patterns, patterns, patterns… · 11/18/2013 · remembrance of her achievement. she will add...

Chapter 2 Assignments • 15

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Lesson 2.1 Assignment

Name ________________________________________________________ Date _________________________

Patterns, Patterns, Patterns…Developing Sequences of Numbers from Diagrams and Contexts

1. Amanda is training to run a marathon. She must follow a strict schedule to make sure she is ready

for the race. She will start her training by running two miles the first week. She wants to run one

fewer mile the next week, then run three more miles the week after that. She will continue this

pattern during her entire training regimen.

a. Write a sequence for the number of miles that Amanda will be running the first 10 weeks of her

training. Explain your reasoning.

b. In which week of training will Amanda run seven miles?

c. Amanda needs to run 26 miles in the final week of her training. In which week will Amanda

reach her goal? Explain your answer.

d. Amanda considered changing her regimen by running 2 miles the first week and then running

an additional 2 miles each subsequent week. Write a sequence for the number of miles that

Amanda would be running the first 10 weeks of her training if she follows the new regimen.

Explain your reasoning.

16 • Chapter 2 Assignments

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Lesson 2.1 Assignment page 2

e. In which week would Amanda reach her goal of 26 miles, if she follows the new regimen?


f. Amanda chooses to continue with the first training regimen. Because it will take a long time

to train, Amanda decides that during her periods of rest, she will sew a quilt to have as a

remembrance of her achievement. She will add squares to the quilt every two weeks using the

pattern shown (added squares are shaded).

Weeks1 and 2

Weeks3 and 4

Weeks5 and 6

Write a sequence for the first 10 terms generated by this situation. Each term should

represent the number of squares that the quilt will have. The first term has 1 square.



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Name ________________________________________________________ Date _________________________

g. By the end of her training regimen, how many squares will the quilt described in part (f) have?



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Every Graph Tells a StoryDescribing Characteristics of Graphs

1. Grant is recording the hourly temperatures of Grove City for a science project. He starts at 8:00 am

and records the temperature each hour for 24 hours. The graph represents the temperature of the

city x hours after 8:00 am.

x42

10

20

30

40

50

60

70

80

6 8 10 12 14 16 18 20 22

y

90

Tem

pera

ture

(°F

)

Time (h)

a. Is this graph discrete or continuous? Is the graph increasing, decreasing, or both increasing

and decreasing? Is the graph linear or nonlinear? Explain.

b. What was the temperature of Grove City at 8:00 am? What was the temperature of Grove City

at noon?


Name ________________________________________________________ Date _________________________


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c. Did the temperature change at a constant rate from 8:00 am to noon? Describe the change in

terms of the graph.

d. What was the rate of change of the temperature between 8:00 am and noon?

e. How much did the temperature change from noon to 2:00 pm? What was the rate of

temperature change from noon to 2:00 pm?

f. What is the shape of the graph during the time from noon to 2:00 pm?

g. Label each segment of the following graph with letters A through I beginning from the left.

Complete the table by recording the time interval for each segment and describing what

happened in the problem situation represented by that segment of the graph. Then, state the

temperature and whether it was increasing or decreasing.

x42

10

20

30

40

50

60

70

80

6 8 10 12 14 16 18 20 22

y

90

Tem

pera

ture

(°F

)

Time (h)


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Name ________________________________________________________ Date _________________________

SegmentTime Interval

(in hours)Description of the Temperature

A 0–4

The temperature was increasing from 8:00 am to noon. The temperature of Grove City increased at a

rate of 20° per 4 hours, or 5° per hour. At noon, the temperature was 60°F.

B 4–6 From noon to 2:00 pm, the temperature of Grove City remained constant at 60°F.

C

D

E

F

G

H

I


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h. Why does it make sense for the graph of this situation to be continuous rather than discrete?

2. Grant’s teacher gave them the following graph of temperatures for a 24-hour period in a different

city. Write a story to describe the graph.


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To Be or Not To Be a Function?Defining and Recognizing Functions

1. A history teacher asks six of her students the number of hours that they studied for a recent test.

The following diagram maps the grades that they received on the test to the number of hours that

they studied.

