ARE YOU WORTH YOUR SALT



WORK AT THE DEPARTMENT STORE

Teacher Edition

List of Activities for this Unit:

|ACTIVITY |STRAND |DESCRIPTION |

|1 - Saving Accounts |AS |Graphing points, fitted line, and write equations of |

| | |lines. |

|2 - Work at the Department Store |AS |Hourly Rate and Commission |

|3 - Are You Worth Your Salt? |AS |Graphing points, fitted line, and write equations of |

| | |lines. |

|4 - Multiple Choice Items |AS & NS |Large Selection of items – not intended to be given |

| | |to students in one ‘packet’ |

|COE Connections |Fundraiser |

| |Ryan's Summer Earnings |

|MATERIALS |Graph paper (if preferred) |

| |Ruler |

| |Calculator |

|Warm-Ups |Payday |

|(in Segmented Extras Folder) | |

| |Ernie Elephant |

| |Patience’s Patience |

Length of the Lesson: 200 minutes

Essential Questions:

• What is an informative title for a graph?

• What are appropriate intervals for the scale on the x- and y-axes? Should they be the same or different?

• How is a fitted line determined?

• How is an equation of a fitted line determined?

• How are variables used and described?

• How do you identify the x- and y-intercepts?

• What do the x- and y-intercepts of a line represent in the context of a given situation?

• How can a graph be used to make predictions and answer questions?

• What is meant when two graphs intersect?

• How can a conclusion be supported using mathematical information and calculations?

Lesson Overview:

• Activity 1 is an introduction to the rest of the “Are You Worth Your Salt?” activity. The activity is meant to generate discussion about different systems for earning wages. It is intended to allow you to assess student’s prior knowledge with regards to how people get paid—hourly, yearly contract, combination of hourly/monthly plus commission, straight commission, etc. The introduction activity takes students back to multiplication and division and asks them to write equations, generalize the arithmetic, and consider what happens when rate changes, which is a lead into the concept of slope.

• Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to how people get paid—hourly, yearly contract, combination of hourly/monthly plus commission, straight commission, etc.

• A good warm-up could be Payday, Ernie Elephant, or Patience’s Patience.

• What is meant by “base salary”? Are there advantages/disadvantages to getting a base salary versus getting a commission?

• Discuss a “fitted line” – what is it? How would a person use a fitted line? How would you show an understanding of a fitted line? Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?

• What is the relationship between the intercepts and the context of any problem?

• Discuss appropriate scale and intervals.

• What is meant when two lines on a graph intersect?

• What evidence from graphs can be used to support/justify a conclusion?

• Some of the multiple choice items could be used for warm-ups.

• Suggestion: Graph Catherine and John on the same grid with two different colors in order to compare

• Use resources from your building.

Vocabulary: Mathematics & ELL

|accurate |diagrams |rate |

|annual |display |recite |

|appropriate |effect |represent |

|axis |equation |scatter plot |

|balance |infants |service |

|commission |interest |slope |

|construct |intervals |tensile |

|corresponds |justified |trend line |

|data |models |variables |

|decreased |perpendicular |variations |

|depicting |predict |withdraw |

|deposits |radius |x-intercept |

|determine |raise |x-intercept |

|  |  |y-intercept |

Performance Expectations:

4.5.E Select and use one or more appropriate strategies to solve a problem and explain why that strategy was chosen.

5.4.B Write a rule to describe the relationship between two sets of data that are linearly related.

5.6.E Select and use one or more appropriate strategies to solve a problem, and explain the choice of strategy.

6.2.A Write a mathematical expression or equation with variables to represent information in a table or given situation.

6.3.B Write ratios to represent a variety of rates.

6.3.D Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions.

6.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

7.2.G Determine the unit rate in a proportional relationship and relate it to the slope of the associated line.

7.2.I Solve single- and multi-step problems involving conversions within or between measurement systems and verify the solutions.

7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

8.1.A Solve one-variable linear equations.

8.1.C Represent a linear function with a verbal description, table, graph, or symbolic expression, and make connections among these representations.

