x by -2 and then add 5
x
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
-4
Out
(y) 16
0
1.5
8
0 2.25 64
0
50
-2
0 2500 4
6
12
36 144
RULE: Multiply the x by itself (square x)
x
x2
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
7
Out
(y) -17
-0.5 10
-2
11
-23 -25
-4
½
1
0
5
-4
-5
-3
8
x
-19 -2x-3
RULE: Multiply the x by -2 and then subtract 3
Different Representations
Table:
Years
(x)
Graph:
0
1
2
3
4
5
5
9
13
17
21
25
Height
(y)
-4
-4
-4
+4
+4
The change in height
after one year
Initial Height
before planting
RULE:
y=4
4x+5
5
Day 13: September
rd
23
Objective: Graph data points from a pattern on the x->y coordinate
plane. Learn how to use graphing technology to graph data
points and equations. Learn the difference between a continuous
and discrete graph. THEN Practice plotting points from an x->y
table and practice setting up appropriate axes for a data set.
•
•
•
•
•
Homework Check
3-18 to 3-22 (pgs 100-101, RsrcPg)
Wells Time
3-32 to 3-35 (pgs 105 to 106)
Conclusion
Homework: 3-23 to 3-31 (pgs 103-104) AND 3-36 to 3-40 (pgs 106107)
Day 14: September
th
26
Objective: Complete a table (including decimals), plot the
points, and draw the graph for a linear situation and
equations. THEN Given a linear or quadratic equation,
create x->y tables, scale axes, plot points, and draw
complete graphs.
•
•
•
•
•
Notebook Quiz
3-41 to 3-44 (pgs 108-109)
Wells Time
3-51 to 3-54 (pgs 112 to 113)
Conclusion
Homework: 3-45 to 3-49 (pgs 110-111) AND 3-55 to 3-59
(pg 113)
Notebook Quiz 9/26
Provide the following on a sheet of paper to
be turned in. You have 10 minutes.
•
Homework: The solutions to a-d from
2-29 assigned on September 15th
•
Classwork: The answers to 1-51 (b)
assigned on September 12th
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
-6
2
½
10
-2
1
5
0
-1.5
Out
(y) 13
-3
0
-19
5
-1
-9
1
4
RULE: Multiply the x by -2 and then add 1
x
-2x+1
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
2
Out
(y) -2
11
-3
-½
6
2.5 -4.5 -3.25 0
100 -8
5
0
x
47 -7 -0.5 -3 0.5x-3
RULE: Multiply the x by 0.5 and then subtract 3
Silent Board Game
Rules:
• Copy the table.
• In silence, study the input and output values and look for a pattern.
• Raise your hand if you know a missing cell.
• Find the rule in words and symbols.
In
(x)
7
-0.5 10
11
-4
½
Out
(y) -16 6.5 -25 -28 17 3.5
1
0
2
5
8
x
-19 -3x+5
RULE: Multiply the x by -3 and then add 5
What is wrong with the Graph?
The graph needs to have
numeric labels on the
axes. We can not
determine a coordinate
without them.
Does the graph stop or The graph needs to have
variable labels on the
go on forever? If it stops,
axes. We can not
there should be closed
determine a coordinate
dots, if it continues there
without them.
should be arrows.
Qualities of a Complete Graph
y  3x  2
y
5
5
5
5
Every complete graph MUST have:
• Graph Paper
• Axes
• Variable Labels for the Axes
• Scale the Axes
• Accurately Plot Points
x • Accurately Plot Key Points
• If necessary, connect the
points
• If necessary, draw arrows
on the curve
Day 15: September
th
27
Objective: Use graphs and rules to analyze a contextual
situation with a limited domain. Identifying common
errors in scaling and plotting points. THEN Review and
practice equation-solving skills. Also, learn how to
check answers and recognize that a solution is a value
that makes an equation true.
•
•
•
•
•
Homework Check
3-60 to 3-62 (pgs 114-116, RscrcPg)
Wells Time
3-69 to 3-72 (pgs 118 to 119)
Conclusion
Homework: 3-64 to 3-68 (pgs 116-117) AND 3-73 to 3-77
(pg 120)
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.
Day 16: September
th
28
Objective: Understanding what makes an equation have
