unit 1 unit 2 unit 3 unit 4 unit 5 unit 6 unit 7 unit 8 ... 5 - formatted.pdf · unit 1 unit 2 unit...
TRANSCRIPT
Unit 5 – Inequalities and Scatterplots 1
Name: ____________________ Teacher: _____________ Per: ___
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
– Unit 5 – [Inequalities and Scatterplots]
Unit 5 – Inequalities and Scatterplots 2
To be a Successful Algebra class,
TIGERs will show…
#TENACITY during our practice, have…
I attempt all practice I attempt all homework I never give up when I don’t understand
#INTEGRITY as we help others with their work, maintain a…
I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them
#GO-FOR-IT attitude, continually…
I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset
#ENCOURAGE each other to succeed as a team, and always…
I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up
#REACH-OUT and ask for help when we need it!
I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to
Unit 5 – Inequalities and Scatterplots 3
Unit Calendar
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
November 17 18 19 20 21
…
…
…
…
Scatterplots
24 25 26 27 28
Scatterplots
In Class Activity
Student Holiday
Student Holiday
Student Holiday
December 1 2 3 4 5
Graph 1 Variable
Inequalities
Solve 1 Variable
Inequalities
Graph 2 Variable Inequalities
Solve 2 Variable Inequalities
Review
8 9 10 11 12
TEST
Applications of
Inequalities
Review 6-Weeks
TEST
…
Essential Questions
Why is it necessary to write and graph inequalities in real world situations instead of always using equations?
How do I verify a solution to an inequality?
Unit 5 – Inequalities and Scatterplots 4
Critical Vocabulary
Scatterplot
Correlation
Line of Best Fit
Inequality
Less Than
Less Than or Equal to
Greater Than
Greater Than or Equal to
Unit 5 – Inequalities and Scatterplots 5
Scatterplots
Scatterplot: Data from 2 variables are plotted to reveal a possible ____________.
Positive Correlation:
Negative Correlation:
No Correlation:
When there is a correlation, the ______ of ______ ____ is the straight line that BEST models the data. It can be used to make predictions.
Examples:
What’s the correlation?
______The temperature of hot chocolate sitting on a table.
______ The number of pets a person owns and the number of books that person read last year.
______ A person's age and their height in elementary school.
Which of the following equations most
closely represents the line of best fit?
A. y = 2/3x
B. y = x + 4 C. y = 2/3x + 3
D. No correlation
Which of the following equations most
closely represents the line of best fit?
A. y = -x + 6
B. y = -3/4x + 8 C. y = -4/3x + 8
D. No correlation
Practice:
Unit 5 – Inequalities and Scatterplots 6
What’s the correlation?
______ The number of members in a family and the size of the family's grocery bill.
______ The amount of income and the years of education.
______ As temperature get colder, electric bill rises.
______ The more time I spend at the mall, the less money I have.
______ The height of the water in a swimming pool as the pool is drained for cleaning.
______ The length of a person's hair related to their shoe size.
______ The number of hours worked and the paycheck amount.
______ The temperature of a hot oven over a period of time once it is turned off.
Which of the following equations most closely represents the line of best fit?
A. y = 2/3x + 5 B. y = x + 4
C. y = 1/3x + 5 D. No correlation
A. y = x + 2 B. y = 3/4x
C. y = 2/3x + 3 D. No correlation
A. y = x + 2 B. y = 2x + 1
C. y = 1/2x + 5 D. No correlation
A. y = 1/3x + 1 B. y = x
C. y = 2/3x + 1 D. No correlation
A. y = -x + 6
B. y = -4x + 10 C. y = -x + 9
D. No correlation
A. y = -x + 6
B. y = -3/4x + 8 C. y = -4/3x + 8 D. No correlation
Unit 5 – Inequalities and Scatterplots 7
Scatterplots
Examples:
Mr. Thomas wanted to know if the amount
of class time he gave to study before a test affected their test scores. The scatter plot
below shows the results.
What kind of correlation is this?
If they study 13 minutes, what is a good prediction for the average test score?