8.1.E Interpret the slope and y-intercept of the graph of a linear function representing a contextual situation.

8.1.F Solve single- and multi-step word problems involving linear functions and verify the solutions.

8.3.C Create a scatterplot for a two-variable data set, and, when appropriate, sketch and use a trend line to make predictions.

8.5.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

A1.1.A Select and justify functions and equations to model and solve problems.

A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities.

A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.

G.6.F Solve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units. Note: all linear equations in a context are conversions between various units. The slope is the unit converter and the y-intercept is the unit to convert to as is the y-value in y = mx + b.

Performance Expectations and Aligned Problems

|Chapter 1 “Work at the |1-Savings Account |2-Work at the Department Store |3-Are you Worth Your Salt |4-Multiple Choice Practice |

|Department Store” | | | | |

|Subsections: | | | | |

|Problems Supporting: | |4, 6, 7 |7 | |

|PE 4.5.E ≈ 5.6.E | | | | |

|Problems Supporting: |7, 15 |2, 6, 7 |3 |4, 6, 7, 8, 9, 10, 11, 14, |

|PE 5.4.B | | | |16, 17, 19, 20, 21, 23, 24 |

|Problems Supporting: | |4, 6, 7 |7 | |

|PE 5.6.E | | | | |

|Problems Supporting: |6, 7, 8, 14, 15, 16, 17 |2, 5, 6, 7 |3, 5, 6, 7, 8, 9 |2, 4, 6, 7, 8, 9, 10, 11, |

|PE 6.2.A | | | |14, 16, 17, 19, 20, 21, 23, |

| | | | |24 |

|Problems Supporting: |6, 7, 14, 15, 16, 17 |5, 6, 7 |3, 5, 6, 7, 9 |2, 4, 6, 7, 8, 9, 10, 11, |

|PE 6.3.B | | | |14, 16, 19, 20, 21, 23, 24 |

|Problems Supporting: |6, 7, 14, 15, 16, 17 |5, 6, 7 |3, 5, 6, 7, 9 |2, 4, 6, 7, 8, 9, 10, 11, |

|PE 6.3.D ≈ 7.2.I ≈ G.6.F | | | |14, 16, 19, 20, 21, 23, 24 |

|See Note on previous page | | | | |

|Problems Supporting: |5, 6, 13, 14 |3, 4, 6, 7 |4, 5, 7, 9 |2 |

|PE 6.6.E ≈ 7.6.E | | | | |

|Problems Supporting: |6, 14, 15 |2, 5, 6 |3, 5 |2, 9, 10, 19, 20 |

|PE 7.2.G | | | | |

|Problems Supporting: | |6, 7 |9 | |

|PE 7.6.C ≈ 8.6.C | | | | |

|Problems Supporting: |8, 16, 17 |5, 7 |6, 7 |2 |

|PE 8.1.A | | | | |

|Problems Supporting: |1-18 (work in collaboration|1-7 (work in collaboration to | 1-8 (work in |3, 9, 11, 19, 20, 26, 27 |

|PE 8.1.C |to satisfy 8.1.C) |satisfy 8.1.C) |collaboration to satisfy | |

| | | |8.1.C) | |

|Chapter 1 “Work at the |1-Savings Account |2-Work at the Department Store |3-Are you Worth Your Salt |4-Multiple Choice Practice |

|Department Store” | | | | |

|Subsections: | | | | |

|Problems Supporting: |5, 6, 13, 14 |2, 6, 7 |4, 5 |2, 6, 8, 9, 11, 14, 19, 20, |

|PE 8.1.E ≈ A1.4.C | | | |21, 23, 26, 27 |

|Problems Supporting: |2, 3, 4, 8, 10, 11, 12, 16, |2, 6 | |3, 18, 22 |

|PE 8.3.C ≈ A1.6.D |17, 18 | | | |

|Problems Supporting: |7, 15 |2 |3 |4, 6, 7, 9, 10, 11, 13, 14, |

|PE A1.1.A | | | |16, 17, 19, 20, 21, 23, 24 |

|Problems Supporting: |1-18 (work in collaboration|1-7 (work in collaboration to | 1-8 (work in |2, 3, 5, 6, 8, 9, 10, 11, |

|PE A1.1.B ≈ 8.1.F |to satisfy these PEs) |satisfy these PEs) |collaboration to satisfy |14, 19, 20, 21, 23, 26 |

| | | |these PEs) | |

Assessment: Use the multiple choice and short answer items from Algebraic Sense and Number Sense that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.

