Honors Algebra 1

1
Honors Algebra 1

• Mr. Wells

2
Day One September 6th

• 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)

3
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

4
Getting To Know You, Part 1

1. Find the other students who have the missing
   pieces of your graph. Every graph will have
   sections 1, 2, 3, and 4.
2. Locate a group of desks to sit in (Not
   permanent).
3. Choose a scenario for your graph from the list
   below. Make sure to discuss how the graph fits
   the scenario.
4. A Runner in a timed race
5. Temperature changing over time
6. Babysitting earnings over time
7. 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.)

5
Getting To Know You, Part 2
6
Area and Perimeter





Perimeter The distance around the edge of a
figure Area The number of square units the
figure covers
40 units
75 square units
7
Day Two September 7th

• 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)

8
Diamond Problems

• Use the pattern we discovered in the homework to
  complete the diamonds below.

15
10
ab
5
1
10
a
b
3
8
11
ab
9
Coordinate Plane

y-axis goes up and down just like the tail in the
letter
y-axis
Quadrant I
Quadrant II


x-axis
Quadrant III
Quadrant IV

10
How to Plot or Name a point

• A coordinate point describes a position on the
  Cartesian Plane. A point is always listed as
• ( x , y )

Alphabetical
The first number tells how far left (-) or right
()
The second number tells far down (-) or up ()
Example Plot (-4,3)
4 left since it is negative
3 up since it is positive
11
Day Three September 9th

• 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)

12
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.
Feet
13
1-31 Growing, Growing, Growing
Fig. 2
Fig. 3
Fig. 4
Fig. 1
Fig. 5
Fig 0 1 2 3 4 5 100
Tiles 8 15 24
Generalize Pattern/Find a Rule
14
1-31 Find a Convenient Shape
Fig. 2
Fig. 3
Fig. 4
Fig. 1
Fig. 5
Fig 0 1 2 3 4 5 100
Tiles 8 15 24
0
3
35
10200
Generalize Pattern/Find a Rule
15
1-31 Make a Convenient Shape
Fig. 2
Fig. 3
Fig. 4
Fig. 1
Fig. 5
Fig 0 1 2 3 4 5 100
Tiles 8 15 24
0
3
35
10200
Generalize Pattern/Find a Rule
16
1-32 New Tile Patern
Fig. 2
Fig. 3
Fig. 4
Fig. 1
Fig. 5
19
Fig 0 1 2 3 4 5
Tiles 11 15 19 79
3
7
24
Generalize Pattern/Find a Rule
17
Fig. 2
Fig. 3
Fig. 4
5
Fig 2 3 4
Tiles
0
1
6
1
3
5
7
9
11
13
LINEAR
How is the pattern changing?
The growth rate is consistent. From one figure
to the next, 2 tiles are always added.
OF TILES Fig 2, 1
Rule?
18
Fig. 2
Fig. 3
Fig. 4
5
Fig 2 3 4
Tiles
0
1
6
1
4
7
10
13
16
19
LINEAR
How is the pattern changing?
The growth rate is consistent. From one figure
to the next, 3 tiles are always added.
Rule?
OF TILES Fig 3, 1
19
Day 4 September 12th

• 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)

20
1-50 Bulls-Eye
Guess of Bulls-eyes 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!
21
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

22
Day 5 September 13th

• 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)

23
Day 6 September 14th

• 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)

24
Algebra Tiles

• Make sure all tiles are positive side up
  (negative red side down)

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
xy Tile
x
y Tile
y
Area xy
25
Algebra Tiles Perimeter

• Make sure all tiles are positive side up
  (negative red side down)

y
1
1
1
1
x
1
1
1
x
x
x
x
4
P
5
5
y
y
y
y
x
1
4x
P
2x 2
P
1
P
12
y
1
y
y y y y
P
P
2y 2
4y
x
x
y
2x 2y
P
26
Answers to 2-13
27
Commutative Properties

• Are two the expressions equivalent?

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 there Commutative Properties for Subtraction
and Division?
28
Variable

• A symbol which represents an unknown.
• Examples

m
x
z
y
29
Day 7 September 15th

• 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)

30
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
6x2 4x 5 2x2 3x 6
The x2 Tile
The x Tile
5
x
6
x2
x
x2
8x2 7x 11
Unit Tiles
56
62
43
31
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
32
Legal Mat Move Flipping


To move a tile between the positive and opposite
regions, it must be placed on the opposite
side. Algebra
33
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!