1, infinite, or no solutions. And start to solve equations
without manipulatives. THEN Continue to practice
solving equations.
•
•
•
•
•
Homework Check
3-78 to 3-80 (pg 121, RscrcPg)
Wells Time
3-87 to 3-91 (pgs 123 to 124)
Conclusion
Homework: 3-82 to 3-86 (pgs 122-123) AND 3-92 to 3-96
(pg 125)
Guess my Number
I’m thinking of a number that…
When I…
I get…
My number is…
Ten
Two
• Double my number
AND
• Add Four
My Number plus
Seven
Three
• Double my number
• Add three
• Subtract my number
AND
• Subtract one
My Number plus
Two
Infinite
Answers
No Solutions
• Triple my number
AND
• Add four
• Double my number
• Subtract three
• Subtract my number
AND
My Number plus
Two
Using an Equation to Solve and
then Checking the Answer
When I double my number and add four, I get my number
plus seven. What is my number?
2x  4  x  7
x
x
x47
4 4
x 3
Express the
question as
an equation
with a
variable.
Your number
is 3
Check:
2  3  4  3  7
6  4  3 7
10  10
The left side must
equal the right side.
Don’t forget to answer
the question
3-90: Solutions
(c)
x  2  0.5x  1  0.5x  1
0.5x  2  0.5x  2
0.5x
0.5x
22
TRUE!
(a) 4;
(b) 8;
Any Number
(d) 0.15
Day 17: September
th
30
Objective: Continue to practice solving equations that
cannot be solved using algebra tiles. These equations
will come from real-world contexts. THEN Discover
connections between all of the representations of a
pattern: a graph, a table, a geometric presentation,
and an equation.
•
•
•
•
•
Homework Check
3-97 to 3-99 (pgs 126 to 127)
Wells Time
4-1 (pg 139)
Conclusion
Homework: 3-100 to 3-104 (pg 128) AND 4-2 to 4-7 (pgs
140-141)
Describing a Variable in Words
John invests $30 into a government bond that increases in
value $1.50 every year.
1. Assuming the bond continues to grow at a constant
rate, find a rule for the total amount of money of the
bond using x and y.
y  1.5 x  30
2.
In your rule, what real-world quantity does x stand for?
x is the number of years after investing
3.
In your rule, what real-world quantity does y stand for?
y is the total amount of dollars in the bond
Tile Pattern Team Challenge
1.
2.
3.
4.
DRAW figures 0, 4, and 5
DESCRIBE Figure 100
DESCRIBE how the figures grow
FIND the number of tiles in each figure and
record your information in a TABLE and
GRAPH.
5. Find a RULE for the number of tiles in terms of
the figure number
6. COMPARE the graph, figures, and x-> table
3-90: Solutions
a)c = 10
b)No Solution
c) x = 12
d)t = 0.2
Day 18: October
rd
3
Objective: Write linear algebraic rules relating the figure number of a
geometric pattern and its numbers of tiles. Identify connections
between the growth of a pattern and its linear equation. THEN
Discover connections between all of the representations of a
pattern: a graph, a table, a geometric presentation, and an
equation.
•
•
•
•
•
Homework Check
4-8 to 4-12 (pgs 142-144, RscrPg)
Wells Time
4-18 to 4-20 (pgs 146-147, RscrPg)
Conclusion
Homework: 4-13 to 4-17 (pg 145) AND 4-21 to 4-25 (pg 148)
Exponential Function Web
NonAlgebraic
Table
Rule or
Equation
Graph
Pattern
Algebraic
Tile Patterns
Pattern
+ 4 tiles
+ 4 tiles
+ 4 tiles
101
Figure 0
2 tiles
initially Figure 1
Figure 2
Graph
Figure 3
4
1
y-intercept
(0,2)
Growth Triangle
Figure 100
Growth
Initial
y  4x  2
Rule
Exponential Function Web
NonAlgebraic
Table
Rule or
Equation
Graph
Pattern
Algebraic
Day 19: October
rd
4
Objective: Develop connections between multiple representations of
patterns and identify rules for these patterns using the y=mx+b
form of a linear equation. THEN Apply your understanding of
growth, Figure 0, and connections between multiple