1 - Savings Accounts

1. Catherine has a balance (amount of money in the bank) of $200.00 in her checking account that doesn't pay interest (money bank adds to the account). Each week she deposits (adds) $75.00 into her account. She does not make any other deposits and does not withdraw (take out) any money.

Fill in the table to show the weekly balance of her checking account.

Catherine’s Bank Balance

|Week |Balance |

|0 | $200.00 |

|1 | $275.00 |

|2 | $350.00  |

|3 | $425.00 |

|4 | $500.00 |

|5 | $575.00 |

|6 | $650.00 |

|7 | $725.00 |

|8 | $800.00 |

|9 | $875.00 |

|10 | $950.00 |

2. On the grid, graph the data from the table.

Be sure to include an appropriate (use key words from the labels) title, labels for the each axis (the two main lines going up/ down and left/ right), consistent and appropriate scales (choose the lowest and highest number separated by equal steps), and accurate data display

(correct point location on the graph). (Trend line)

Make sure your graph goes to at least 15 weeks.

3. Draw a trend line (a line that fits the points or data) that fits the data displayed on your scatter plot (graph). See the red line on the graph.

4. Use the graph to predict (guess) Catherine's balance in her checking account at week 15.

$1325.00 = $200.00 + $75.00 •15

5. What is the y-intercept (point where the trend line crosses the axis going up/down) of your line?

$200.00 from (0 weeks, $200.00)

What does the y-intercept represent (stand for) in the context of this situation?

The original balance of $200.00 dollars in Catherine’s account at the time she started the weekly savings of seventy-five dollars..

6. What is the slope (rise/run) of your line? [pic] = [pic]

a. What does the slope represent in the context of this situation?

Catherine saving $75.00 each week…her consistently saving the same amount each week is seen graphically in the straight trend line on the graph.

7. Write an equation (mathematical sentence with an equal sign) that describes your trend line. Be sure to define all the variables (letters) you use.

Let the accumulated savings = s

Let the number of weeks = w

s = $200.00 + $75.00w

8. Use your table, graph, and/or equation to determine the balance of Catherine’s checking account during weeks 14 and 32.

Show your work using words, numbers and/or diagrams (pictures, graphs or tables).

a. Week 14 $1250.00 = s s = $200.00 + $75.00(14 weeks)

b. Week 32 __ $2600.00 = s s = $200.00 + $75.00(32 weeks)

9. John works during the summer and puts money into a checking account that does not pay interest. At the end of the summer he has a balance of $1000.00 in his account. During the school year, he withdraws $25.00 each week.

Complete the table to show the amount of money left in John’s checking account each week.

|Week |Balance |

|0 |$1000.00  |

|1 |$975.00  |

|2 |$950.00  |

|3 |$925.00  |

|4 | $900.00 |

|5 | $875.00 |

|6 | $850.00 |

|7 | $825.00 |

|8 | $800.00 |

|9 | $775.00 |

|10 | $750.00 |

10. On the grid, graph the data from the table.

Be sure to include an appropriate title, labels for the axes, consistent and appropriate scales, and accurate data display.

Make sure your graph goes up to at least 15 weeks.

11. Draw a trend line on your scatter plot.

12. Use the graph to predict John’s balance in his checking account at week 15. $625.00

13. What is the y-intercept of your line? $1,000.00

a. What does the y-intercept represent in the context of this situation?

$1,000.00 is the money saved up over summer by John; his beginning balance at the start of school.

14. What is the slope of your line? -$25.00 per week.

a. What does the slope represent in the context of this situation?