34
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
35
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
36
Day 8 September 16th

• 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)

37
Legal Mat Move Balancing


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


?
38
Day 9 September 19th

• 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)

39
2-65 Recording Your Work




Left
Right
Explntn
Original
Flip
Remove 0s
Balance
?
Right Side is Greater
40
2-75 Solving for x




Explntn
Original
Flip
Remove 0s
CLT

Balance
Balance
Divide
x 3
41
Day 11 September 21st

• 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 2-112
  to 2-116 (pgs 82-83)

42
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
x6
x6
60
?
42
42 Tubes
43
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
x14.286
x14.286
100
?
142.86
142.86 Months
44
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
45
Day 11 September 21st

• 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)

46
3-2 Finding Rules from Tables
A
Hard
Dark
Heptagon
D
Quadrilateral
S
Right
Decagon
47
3-2 Finding Rules from Tables
-3
3
4
3
144
60
36
48
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 x
Out (y) 2 26 -4
-22
-2.5
-10
-1
11
-8.5
3x-4
RULE
Multiply the x by 3 and then subtract 4
49
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 20 -5 7 3 x
Out (y) 24 7 12
4
6
14
46
-4
20
2x6
RULE
Multiply the x by 2 and then add 6
50
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 6 100 -8 5 0 x
Out (y) -17 11 -5
1
-7
6
-195
21
5
-2x5
RULE
Multiply the x by -2 and then add 5
51
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 0 1.5 8 0 50 -2 6 12 x
Out (y) 16 64 36
0
0
2.25
2500
4
144
x2
RULE
Multiply the x by itself (square x)
52
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 1 0 8 x
Out (y) -2 5 -19
-17
-23
-25
-4
-5
-3
-2x-3
RULE
Multiply the x by -2 and then subtract 3
53
Different Representations

• Table

Graph
Years (x) 0 1 2 3 4 5
Height (y) 17 21 25
5
9
13
4
-4
-4
4
-4
The change in height after one year
Initial Height before planting
4
y 4x5
5
RULE
54
Day 13 September 23rd

• Objective Graph data points from a pattern on
  the x-gty 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-gty 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 106-107)

55
Day 14 September 26th

• 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-gty 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)

56
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

57
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 x
Out (y) -3 -19 4
13
0
5
-1
-9
1
-2x1
RULE
Multiply the x by -2 and then add 1
58
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 6 100 -8 5 0 x
Out (y) 2.5 -4.5 -0.5
-2
0
-3.25
47
-7
-3
0.5x-3
RULE
Multiply the x by 0.5 and then subtract 3
59
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 1 0 8 x
Out (y) 6.5 17 -19
-16
-25
-28
3.5
2
5
-3x5
RULE
Multiply the x by -3 and then add 5
60
What is wrong with the Graph?
The graph needs to have numeric labels on the
axes. We can not determine a coordinate without
them.
The graph needs to have variable labels on the
axes. We can not determine a coordinate without
them.
Does the graph stop or go on forever? If it
stops, there should be closed dots, if it
continues there should be arrows.
61
Qualities of a Complete Graph
Every complete graph MUST have
y

• Graph Paper

• Axes

• Variable Labels for the Axes

5

• Scale the Axes

• Accurately Plot Points

• Accurately Plot Key Points

x
5
5

• If necessary, connect the points

• If necessary, draw arrows on the curve

5
62
Day 15 September 27th

• 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)

63
Solving for x and Checking the Answer




Explntn
Original
Balance
Divide

The left side must equal the right side.
Check
64
Day 16 September 28th

• 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)

65
Guess my Number

• Im thinking of a number that

When I I get My number is
Triple my number AND Add four Ten
Double my number AND Add Four My Number plus Seven
Double my number Add three Subtract my number AND Subtract one My Number plus Two
Double my number Subtract three Subtract my number AND Add four My Number plus Two
Two
Three
Infinite Answers
No Solutions
66
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?
Check
Express the question as an equation with a
variable.
The left side must equal the right side.
Your number is 3
Dont forget to answer the question
67
3-90 Solutions
(c)
Any Number
TRUE!
(a) 4 (b) 8 (d) 0.15
68
Day 17 September 30th

• 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)

69
Describing a Variable in Words

• John invests 30 into a government bond that
  increases in value 1.50 every year.
• 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.
• In your rule, what real-world quantity does x
  stand for?
• In your rule, what real-world quantity does y
  stand for?

x is the number of years after investing
y is the total amount of dollars in the bond
70
Tile Pattern Team Challenge

1. DRAW figures 0, 4, and 5
2. DESCRIBE Figure 100
3. DESCRIBE how the figures grow
4. 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-gt table

71
3-90 Solutions

• c 10
• x 12

• No Solution
• t 0.2

72
Day 18 October 3rd

• 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)