representations to generate a complete pattern.
•
•
•
•
•
Homework Check
4-26 to 4-30 (pgs 149-150)
Wells Time
4-37 (pgs 152-153)
Conclusion
Homework: 4-32 to 4-36 (pg 151) AND 4-39 to 4-48 (pgs 154-155)
Equation of a Line
Variable: The Input
y  mx  b
Variable: The Output
Parameter: Growth
Parameter: Starting Value
Parameter = Constant value
Variable = The value can vary
Exponential Function Web
NonAlgebraic
Table
Rule or
Equation
Graph
Pattern
Algebraic
Day 20: October
th
5
Objective: Assess Chapters 1, 2, and 3 in an individual
setting. THEN Apply m as growth factor and b as Figure
0 or the starting value of a pattern to create graphs
quickly without an x->y table.
•
•
•
•
•
Homework Check
Chapters 1-3 Individual Test
Wells Time
4-49 to 4-53 (pgs 156-157)
Conclusion
Homework: 4-54 to 4-58 (pg 158)
Graphing a Line without a Table
Graph y = 4x + 3 without making a table.
y = 4x + 3
4
1. Plot the starting value on the y-axis
1
4
1
4
1
4
1
2. Use the change to find at least 2 more points
3. Don’t forget to connect the points
Graphing a Line without a Table
Graph y = -3x + 8 without making a table.
y = -3x + 8
1
-3
1
1. Plot the starting value on the y-axis
-3
1
2. Use the change to find at least 2 more points
-3
1
3. Don’t forget to connect the points
-3
1
-3
1
-3
Exponential Function Web
NonAlgebraic
Table
Rule or
Equation
Graph
Pattern
Algebraic
Day 21: October
th
6
Objective: Practice moving directly from one representation
to another in the representation web. THEN Focus on
systems of equations and examine the meaning of points
of intersection.
•
•
•
•
•
Homework Check
4-59 to 4-60 (pgs 159-160)
Wells Time
4-67 to 4-69 (pgs 162-164, RscrcPg)
Conclusion
Homework: 4-62 to 4-66 (pgs 161-162) AND 4-71 to 4-75
(pgs 165-166)
Exponential Function Web
NonAlgebraic
Table
Rule or
Equation
Graph
Pattern
Algebraic
Race Scatter Plot
System of Equations
y  2 x  6
Point of Intersection
Where two curves cross. Can
be written as a coordinate
point or (x,y). This point is on
BOTH curves.
System of Equations
A collection of two or more
curves with the same
variables. For example:
y  3x  4
y  3x  4
y  2 x  6
Contextual Systems of Equations
Day 22: October
th
7
Objective: Develop an understanding of solving systems of
equations through multiple representations. Continue to
write rules and find intersections from contexts. THEN
How to solve systems of equations algebraically when
both equations are in y=mx+b form.
•
•
•
•
•
Homework Check
4-76 to 4-79 (pgs 167-168)
Wells Time
4-85 to 4-88 (pgs 169-171)
Conclusion
Homework: 4-80 to 4-84 (pgs 168-169) AND 4-90 to 4-94
(pg 172)
Buying Bicycles
Latanya and George are saving up money to buy new bicycles.
Latanya opened a savings account with $50. She is determined to
save an additional $30 a week. George started a savings account
with $75. He is able to save 25 a week. When will they have the
same amount in their savings accounts?
Solution Method 2:
Weeks Dollars
0
50
Weeks Dollars
0
75
1
100
1
80
2
110
2
125
3
140
3
150
4
170
4
175
5
200
5
200
6
230
6
225
7
260
7
250
Money (y)
depends on the
weeks (x) it has
been saved
5 weeks
The answer is
where the input
AND the output
are identical
Create one Graph for both
Dollars
Solution Method 1: Create tables
Latanya
George
(5, 200)
The solution is where
the two curves intersect
Weeks
Use the tables to set up a good window
Chubby Bunny
Barbara has a bunny that weighs 5 lbs and gains 3 lbs per
year. Her cat weighs 19 lbs and 1 lbs per year.
(a) When will the bunny and cat weigh the same amount?
Write rules where x represents the number of years and y represents the weight of the animal.
3x  5y  x  19
y  3x  5