The negative $25.00 represents withdrawing money weekly during school.

15. Write an equation that describes your trend line. Be sure to define all the variables you use.

Let S = savings balance, w = number of weeks of withdrawing money.

S = $1,000.00 − [pic] • w

16. Use your table, graph, and/or equation to determine the balance of John’s checking account during weeks 14 and 32.

Show your work using words, numbers and/or diagrams.

a. Week 14 S = $1,000.00 − [pic] • w = $1,000.00 − [pic] • 14 weeks = $650.0

b. Week 32 S = $1,000.00 − [pic] • w = $1,000.00 − [pic] • 32 weeks = $200.00

17. After how many weeks will John have a balance of $0 in his checking account?

Show your work using words, numbers and/or diagrams.

$0.00 = $1,000.00 − [pic] • w ( − $1,000.00 = − [pic] • w

( ([pic])(− [pic]) = 40 weeks

18. Look at both Catherine’s and John’s information.

At which week will they have the same amount of money? Week 8 from the tables.

How much will they have? $800.00

Show work using information from the tables, graphs, and/or equations.

I used the tables at week 8 for both students they each have $800.00 in their accounts.

2 - Work at the Department Store

Last summer, Manuel worked for 9 weeks at the local department store. Each week he worked a different number of hours, as shown in the table. His salary was $10.90 per hour.

1. Fill in the table to show how much Manuel earned each week based on the number of hours he worked during that week. Be sure all your answers are reasonable and make sense for the situation.

Manuel's Summer Earnings

|Week |Hours Worked |Money Earned |

|1 |21 |$229.11 |

|2 |24 |$261.84 |

|3 |30.5 |$332.76 |

|4 |19 |$207.29 |

|5 |37.25 |$406.40 |

|6 |25 |$272.75 |

|7 |29 |$316.39 |

|8 |13.75 |$150.01 |

|9 |26 |$283.66 |

2. Write an equation for the amount of money Manuel will make for any number of hours he works in a week.

Be sure to define all variables you use.

Let h = number of hours worked by Manuel. Let M = the amount of money Manuel earns.

M = $10.90h

3. Describe the effect (change) on Manuel’s weekly earnings when his hours worked for a week increase.

As the number of hours worked increases Manuel's money earned increases. This Increase is a constant $10.90 per each hour worked.

4. Manuel decides to work at the same department store during the next summer. He is told that because he has worked for the store before, he will receive a one dollar per hour raise (increase).

How does this raise affect the amount of money Manuel will earn each week compared to the amount of money he earned each week last summer? Describe an easy way to determine how much more he will earn this summer than last summer, if he works the same number of hours.

Manuel will earn $1.00 per hour more than last year's weekly earnings.

Add up the hours worked last summer, multiply by $1.00; this is how much more Manuel will earn this summer, if the number of hours worked are the same.

5. How much does Manuel earn if he works 30 hours in one week at $11.90 per hour?

$357.00

Show your work using words, numbers and/or diagrams.

([pic])(30 hours) = $360.00 − $3.00 = $357.00

-OR-

([pic])(30hours) = $357.00

6. Carl works at the same store as Manuel and is paid a base pay of $8.30 per hour plus a commission (added pay) of 10% of his sales. During one week, Manuel and Carl

each worked 30 hours.

What dollar sales would Carl need to make in order to have the same week’s earning as Manuel?

s = $1080.00

Show your work using words, numbers and/or diagrams.

Let s = the amount of sales Carl made in a week.

Let h = the number of hours worked by Carl.

Let C = the amount of money Carl earns.

C = [pic]•h + .10s

$357.00 = [pic]• 30hour + .10s ( $357.00 = $249.00 + .10s ( $108.00 = .10s

( s = $1080.00

7. Tasha is an area supervisor at the same department store and works on commission only. Tasha earns a 15% commission of all sales (in dollars) made in her area of the store.

In one week, Tasha earned two times the amount of money Manuel earned for 30 hours at his $11.90 per hour salary.