If the average test score is a 70, what do you predict was the MOST time they spent
studying?
The New York Zoo has been keeping track of the population of a certain type of penguin
over the years.
Year Population
1970 68,000
1980 63,000
1990 59,000
2000 54,000
Based on the data, what is a good prediction for what the population was in 1960?
If the pattern continues, between what years
would we expect the population to drop below 40,000?
A. 2010 – 2020 C. 2030 – 2040
B. 2050 – 2060 D. 2070 – 2080
Unit 5 – Inequalities and Scatterplots 8
Practice:
A piano teacher wanted to see if there was
a correlation between the hours spent practicing and the number of incorrect
notes played. His results are shown below:
What kind of correlation is this?
If they practice 4.5 hours, what is a good prediction for the number of incorrect notes
played?
If there were 8 incorrect notes played, what is a good prediction of the time spent practicing?
Tuan is trying to get faster and faster at
typing, but he notices that the faster he types, the less accurate he is. The
scatterplot below shows some of his data.
What kind of correlation is this?
If Tuan types 65 words per minute, what is a good prediction of his accuracy?
If Tuan types a report with an accuracy of 75%, what is a good prediction of the
speed he was writing?
Continued…
Unit 5 – Inequalities and Scatterplots 9
The table below shows salaries for teachers in a nearby district.
Years of Teaching
Salary
1 $42,000
2 $44,000
3 $45,000
4 $47,000
Based on the data, what is a good prediction for the salary of a teacher with 6 years of experience?
If the pattern continues, about how many years would a teacher need to teach to earn
$60,000?
A. 8 - 10 years C. 16 – 20 years
B. 12 - 15 years D. 22 – 24 years
The New York Zoo has been keeping track of the population of a certain type of penguin
over the years.
Year Population
1970 68,000
1980 63,000
1990 59,000
2000 54,000
If the pattern continues, between what years
would we expect the population to drop below 30,000?
A. 2010 – 2030
B. 2030 – 2050
C. 2050 – 2070
D. 2070 – 2090
Unit 5 – Inequalities and Scatterplots 10
Below is a table of data collected of random students of how much time they watch TV and their test scores.
Graph the data onto the grid. Be sure to label and number your axis.
Time spent watching TV
(hours) Test Score
1 95
1.25 92
4 75
6 60
5.5 70
5 70
3.75 77
2 86
2.5 80
3 75
1.75 78
1. Describe your scatterplot. Where there any patterns that you observed?
2. How does the test scores change with the more time you spend watching TV?
3. Predict the test score of someone who watches 7 hours of TV.
4. Based on this data, if a student wants to score at least an 80, what is the most number of hours they
should spend watching TV?
Unit 5 – Inequalities and Scatterplots 11
Unit 5 – Inequalities and Scatterplots 12
1 Variable Inequalities: Graphing
Symbols used when graphing single variable inequalities:
<
>
≤
≥
Examples: Graph the following Inequality:
m < -5
Graph the following Inequality:
b ≥ 2
Graph the following Inequality:
-2 ≤ x < 6
Write the Inequality for this:
Write the Inequality for this:
Write the Inequality for this:
Practice: Graph the following Inequality:
v ≤ 4
Graph the following Inequality:
x < -3
Graph the following Inequality:
1 < c ≤ 8
Write the Inequality for this:
Write the Inequality for this:
Write the Inequality for this:
Graph the following Inequality: k < 0
Graph the following Inequality: j ≥ -8
Graph the following Inequality: -1 ≤ x < 7
Unit 5 – Inequalities and Scatterplots 13
Examples: Is h=-3 is a solution to the following
inequality? 3h – 4 < -15
Is x=2 is a solution to the following inequality?
6x - 5 ≥ 2x
Solve the following inequality then graph 4y – 8 > 12
Solve the following inequality then graph 16 ≥ 2x + 10
Practice: Is d=4 is a solution to the following inequality?