x
x
3
x

5
3x  5
2x  5  19
Since we want
to know when
the weights (y)
are equal, the
right sides need
to be equal too.
7 years
5 5
2x  14
2 2
x7
(b) How much do the cat and bunny weigh at this
Substitute the x from (a) into an equation:
Both
equations
SHOULD
give you
the same
time? answer.
y3
19
y
7 75  26 pounds
Day 23: October
th
10
Objective: Identify dimensions of rectangles formed
with algebra tiles and will identify factors of
quadratics. Also write the area as a sum and a
product while learning not all expressions are
factorable. THEN Assess Chapter 4 in a team setting.
•
•
•
•
•
Homework Check
5-1 to 5-3 (pg 191)
Wells Time
Chapter 4 Team Test
Conclusion
Homework: 4-96 to 4-106 (pgs 176-178) AND 5-4 to 5-9
(pg 192)
Example: Equal Values Method
Solve the following system of equation algebraically:
Both equations equal
y. Set them equal to
each other.
y  2x  22
y  3x  28
2x  22  3x  28
22  5x  28
50  5x
10  x
y  3 10  28
y  30  28
y2
10, 2
Exploring an Area Model
Arrange the tiles into one rectangle.
Area as a Product:
Area as a Sum:
Dimensions:
Exploring an Area Model
Arrange the tiles into one rectangle.
Area as a Product:
Area as a Sum:
Dimensions:
Exploring an Area Model
Arrange the tiles into one rectangle.
Rearrange. Put the x2 in the
bottom left corner and the units in
the top right.
Area as a Product:
Area as a Sum:
Dimensions:
Exploring an Area Model
Make your own corner piece
Arrange the tiles into one rectangle.
Rearrange. Put the x2 in the
bottom left corner and the units in
the top right.
Dimensions:
These
represent the
same area.
They must be
equal.
Don’t forget
parentheses
Area as a Product:
 xx44 xx22
Area as a Sum:
x  6x  8
2
Therefore:
 x  4 x  2  x
x + 4 by x + 2
2
 6x  8
Day 24: October
th
11
Objective: Multiply expressions using algebra tiles.
Identify, use, and describe the distributive property.
THEN Assess Chapter 4 in a team setting.
•
•
•
•
•
Homework Check
5-10 to 5-14 (pgs 193-194)
Wells Time
5-21 to 5-26 (pgs 196-198)
Conclusion
Homework: 5-15 to 5-20 (pgs 194-195) AND 5-27 to 5-32
(pg 199)
Product v Sum
Product
Sum
a
(2x)(4x)
8x2
b
(x+3)(2x+1)
2x2+7x+3
c
2x(x+5)
2x2+10x
d
(2x+1)(2x+1)
4x2+4x+1
e
x(2x+y)
2x2+xy
f
(2x+5)(x+y+2)
2x2+2xy+9x+5y+10
g
2(3x+5)
6x+10
h
y(2x+y+3)
y2+2xy+3y
The Distributive Property:
Multiply a Binomial by a Monomial
The product of a and (b+c) is given by:
a( b + c ) = ab + ac
Every term inside the parentheses is multiplied by a.
Example: Simplify 2x(x – 9)
Area Method:
x
-9
2
2x 2x -18x
“Arrow” Method:
2 x  x  9  2x 18x
2
2 x  18 x
2
Do NOT forget to answer
the question.
The Distributive Property:
Multiply with the Area Model
2
3 terms times 2 terms
Distribute: ( x - x + 3 )( x + 5)
x2
-x
+3
x
x3
-x2
+3x
+5
+5x2
-5x
+15
A 3x2 box:
x3 – x2 + 3x + 5x2 – 5x + 15 = x3 + 4x2 – 2x + 15
The Distributive Property:
FOIL
Write the following as a sum:
Multiply the…
•
•
•
•
•
( 3x – 2 )( 2x + 7)
Firsts
Outers 6x2 + 21x + -4x + -14
Inners
Lasts
= 6x2 + 17x – 14
Simplify
This only works for a binomial multiplied by a binomial.
Day 25: October
th
12
Objective: Solve linear equations that involve
multiplication. Solve quadratic equations that
simplify to linear equations. THEN Solve twovariable linear equations for one variable.
•
•
•
•
•
Homework Check
5-33 to 5-36, 5-37 (a,b,d), 3-38 (pgs 200-201)
Wells Time
5-45 to 5-48 (pgs 203-204)
Conclusion
Homework: 5-39 to 5-44 (pg 202) AND 5-49 to 5-54
(pgs 205-206)
The Distributive Property and Solving
Equations
Solve: 5  x  x  3    x  5 x  1
-x
x
2
-x
+3
-3x
+1
x
5
x
x2
5x
x
+5
5  x  3x    x  6 x  5
2
2
5  x  3x   x  6 x  5
5  3x  6x  5
5  3x  5
3x  10
x  10 3
2
2
Solutions
3-37
a) x = 9
c) y = 6
e) x = 2
b) x = 0
d) x = -3.5
f) x = -10/3
3-38
a) y = -1
c) x = -2.5
b) x = 5
d) x = 8
Solving for y in terms of x
+
+
x  2 y  3x  4
x
x
2 y  2x  4
Make sure
to divide
2 2 2
every term
by 2.
=
y  x2
Solving for will allow us to
easily find the change and
starting point for a linear
equation.
–
–
Change: 1
Start: 2
Solving for y in terms of x
+
x   y  2  2  2 x  1
+
x  y  2  2  2 x  1
x  y  2  4x  2
x
x
 y  2  3x  2
2
2
  y  3x  4   1
=