What were the total sales in Tasha’s area for that week? $4,760.00 in sales.

Show your work using words, numbers and/or diagrams.

($357.00)(2) = $714.00

Let T = Tasha's earnings. Let s = the amount of sales Tasha made.

T = .15s So, $714.00 = .15s ( [pic] = s = $4,760.00

3 - Are You Worth Your Salt?

Staci has graduated high school and is working in sales. Each month she earns a base salary, plus commission, which is why there are monthly variations (changes). She keeps a record of her take home pay, income after taxes, for several months during the first 24 months.

Staci’s Monthly Take Home Pay

|Pay Period |Take-home Pay |

| Month 1 |$1,500 |

| Month 4 |$1,600 |

| Month 8 |$1,700 |

| Month 12 |$1,850 |

| Month 16 |$2,000 |

| Month 20 |$2,050 |

| Month 24 |$2,200 |

1. On the grid, graph the data from the table. Be sure to include an appropriate title, labels for the axes, consistent and appropriate scales, and accurate data display.

Make the graph large enough to include Staci’s first 60 months of work.

[pic]

2. Draw a line that fits the data (trend line) displayed on your scatter plot. (See Graph in red)

3. Write an equation that describes your line. Be sure to define all the variables you use.

Take Home Pay ≈ ([pic])(number of months worked) + $1,466.66

4. What is the y-intercept of your line? $1,466.66

What does the y-intercept represent in the context of this situation?

It could be thought of as the Base pay per month

5. What is the slope of your line? [pic]

What does the slope represent in the context of this situation?

Staci's take home pay is increasing at approximately an average rate of $33.33 per month

6. How much take-home pay would you predict Staci would make during these months:

Show your work using information from the tables, graphs, and/or equations.

b. Month 14? ≈ $1,900.00 ≈ ([pic])(14 months) + $1,466.66 = $1,933.28

b. Month 32? ≈ $2,500.00 ≈ ([pic])(32months) + $1,466.66 = $2,533.22

7. What is the x-intercept (point where the trend line crosses the axis going left/right) of your line? -44

Show your work using words, number, and/or diagrams.

0 = ([pic])(number of months worked) + $1,466.66

-$1,466.66 = ([pic])( number of months worked)

(-$1,466.66)([pic]) = number of months worked

-44 = number of months worked

What does the x-intercept mean in the context of this situation? Explain.

This trend line model fails to have meaning for the months before the first month’s take home pay. Further it will not be a good predictor if used to far away from the original data set. For example: Stacy (after 20 years of working) would be making $9,465.85 take home per month or $113,590.20 per year for a sales position; not a likely scenario!

Literally the x-intercept means 44 months prior to working in sales Staci had no take home pay. However, Stacie’s work history is just within this job after “graduated high school”, so 44 months ago she would have been in school!

Just because we can find a value does not mean that value is of significance.

8. Staci’s friend, Derek, started working for another company on the same day Staci started her job. Derek did not receive an increase in pay during his first year. He started making $2,250 per month in take-home pay and still made $2,250 per month during his 12th month on the job. He received a 5% increase in his monthly salary at the end of each year he worked

On the same graph depicting (showing) Staci’s earnings, graph Derek’s monthly take-home pay for the first 4 years he worked. (See graphed in Green)

Show your work using words, number, and/or diagrams.

|Years Worked |Monthly Pay |Calculations |

|1 |$2,250.00 |None |

|2 |$2,362.50 |$2,250.00 • 1.05 = $2,362.50 |

|3 |$2,480.63 |$2,362.50 • 1.05 = $2,480.63 |

|4 |$2,604.66 |$2,480.63 • 1.05 = $2,604.66 |

|5 |$2,734.89 |$2,604.66 • 1.05 = $2,734.89 |

-OR- we can use the equation: Monthly Pay = ($2,250.00)([pic], where years employed is 0 up until one year has been completed then is 1 up until two years have been completed and so on.