73
Exponential Function Web
Table
Non-Algebraic
Rule or Equation
Graph
Algebraic
Pattern
74
Tile Patterns
4 tiles
4 tiles
4 tiles
101
Figure 0
Pattern
2 tiles initially
Figure 1
100
Figure 2
Figure 3
Figure 100
Growth Triangle
Growth
4
Initial
Graph
1
y-intercept
(0,2)
Rule
75
Exponential Function Web
Table
Non-Algebraic
Rule or Equation
Graph
Algebraic
Pattern
76
Day 19 October 4rd

• Objective Develop connections between multiple
  representations of patterns and identify rules
  for these patterns using the ymxb 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)

77
Equation of a Line
Variable
The Input
Variable
The Output
Parameter
Growth
Parameter
Starting Value
Parameter Constant value
Variable The value can vary
78
Exponential Function Web
Table
Non-Algebraic
Rule or Equation
Graph
Algebraic
Pattern
79
Day 20 October 5th

• 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-gty
  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)

80
Graphing a Line without a Table
Graph y 4x 3 without making a table.
y 4x 3
1. Plot the starting value on the y-axis
2. Use the change to find at least 2 more points
3. Dont forget to connect the points
81
Graphing a Line without a Table
Graph y -3x 8 without making a table.
y -3x 8
1. Plot the starting value on the y-axis
2. Use the change to find at least 2 more points
3. Dont forget to connect the points
82
Exponential Function Web
Table
Non-Algebraic
Rule or Equation
Graph
Algebraic
Pattern
83
Day 21 October 6th

• 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)

84
Exponential Function Web
Table
Non-Algebraic
Rule or Equation
Graph
Algebraic
Pattern
85
Race Scatter Plot
86
System of Equations
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
87
Contextual Systems of Equations
88
Day 22 October 7th

• 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 ymxb 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)

89
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 Create one Graph for both
Money (y) depends on the weeks (x) it has been
saved
Solution Method 1 Create tables
Latanya
George


















Weeks
Weeks
Dollars
Dollars
Dollars
0
0
50
75
1
1
80
100
5 weeks
(5, 200) The solution is where the two curves
intersect
2
2
110
125
3
3
140
150
4
4
170
175
The answer is where the input AND the output are
identical
5
5
200
200
6
6
230
225
Weeks
7
7
260
250
Use the tables to set up a good window
90
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.
Since we want to know when the weights (y) are
equal, the right sides need to be equal too.
Both equations SHOULD give you the same answer.
7 years
(b) How much do the cat and bunny weigh at this
time?
pounds
Substitute the x from (a) into an equation
91
Day 23 October 10th

• 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)

92
Example Equal Values Method

• Solve the following system of equation
  algebraically

Both equations equal y. Set them equal to each
other.
93
Exploring an Area Model

• Arrange the tiles into one rectangle.

Area as a Product
Area as a Sum
Dimensions
94
Exploring an Area Model

• Arrange the tiles into one rectangle.

Area as a Product
Area as a Sum
Dimensions
95
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
96
Exploring an Area Model

• Arrange the tiles into one rectangle.

Dont forget parentheses
Rearrange. Put the x2 in the bottom left corner
and the units in the top right.
Area as a Product
These represent the same area. They must be
equal.
Area as a Sum
Make your own corner piece
Therefore
x 4 by
x 2
Dimensions
97
Day 24 October 11th

• 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)

98
Product v Sum
Product Sum
a (2x)(4x) 8x2
b (x3)(2x1) 2x27x3
c 2x(x5) 2x210x
d (2x1)(2x1) 4x24x1
e x(2xy) 2x2xy
f (2x5)(xy2) 2x22xy9x5y10
g 2(3x5) 6x10
h y(2xy3) y22xy3y
99
The Distributive Property
Multiply a Binomial by a Monomial

• The product of a and (bc) is given by
• a( b c ) ab ac
• Example Simplify 2x(x 9)

Every term inside the parentheses is multiplied
by a.
x
-9
Area Method
Arrow Method
2x
2x2
-18x
Do NOT forget to answer the question.
100
The Distributive Property
Multiply with the Area Model
3 terms times 2 terms

• Distribute ( x2 - x 3 )( x 5)

x2 -x 3
A 3x2 box
x 5
x3
-x2
3x
-5x
15
5x2
x3 x2 3x 5x2 5x 15
x3 4x2 2x 15
101
The Distributive Property FOIL

• Write the following as a sum
• ( 3x 2 )( 2x 7)
• Firsts
• Outers
• Inners
• Lasts
• Simplify

Multiply the
-4x
21x
6x2
-14
6x2 17x 14
This only works for a binomial multiplied by a
binomial.
102
Day 25 October 12th

• Objective Solve linear equations that involve
  multiplication. Solve quadratic equations that
  simplify to linear equations. THEN Solve
  two-variable 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)

103
The Distributive Property and Solving Equations
Solve
x
3
5
1
x
-x
-x2
-3x
x2
5x
x
x
5
104
Solutions

• 3-37

• x 9
• y 6
• x 2

• x 0
• x -3.5
• x -10/3

3-38

• y -1
• x -2.5

• x 5
• x 8

105
Solving for y in terms of x




Make sure to divide every term by 2.