–
–

Change: -3
y  3x  4
Start: -4
Day 26: October
th
13
Objective: Solve single- and multi-variable linear
equations. THEN Through the use of a table, learn
how to write and solve a proportional equation
based on a proportional relationship.
•
•
•
•
•
Homework Check
5-55 (pgs 207)
Wells Time
5-63 to 5-66 (pgs 209-210)
Conclusion
Homework: 5-57 to 5-62 (pg 208) AND 5-67 to 5-71
(pgs 211-212)
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
• One chair/desk per team is set up in the front of the
room.
• Using Numbered Heads, Person #1 from each team
comes to the front of the room and sits.
• Teacher gives everyone a problem to work on in a
specified amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for
correct individual answers and 1 point for correct
team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x : 5  4x  3  75
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for y : x  2 y  4
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x :  6  6  3x  8
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for y : 3x  6 y  24
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x : 2  3 2 x  1  17
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for y : 5  2  x  y   11
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x : y  3x  4
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x : x  2x 1  2x  5x 12
2
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for w : 2  v  3  1   w  4
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
CLOSE YOUR
TEXTBOOK!
Hot Seat
In the Hot Seat?
Bring something
to write on.
Solve for x : 4x  x  1   2x  3 2 x  5
• One chair/desk per team is set up in the front of the room.
• Using Numbered Heads, Person #1 from each team comes
to the front of the room and sits.
• Teacher gives everyone a problem to work on in a specified
amount of time.
• Teams can talk, but not the individuals in front.
• Check individual and team answers; two points for correct
individual answers and 1 point for correct team answers.
• Person #2 from each team is up next and repeat.
Solving a Proportion
Solve:
3
2
5
15
Cancel 2
the
divide
by 2
2

x 3
5
5
Solve:
Cancel
the
divide
by 5
 x3
2
15  2  x  3
15  2x  6
9  2x
4.5  x
7
3