2d – 5 ≤ -7
Is p=-5 is a solution to the following
inequality? 3p - 5 < 2p
Solve the following inequality then graph
3g + 6 ≤ -9
Solve the following inequality then graph
22 < 5w – 8
Solve the following inequality then graph 10 ≥ 6r – 2
Solve the following inequality then graph 2x + 5 > -3
Unit 5 – Inequalities and Scatterplots 14
1 Variable Inequalities: Solving
<
>
≤
≥
Review Practice:
Find the value of x for which the inequality
3x – 4 > 2x is true.
A. 2
B. 4 C. 5
D. 0
What inequality is represented by this number
line?
A. -8 < x ≤ 4
B. -8 > x ≥ 4 C. -8 ≥ x > 4
D. -8 ≤ x < 4
Which graph represents the solution to the inequality
4x – 6 > -2
A.
B.
C.
D.
Let’s discover a rule about Solving Inequalities…
-12 < 24 Step: Add 3
T / F
-12 < 24 Step: Subtract 4
T / F
-12 < 24 Step: Multiply 2
T / F
-12 < 24 Step: Multiply -2
T / F
-12 < 24 Step: Divide 6
T / F
-12 < 24 Step: Divide -4
T / F
Rule:
Unit 5 – Inequalities and Scatterplots 15
Examples: Solve the following:
2
3x + 9 ≥ -2
Solve the following:
-2x – 6 < -10
Solve the following:
-2x + 8 > -5x + 17
Solve the following:
4x – 5 ≤ 6x + 7
Practice: Solve the following:
4
5x + 3 > 10
Solve the following:
-5x + 3 ≥ -7
Solve the following:
-3x + 8 < -6x + 20
Solve the following:
10x + 5 ≤ 15x + 30
Solve the following: 3
2x – 1 ≥ 4
Solve the following: 9x < 2x + 21
Solve the following: 7x + 2 > 4x + 8
Solve the following: 10x + 2 ≤ 12x + 6
Unit 5 – Inequalities and Scatterplots 16
Unit 5 – Inequalities and Scatterplots 17
2 Variable Inequalities: Graphing
< “Less Than”
> “Greater Than”
≤ “Less Than or Equal to”
≥ “Greater Than or Equal to”
Examples: Graph y > -3x + 1
Graph y ≤ 2/3x – 4
Graph y < -4
Graph x ≥ 5
Practice: Graph y ≥ 2x – 5
Graph y > -1/2x + 6
Graph y ≤ 7
Graph x < -3
Graph y > 2
Graph y < -x + 5
Graph x ≤ 0
Graph y ≥ 2/3x
Unit 5 – Inequalities and Scatterplots 18
Examples: Write the Inequality
for the graph below:
Write the Inequality
for the graph below:
For the graph below,
state if each ordered pair is a solution:
( -1 , 2 ) _______ ( 3 , 0 ) _______ ( -4 , -5 ) _______ ( 0 , 0 ) _______
For the inequality
below, state if each ordered pair is a
solution: 6x – 4y > -5
( -3 , -2 ) _______ ( 3 , 4 ) _______
Practice: Write the Inequality
for the graph below:
Write the Inequality
for the graph below:
For the graph below,
state if each ordered pair is a solution:
( 4 , 0 ) _______ ( -2 , 3 ) _______ ( 0 , 3 ) _______ ( -5 , 6 ) _______
For the inequality
below, state if each ordered pair is a
solution: 4x – 3y ≤ 8
( -3 , 2 ) _______ ( 1 , -2 ) _______ ( 0 , 0 ) _______
Write the Inequality
for the graph below:
Write the Inequality
for the graph below:
Unit 5 – Inequalities and Scatterplots 19
2 Variable Inequalities: Solving
< “Less Than”
> “Greater Than”
≤ “Less Than or Equal to”
≥ “Greater Than or Equal to”
Examples: Graph
3x + y < 4
Graph 3x + 2y ≥ 10
Graph -4x – 5y < 15
Graph -3 ≥ y – 7
Practice: Graph
4x + y ≥ -1
Graph 4x + 3y ≥ 9
Graph 2x – 3y < 18
Graph 3 ≥ x + 1
Unit 5 – Inequalities and Scatterplots 20
Examples: Solve
3(𝑤 + 2) ≥ 21
Solve −3(2𝑑 + 2) < −18
Solve 3(𝑥 − 3) − 5𝑥 ≥ 3
Practice:
Solve 4(𝑝 − 3) < 12
Solve −2(3𝑑 − 1) > 14
Solve 5(𝑥 − 2) − 8𝑥 ≤ 2
Unit 5 – Inequalities and Scatterplots 21
Applications of Inequalities
Examples:
1. For the inequality 0 ≤ x ≤ 50, which of the following choices would a whole number solution, x, be
reasonable?