6

5

4

3

2

1

95

Grade Hours Studied

70

85

a. Is the relation a function? If the relation is not a function, state why not.

b. Write the set of ordered pairs to represent the mapping.

c. What does the first value in each ordered pair in part (b) represent? What does the second

value in each ordered pair represent?


Name ________________________________________________________ Date _________________________


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d. Complete the following scatter plot. Does the graph agree with your conclusion from part (a)?


x2010

1

2

3

4

5

6

7

8

30 40 50 60 70 80 90

y

9

Hou

rs S

tudi

ed

Grade

2. Suppose a teacher asks six students the number of hours they studied, and the set of ordered

pairs was {(100, 6), (90, 5), (80, 3), (70, 1), (90, 4), (80, 2)}. Create a mapping from this set of

ordered pairs.

a. Is the relation a function? If the relation is not a function, state why not.


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Name ________________________________________________________ Date _________________________

b. List all the inputs of the relation.

c. List all the outputs of the relation.

d. Instead of mapping grades to hours studied, the teacher decides to create a new diagram for

her first set of students. This diagram maps hours studied to grades. Show the mapping that

would result.

e. Write the set of ordered pairs to represent the mapping in part ( d).

f. Is the relation in part ( d) a function? If the relation is not a function, state why not.


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g. Complete the scatter plot shown. Does the graph agree with your conclusion from part (f)?


x21

10

20

30

40

50

60

70

80

3 4 5 6 7 8 9

y

90G

rade

Hours Studied

2. At the end of the year, a principal decides to create the following mapping.

Input: The 82 total students in the history class

Output: The final grades they received for the class

Does this mapping fit the definition of a function? Explain your reasoning.


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Name ________________________________________________________ Date _________________________

3. Suppose a teacher writes the following equation that relates the amount of time the students

studied to their final grades.

y 5 10x 1 40

Let x represent the number of hours studied and y represent the grade.

a. Determine whether the equation is a function. Explain your reasoning.

b. List three ordered pairs that are solutions to the equation.

c. What conclusion can the students make about the relationship between hours studied and grade?


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Name ________________________________________________________ Date _________________________

Scaling a CliffLinear Functions

1. In 1980, George Adrian set the world record for the most apples picked in 8 hours. He picked a

total of 15,830 pounds of apples. That’s almost 8 tons of apples! Delilah is practicing so that she

can try to beat George’s record. After picking for awhile, she finds that she has picked 2 tons of

apples. She hopes to pick 2 tons per hour for the next several hours.

a. If Delilah manages to pick at a rate of 2 tons per hour, how many tons of apples will Delilah

have picked 1 hour after she starts picking again? Show your work.

b. Which quantities are changing? Which quantities remain the same?

c. Use the information in parts (a) through (c) to complete the table.

Quantity Name Time Weight of Apples

Unit of Measure

Expression

1

2

3

10

12


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d. How many more hours will it take Delilah to pick a total of 8 tons of apples?

e. Which variable is the independent variable? Which variable is the dependent variable?


f. Create a graph to represent the values in the table. Remember to label your axes.

0

4

2

210 3 4 5 6 7 8 9

6

8

10

12

14

16

18

y

x

g. Write each row of numbers in your table as an ordered pair. Plot each ordered pair on the grid in

part (f). Then, draw a straight line connecting the points and describe the line.

h. Is the relation shown in the graph a linear function? Explain your reasoning.


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U.S. ShirtsUsing Tables, Graphs, and Equations, Part 1

1. You want to save money for a new bicycle. You have already saved $50.00, and you are able to

save $7.50 each week.

a. If you continue to save money at this rate, what will your total savings be in 3 weeks? What will

your total savings be in 10 weeks? What will your total savings be in 6 months? (Hint: There are

4 weeks in 1 month.)

b. How did you determine the total savings in part (a)?

c. If you continue to save money at this rate, how long will it take you to save $275? How long will

it take you to save $800? How long will it take you to save $1175?


Name ________________________________________________________ Date _________________________


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d. How did you determine the number of weeks to save the amounts of money in part (c)?

e. Complete the table using the data of values from parts (a) and (c).