4
x
x x
Cancel
the
divide
by 3
7x
3
4
3 3
7 x  12
12
x 7
Cancel
the
divide
by X
Day 27: October
th
14
Objective: Practice setting up and solving proportions
involving quantities taken from a variety of contexts.
THEN Apply proportional understanding to solve an
application problem.
•
•
•
•
•
Homework Check
5-72 to 5-76 (pgs 212-214)
Wells Time
5-83 to 5-84 (pgs 216-217)
Conclusion
Homework: 5-77 to 5-82 (pgs 214-215) AND 5-85 to
5-89 (pgs 218-219)
Solving a Proportion
Solve:
3
2
5
15
2
2

x 3
5
5
 x3
2
Solve:
Cross
Multiplication
can be used to
solve a
proportion.
15  2  x  3
15  2x  6
9  2x
4.5  x
7
3

4
x
x x
7x
3
4
3 3
7 x  12
12
x 7
Solving a Proportion
Solve:
x 4
12

7
3
3  x  4  84
3x 12  84
12 12
3x  96
3
3
x  32
Solve:
100
30

4
3x
300x  120
300
300
x  0.4
Multiply each numerator
by the opposite
denominator.
Estimating the Fish Population
Team
Actual
Estimated
Population Population
Cost
SCORE
Day 28: October
th
17
Objective: Learn how to write and interpret
mathematical sentences and begin to write
equations from word problems. THEN Continue to
learn how to define variables and how to write and
solve equations to solve word problems.
•
•
•
•
•
Homework Check
6-1 to 6-5, 6-7 (pgs 231-234)
Wells Time
6-13 to 6-15 (pgs 236-237)
Conclusion
Homework: 6-8 to 6-12 (pgs 234-235) AND 6-16 to
6-21 (pg 238)
Guess and Check to Algebraic
The perimeter of a triangle is 31 cm. Sides #1 and #2 have
equal length, while Side #3 is one centimeter shorter
than twice the length of side #1. How long is each side?
Length of Side
#1
Length of Side
#2
Length of Side
#3
Perimeter of
Triangle
Check
5
2  5 1  9 5  5  9  19 Too Low
2  9 1  17 9  9 17  35 Too High
9
31
x
x
2  x  1 x  x  2 x 1
x  x  2x 1  31
Side One: 8 cm
4x 1  31
1 1
Side Two: 8 cm
 4x  32   3 Side Three: 2 8 1 15cm
x 8
5
9
Day 29: October
th
18
Objective: Learn how to write equations from word
problems. Also, compare writing a single equation
with one variable to writing a system of equations with
two variables. THEN Understand how to use AND the
benefits of using substitution to solve systems of linear
equations.
•
•
•
•
•
Homework Check
6-22 to 6-25 (pgs 239-240)
Wells Time
6-32 to 6-36 (pgs 242-243)
Conclusion
Homework: 6-26 to 6-31 (pgs 240-241) AND 6-37 to 6-42
(pgs 243-244)
Guess and Check to Algebraic
Elise took all of her cans and bottles from home to the recycling plant. The
number of cans was one more than four times the number of bottles. She
earned 10¢ for each can and 12¢ for each bottle, and ended up earning
$2.18 in all. How many cans and bottles did she recycle?
Guess # of bottles
10
2
# of cans
Total Earnings
4 10 1  41 10  0.12  41 0.1  $5.30
4  2 1  9
2  0.12  9  0.1  $1.14
Check
Too High
Too Low
$2.18
0.12  x  0.1 4 x  1
x
4  x 1
0.12  x  0.1 4x  1  2.18
0.12x  0.4x  0.1  2.18 Bottles: 4 bottles
0.52x  0.1  2.18 Cans: 4  4   1 17 cans
0.1
0.1
0.52x  2.08   0.52
x4
Writing a system of Equations
Elise took all of her cans and bottles from home to the recycling plant. The
number of cans was one more than four times the number of bottles. She
earned 10¢ for each can and 12¢ for each bottle, and ended up earning
$2.18 in all. How many cans and bottles did she recycle?
b: Number of bottles Elise took to the recycling plant
c: Number of cans Elise took to the recycling plant
c