a. The number of stars in the Milky Way
b. The number of seats in large football stadium
c. The temperature in Alaska in Co, when it is below freezing
d. The number of tickets sold for a play in a theater that has a maximum capacity of 50
2. Sarah wants to buy shirts for her school's graduation party. A company will make the shirts for $10.50
each plus a $50 setup charge. The equation below represents C, the total cost for x number of shirts
purchased.
C = 10.50x + 50
If Sarah has $1000, which inequality could she use to find the maximum number of shirts she can buy?
a. 1000 ≤ 10.50𝑥 + 50
b. 1000 ≥ 10.50𝑥 + 50
c. 1000 < 10.50𝑥 + 50
d. 1000 > 10.50𝑥 + 50
3. Water freezes at 0 degrees and boils at 100 degrees Celsius. Which inequality represents the
temperature between these two points, when the water is neither freezing nor boiling yet.
a. 0 < 𝑥 < 100
b. 0 ≤ 𝑥 ≤ 100
c. 0 > 𝑥 > 100
d. 0 ≥ 𝑥 ≤ 100
4. When you travel on an airplane you are allowed two carry on items whose combined weight cannot
exceed 100 pounds. Which inequality represents the possible weights of your two carry on items?
a. 𝑥 + 𝑦 ≥ 100
b. 𝑥 + 𝑦 ≤ 100
c. 2𝑥 + 2𝑦 ≤ 100
d. 2𝑥 + 2𝑦 ≥ 100
Unit 5 – Inequalities and Scatterplots 22
Practice:
1. Which of the following choices could not be represented by the inequality 20 ≤ x ≤ 38?
a. The temperature on a day when the low was 20o and the high was 38o
b. The total points in a basketball game when Samuel scored 20 points and Barbara scored 38
points
c. The speed Theona is driving when she accelerates from 20 mph to 38 mph
d. The height of a rose bush the month it grew from 20 cm to 38 cm
2. On a road in the city of Katy, the maximum speed is 40 kilometers per hour and the minimum speed is
15 kilometers per hour. If x represents speed, which sentence best expresses this condition?
e. 40 < 𝑥 < 15
f. 40 ≤ 𝑥 ≤ 15
g. 40 > 𝑥 > 15
h. 40 ≥ 𝑥 ≥ 15
3. You are saving up to buy a new video game system for $300. You can earn $8 an hour and have $15
saved up already. Which inequality could be used to solve for the number of hours you need to work
to afford the new system?
a. 15 + 8𝑥 > 300
b. 15 + 8𝑥 < 300
c. 15 + 8𝑥 ≥ 300
d. 15 + 8𝑥 ≤ 300
4. To compete in a piano competition, you need to perform two musical pieces whose combined duration
is no greater than 15 minutes. Which inequality represents the possible duration of your two musical
pieces?
a. 𝑥 + 𝑦 ≥ 15
b. 𝑥 + 𝑦 ≤ 15
c. 2𝑥 + 2𝑦 ≤ 15
d. 2𝑥 + 2𝑦 ≥ 15
5. A carpet cleaner charges a flat fee of $35 plus an additional fee of $12 per room to clean carpets. If
you have $140 dollars, how many rooms can you get cleaned?
a. 35 + 12𝑥 > 140
b. 35 + 12𝑥 < 140
c. 35 + 12𝑥 ≥ 140
d. 35 + 12𝑥 ≤ 140
Unit 5 – Inequalities and Scatterplots 23