9. The trend of their yearly earnings continues for Staci and Derek for the first 5 years of their employment. Who will be making more money per year after the fourth year? Staci

How much will each be making? Staci earns $3,066.50 and Derek earns $2,604.66

Show your work using information from the graphs and/or equations.

Derek’s Monthly Pay = ($2,250.00)([pic] ( ($2,250.00)([pic] = $2,604.66

Staci’s Monthly pay ≈ ([pic])(48) + $1,466.66 = $3,066.50

Recall 12 months • 4 = 48months

4 - Multiple Choice Items

1. On June 1, Mary had a balance of $50 in her bank account. During June she made these

four transactions:

• deposited $25.00

• withdrew $30.00

• wrote a check for $60.00

• paid a bank fee of $25.00

There were no other transactions.

Which was the balance in Mary’s bank account on July 1?

← A. - $90.00

← B. - $40.00

← C. $10.00

← D. $190.00

Show your work using words, numbers and/or diagrams.

June ( 50 + 25 – 30 – 60 – 25

75 – 90 – 25

75 – 115

-40

2. Dianne and Jan planned a cycling trip along the Natchez Trace. The equation [pic] can be used to determine d, the distance in miles they could travel for t hours at a rate (speed) of

10 miles per hour.

Which is the number of miles they could travel if they rode for 2 hours?

( A. 5

( B. 12

( C. 20

( D. 102

Show your work using words, numbers and/or diagrams.

d = r • t

d = 10 ( 2

d = 20

3. The graph models (represents) p, the weekly profit of the Delta Blues Bowling Alley, based on n bowlers per week.

[pic]

Which value is CLOSEST to the profit for a week in which 600 people bowled?

( A. $1200

( B. $2000

( C. $3200

( D. $4400

4. Chris recently accepted a job as an auto salesman for Magnolia Autos. His employer allowed him to choose one of these wage plans in order to determine w, his total weekly salary:

Plan 1: $500 per week plus 5% of s, his total sales for the week

Plan 2: $400 per week plus 6% of s, his total sales for the week

Which pair of equations could be used to determine (find) the value of s total sales for which w total wages would be the same for both plans?

( A. [pic]

[pic]

( B. [pic]

[pic]

( C. [pic]

[pic]

( D. [pic]

[pic]

5. During the summer, Gwenda earns $6.00 per hour when she baby-sits and $7.50 per hour when she works in her aunt’s office. She wants to earn at least $200.

[pic]

Which statement is NOT justified (supported) by the graph?

( A. When she baby-sits for 35 hours, she will reach her goal.

( B. When she does office work for 5 hours and baby-sits for 20 hours, she will reach

her goal.

( C. When she does office work for 20 hours and baby-sits for 15 hours, she will reach her goal.

( D. When she does office work for 30 hours, she will reach her goal.

6. Jan took a taxi to visit the Petrified Forest northwest of Jackson, Mississippi. The taxi fare for the trip was $14.80, based on a fixed charge of $2.00 plus a charge of $0.80 for each mile.

Which equation could be used to determine m, the number of miles that Jan rode in the taxi?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]m

7. The area of a right triangle is 20 square inches. The sum of the length of the two legs (a and b) is 13 inches.

[pic]

Which system of equations could be used to find the length of the legs of the triangle?

( A. [pic]

[pic]

( B. [pic]

[pic]

( C. [pic]

[pic]

( D. [pic]

[pic]

8. William graphed the following two linear equations on a coordinate grid.

[pic]

[pic]

Which statement BEST describes the graph of the two linear equations?

( A. The two lines are parallel.

( B. The two lines are perpendicular.

( C. The two lines have the same graph.

( D. The two lines intersect at only one point.

9. The Pearl High School Band traveled by bus to Washington, D.C. to march in the Inaugural Parade. The graph shows y, the total distance the bus had traveled after x hours.

School Bus Trip

[pic]

Which equation describes the line drawn on the graph?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

10. The following set of ordered pairs, (n, p), represents p, the monthly profit of a store for four different months based on n items sold each month.