4
b

1
Equal Values
Solve the other
Method
equation for c too 0.12b  0.1c  2.18
0.12b  0.1c  2.18
21.8 1.2b  4b 1
0.12b
0.12b
0.1c  2.18  .12b  0.1
c  21.8 1.2b
4 bottles
4  4   1 17 cans
Bottles:
Cans:
1.2b 1.2b
21.8  5.2b 1
1
1
 20.8  5.2b  5.2
4b
Solve:
We can solve
an equation
with one
Variable:
Substitution Method
y y  xy 7
y

x

7
y
5 x  
7 x3 7 x  13
5   x  7   3x  13
5x  35  3x  13
2x  35  13
35
35
2x  22  2
x  11
Don’t forget to
solve for y:
y    11  7
4
Answer the
question:
x  11
y4
6-34: Solutions
a)x=4, y=12
b)x=3, y=-1
c) No Solution d)b=-3, c=-8
Substitution: No Solution
Solve the following system of equation algebraically:
2 x  2 y  18
x  3 y
2  3  y   2 y  18
6  2 y  2 y  18
6  18
FALSE
No Solution.
The two lines are
parallel. They
never intersect.
Day 30: October
th
19
Objective: Examine how a solution to a
system of equations relates to those
equations and to a graph of those
equations. THEN Develop the
Elimination Method for solving systems
of equations.
• Homework Check
• 6-43 to 6-48 (pgs 245-247)
6-44: The Hills are Alive
Focus: The conductor charges $2 for each yodeler and $1
for each xylophone. It costs $40 for the entire club, with
instruments, to ride the gondola.
x: Number of xylophones from the club to ride the gondola
y: Number of yodelers from the club to ride the gondola
x
x  2 y  40
y
6-45: The Hills are Alive
Focus: The number of yodelers is twice the number of
xylophones.
x: Number of xylophones from the club to ride the gondola
y: Number of yodelers from the club to ride the gondola
x
y  2x
y
6-45: The Hills are Alive
A gondola conductor charges $2 for each yodeler and $1 for each xylophone.
It costs $40 for an entire club, with instruments, to ride the gondola. Two
yodelers can share a xylophone, so the number of yodelers on the gondola
is twice the number of xylophones. How many yodelers and how many
xylophones are on the gondola?
x: Number of xylophones from the club to ride the gondola
y: Number of yodelers from the club to ride the gondola
x  2  2x   40
x  4x  40
5x  40
5
5
x 8
x  2 y  40
y  2x
2x
y  2 8  16
8,16
The solution can be written as a
coordinate point
Check in BOTH
equations
8  2 16  40
40  40
good
16  2 8
16  16
good
6-46: The Hills are Alive
y
(8,16)
Graph:
This is the ONLY
point that makes
both equations
true.
x  2 y  40
y  2x
x = 8 and y = 16
y  2x
(8,16)
x  2 y  40
x
The club had 16
yodelers and 8
xylophones.
The Elimination Method
2 x  3 y  2
+
+
5 x  3 y  16
+
=
–
+
=
–
–
–
The Elimination Method
+
+
2 x  3 y  2
 5 x  3 y  16
7 x  14
7
x2
2  2  3 y  2
4  3 y  2
=
4
4
3 y  6
3
–
CHECKS:
3  2  2  2  2
7
–
3 2  5  2  16
3
y  2
 2, 2
Elimination Method
Solve the following system of equation:
2 x  y  2
2 x  3 y  10
Add the equations to
eliminate a variable:
2 x  y  2
2 x  3 y  10
 _____________
2y  8
2
2
y4
Check in both Equations:
2 1  4  2
Solve the other
variable:
2x 44  42
2x  2
2 2
x 1
1, 4
Answer the
question:
2 1  3  4  12
Elimination Method
Solve the following system of equation:
3x  4 y  1
 2 x  4 y  2   1
In order to add, there must
be opposites to eliminate.
Add the equations to
eliminate a variable:
3x  4 y  1
2 x  4 y  2
 _____________
x  1
 1,1
Solve the other
variable:
3 1  4 y  1
3  4 y  1
3
Answer the
question:
Check in both Equations:
3  1  4 1  1
3
4y  4
4
4
y 1
2  1  4 1  2
Day 31: October
th
20
Objective: Assess Chapters 4-5 in an individual setting.
THEN Study more complex applications of the
Elimination Method. Learn that multiplying both sides
of an equation by a number creates an equivalent
equation. Also, there are different approaches to
setting up elimination that yield the same result.
•
•
•
•
•
Homework Check
Chapters 4-5 Individual Test
Wells Time
6-67 to 6-70 (pgs 254-255)
Conclusion
Homework: 6-71 to 6-76 (pg 256)
One Solution
Solve the following system of equation algebraically and
graphically:
Both equations equal
y. Set them equal to
each other.
2x  22  3x  28
22  5x  28
50  5x
10  x
y  2x  22
y  3x  28
10, 2
y  3 10  28  30  28  2
The lines only intersect
once since there is one
solution.
No Solution
Solve the following system of equation algebraically and
graphically:
Add the equations to
eliminate a variable:
2 x  2 y  18
2 x  2 y  6
2 x  2 y  18
2 x  2 y  6
 _____________
0  12
No Solution.
The two lines are
parallel. They
never intersect.
Infinite Solutions
Solve the following system of equation algebraically and
graphically:
The two equations are
y  2 x  5
2 y  4 x  10
2  2 x  5  4 x  10
4x  10  4x  10
10  10
True
Infinite Solutions.
Every point that satisfies:
y  2 x  5
equivalent. They lie on
top of each other. They
intersect everywhere.
Day 32: October
st
21
Objective: Review each strategy for solving systems of
linear equations and choose the best strategy. Also,
all methods will produce the same results but some
are more efficient.
•
•
•
•
•
Homework Check
6-77 to 6-78 (pg 257)
Group Hot Potato
So Many Tools Worksheet
Conclusion
Homework: Finish Worksheet AND 6-81 to 6-86 (pg 259)
Adding and Subtracting Fractions
Subtraction:
Addition:
2
3
2
3