Quantity NameTime

(in weeks)Total Savings

(in dollars)

f. What are the variable quantities in this problem situation? Define the variables that can

represent these quantities including each quantity’s units. Then, identify which variable is

independent and which one is dependent.


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Name ________________________________________________________ Date _________________________

g. Create a graph of the data from part (e). First, choose your bounds and intervals. Remember to

label your graph clearly and name your graph.

Variable Quantity Lower Bound Upper Bound Interval

Time

Total Savings

h. Write an algebraic equation for the problem situation.


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Name ________________________________________________________ Date _________________________

Hot ShirtsUsing Tables, Graphs, and Equations, Part 2

1. Great Freights, a local shipping company, bases its charges on the weight of the items being

shipped. In addition to charging $0.40 per pound, Great Freights also charges a one-time fee of

$10 to set up a customer’s account.

a. How much does Great Freights charge a new customer to ship a package that weighs

20 pounds?

b. How much does Great Freights charge a new customer to ship a package that weighs

50 pounds?

c. Estimate the weight of a package if Great Freights charges a new customer $45 to ship

the package.

d. Write an algebraic equation for the problem situation.


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2. Twin brothers, Mike and Mark, are looking for a week-long winter break job. They are both offered

jobs at grocery stores. Mike is offered a job at Fresh Foods making $10 per hour. Mark is offered

a job at Groovy Groceries making $8 an hour, plus a one-time hiring bonus of $100. Each twin

believes that he has been offered the better job.

a. How much does Mike earn at Fresh Foods if he works 20 hours? 40 hours? 60 hours?

Show your work.

b. Explain how you determined Mike’s earnings in part (a).


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Name ________________________________________________________ Date _________________________

c. How much does Mark earn at Groovy Groceries if he works 20 hours? 40 hours? 60 hours?

Show your work.

d. Explain how you determined Mark’s earnings in part (c).

e. Complete the table using the data and your answers from parts (a) and (c).

Quantity NameTime Worked

(in hours)

Mike’s Earnings at Fresh Foods(in dollars)

Mark’s Earnings at Groovy

Groceries(in dollars)


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f. Create a graph of the data in the table in part (e). First, choose your bounds and

intervals. Remember to label your graph clearly and name your graph.

Variable Quantity Lower Bound Upper Bound Interval

Time Worked

Earnings

g. After how many hours will the twins earn the same amount of money?


h. Whose job is better, Mike’s or Mark’s? Explain how you determined your answer.


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Name ________________________________________________________ Date _________________________

What, Not Lines?Introduction to Non-Linear Functions

1. The area of a rectangle can be found using the formula A 5 l 3 w, where l represents the length

of the rectangle and w represents the width of the rectangle. A sketch of a rectangle with width x

is shown.

x

a. The length of the rectangle above is 3 times the width. Write an expression that represents the

length in terms of the width.

b. Write an equation that you could use to find the area of the rectangle. Simplify your expression.


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c. Calculate the area of the rectangle that has a width of 2 units. Show your work.

d. Use the expression you wrote in part (b) and your answer to part (c) to help you complete

the table.

Width Area

x

0

1

2

e. Do the values in the table represent a function? Explain your reasoning.


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Name ________________________________________________________ Date _________________________

f. Graph the values on the grid. Graph the width on the x-axis and the area on the y-axis.

-12

-16

-6-8 -4 -2 0 2 4 6 8

-8

-4

0

4

8

12

16

y

x

-20

-10 10

20

g. Does it make sense to connect the points? If so, connect them. Explain your reasoning.

h. Use the context of the problem to explain why no negative values were included in the table

and graph.


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2 Use the table shown to answer each question.

x y

x 3x2

22 12

21 3

0 0

1 3

2 12

a. Do the values in the table represent a function? Explain your reasoning.

b. If you graph the values in the table, what shape do you think the graph will have?



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c. Graph the values on the grid.

-12

-16

-6-8 -4 -2 0 2 4 6 8

-8

-4

0

4

8

12

16

y

x

-20

-10 10

20

d. Does it make sense to connect the points? If so, connect them. Explain your reasoning.


Name ________________________________________________________ Date _________________________

patterns, patterns, patterns… · 11/18/2013 · remembrance of her achievement. she will add...

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