Solving for will allow us to easily find the
change and starting point for a linear equation.
Change
Start
1
2
106
Solving for y in terms of x





Change
Start
-3
-4
107
Day 26 October 13th

• 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)

108
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

109
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

110
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

111
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

112
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

113
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

114
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

115
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

116
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

117
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

118
Hot Seat
CLOSE YOUR TEXTBOOK!
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.

119
Solving a Proportion

• Solve

Solve
Cancel the divide by X
Cancel the divide by 5
Cancel the divide by 3
Cancel the divide by 2
120
Day 27 October 14th

• 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)

121
Solving a Proportion

• Solve

Solve
Cross Multiplication can be used to solve a
proportion.
122
Solving a Proportion

• Solve

Solve
Multiply each numerator by the opposite
denominator.
123
Estimating the Fish Population
Team Actual Population Estimated Population Cost SCORE








124
Day 28 October 17th

• 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)

125
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
9

Too Low
Too High
31
Side One
cm
Side Two
cm
cm
Side Three
126
Day 29 October 18th

• 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)

127
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 of cans Total Earnings Check
10
2

Too High
Too Low
2.18
Bottles
bottles
Cans
cans
128
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
Equal Values Method
Solve the other equation for c too
Bottles
bottles
Cans
cans
129
Substitution Method

• Solve

We can solve an equation with one Variable
Dont forget to solve for y
Answer the question
130
6-34 Solutions

• x4, y12
• No Solution

• x3, y-1
• b-3, c-8

131
Substitution No Solution
Solve the following system of equation
algebraically
The two lines are parallel. They never intersect.
FALSE
No Solution.
132
Day 30 October 19th

• 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)
• Wells Time
• 6-56 to 6-60 (pgs 250-252)
• Conclusion
• Homework 6-50 to 6-55 (pgs 248-249) AND 6-61 to
  6-66 (pg 253)

133
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 y





134
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





135
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
Check in BOTH equations
good
The solution can be written as a coordinate point
good
136
6-46 The Hills are Alive
y
Graph
This is the ONLY point that makes both equations
true.
(8,16)
x 8 and y 16 (8,16) The club had 16
yodelers and 8 xylophones.
x
137
The Elimination Method










138
The Elimination Method





CHECKS
139
Elimination Method

• Solve the following system of equation

Add the equations to eliminate a variable
Solve the other variable
Answer the question
Check in both Equations
140
Elimination Method

• Solve the following system of equation

In order to add, there must be opposites to
eliminate.
Add the equations to eliminate a variable
Solve the other variable
Answer the question
Check in both Equations
141
Day 31 October 20th

• 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)

142
One Solution

• Solve the following system of equation
  algebraically and graphically

The lines only intersect once since there is one
solution.
Both equations equal y. Set them equal to each
other.
143
No Solution

• Solve the following system of equation
  algebraically and graphically

The two lines are parallel. They never intersect.
Add the equations to eliminate a variable
No Solution.
144
Infinite Solutions

• Solve the following system of equation
  algebraically and graphically

The two equations are equivalent. They lie on
top of each other. They intersect everywhere.
True
Infinite Solutions. Every point that satisfies
145
Day 32 October 21st

• 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)

146
Adding and Subtracting Fractions
Subtraction
Addition
Least Common Denominator (if you can find it)
Common Denominator
Subtract the Numerators
Add the Numerators
147
Elimination Method

• Solve the following system of equation

Pick a variable to eliminate
x
y
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.
148
Elimination Method

• Solve the following system of equation

Sometimes you need to multiply BOTH equations to
have opposite coefficients on the same variable
Add the equations to eliminate a variable
Solve for the other variable
Answer the question
Check in both Equations
BACK
149
Elimination Method

• Solve the following system of equation

Sometimes you need to multiply BOTH equations to
have opposite coefficients on the same variable
Add the equations to eliminate a variable
Solve for the other variable
Answer the question
Check in both Equations
BACK
150
When each Method is Most Effective
When BOTH equations have the same variable
isolated

• Equal Values
• Substitution
• Elimination

When ONE equation has a variable isolated
When BOTH equations have the both variables on
the same side