1
5
  
5
5
10
15
1
5

13
15
3
15
3
3
Common
Denominator
Add the
Numerators
7
4
7
4

3
10
  
5
5
35
20

29
20
Least
Common
Denominator
(if you can
find it)
3 2
10 2
6
20 Subtract the
Numerators
Elimination Method
Solve the following system of equation:
Pick a variable to eliminate:
x
y
4 x  3 y  10
9x  4 y  1
The Elimination Method is similar to
adding/subtracting fractions, except that you
want opposites. The goal is to multiply
equations, if needed, so the coefficients (the
number before a variable) for one of the
variables is opposite of the other.
Elimination Method
Solve the following system of equation:
Sometimes you need
to multiply BOTH
equations to have
opposite coefficients
on the same variable
 4 x  3 y  10   9
 9 x  4 y  1  4
4
x

3
2

10


36 x  27 y  90
4x  6  10
6
6
36 x  16 y  4
 ______________
4x  4
43 y  86
4 4
43
43
x

1
1, 2 

y2
Add the equations to
eliminate a variable
Solve for
the other
variable
Check in both Equations:
4 1  3  2  10 9 1  4  2  2
Answer the
question
BACK
Elimination Method
Solve the following system of equation:
Sometimes you need
to multiply BOTH
equations to have
opposite coefficients
on the same variable
 4 x  3 y  10   4
9 x  4 y  1  3
4
1

3
y

10


16 x  12 y  40
4  3 y  10
4
4
27 x  12 y  3
 ______________
3y  6
43x  43
3 3
43
43
y2
1,
2


x 1
Add the equations to
eliminate a variable
Solve for
the other
variable
Check in both Equations:
4 1  3  2  10 9 1  4  2  2
Answer the
question
BACK
When each Method is Most Effective
Equal Values:
y  53 x  2
y  10x  1
When BOTH equations
have the same variable
isolated
x  0.5 y  4
Substitution:
8 x  3 y  31
4 x  5 y  11
Elimination:
6 x  2 y  10
When ONE equation has
a variable isolated
When BOTH equations
have the both variables
on the same side