{(2000, 10,000), (4000, 22,000), (1000, 4000), (3000, 16,000)}

Which equation could represent the relationship between n and p in the ordered pairs of the set?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

11. The graph represents the cost of renting a car from Bulldog Rent-A-Car. The total cost of the rental is represented on the graph by y. The total number of miles driven is represented by x.

[pic]

Which equation could be used to determine the total cost of renting a car from

Bulldog Rent-A-Car?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

12. The slope-intercept form of a linear equation is written y = mx + b.

Which equation could be used to solve for b, given the values for y, m, and x?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

13. The table shows the number of bacteria present at 30 minute intervals (steps) during a science experiment.

[pic]

Which graph best shows the relationship between time and the number of bacteria present?

( A. ( C.

[pic]

( B. ( D.

[pic]

14 The relationship between the tensile (stretch) strength, y, of gray iron and its hardness, x, is linear, with a positive slope and a y-intercept of zero. The tensile strength of 24,000 pounds per square inch corresponds (relates) to a hardness of 160.

Which equation relates tensile strength, y, to hardness, x?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

15. For a research project, students were asked to memorize a list of words. After different lengths of time, the students were asked to recite (say) the words on the list. The graph models the average percent of words that students remembered after different lengths of time.

[pic]

In which time interval did the percent of words that the students remembered decrease the most?

( A. Between minutes 0 and 2

( B. Between minutes 3 and 5

( C. Between minutes 9 and 11

( D. Between minutes 13 and 15

16. Doug and Laura sold cans of soda to raise money for a school dance. Doug sold 4 less than 3 times as many cans as Laura. Together they sold 300 cans.

Which system of equations could be used to determine d, the number of cans Doug sold, and l, the number of cans Laura sold?

( A. [pic]

[pic]

( B. [pic]

[pic]

( C. [pic]

[pic]

( D. [pic]

[pic]

17. The table shows the number of slices of pepperoni placed on each size of pizza at

Pepe’s Pizza Shop.

|Size of Pizza |Radius of Pizza |Number of |

| |(inches) |Pepperoni Slices |

|Single |2 |5 |

|Small |4 |17 |

|Medium |5 |26 |

|Large |8 |65 |

|Extra Large |10 |101 |

Which equation best represents the relationship between the radius (distance from the center to the edge) (r) and the number of slices (n) of pepperoni?

( A. r = 2n + 1

( B. n = 2r + 1

( C. r = n² + 1

( D. n = r² + 1

18. The four scatter plots show the average monthly sales made by each of seventeen salespersons, together with his or her years of service (work) to the company.

In which scatter plot does the line drawn represent the trend line?

(

(

(

(

19. A factory purchased a stamping machine for $30,000. The machine has decreased (gone down) in value each year, as shown in the table. The value of the machine continues to change at the same rate.

Which equation shows the relationship between the age, a, of the machine in years and the value, v, of the machine?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

20. The table shows the relationship between x, the age of a girl and y, her average weight.

[pic]

Which equation could represent a linear relationship of the data in the table between the age and average weight?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

21. At Gulfport Electronics, Randy earns a monthly salary of $1,500 plus a 5% commission of

t, his total monthly sales. His March earnings totaled $2,500.

Which equation or expression could be used to determine, t, his total monthly sales for March?

( A. 0.05t

( B. [pic]

← C. [pic]

← D. [pic]

22. Thomas recorded the weight, in pounds, of several infants (babies) of different ages for his science experiment. He made a scatter plot of the data. He drew a trend line through the points

Babies’ Weights

[pic]

In which month should a typical infant weigh 17 pounds?

( A. 6 months

( B. 10 months

( C. 13 months

( D. 16 months

23. Every employee at the Conformity Corporation earns the same base pay of $25,000, and the same rate of commission. The table shows the annual (yearly) sales and total annual salaries for three employees. Let x equal the annual sales and y represent the total annual salary.

Conformity Corporation Sales and Salary Information

|Salesperson |Annual Sales |Total Annual Salary |

| |(dollars) |(dollars) |

|Lauren |$500,000 |$75,000 |

|Kathy |$700,000 |$95,000 |

|Nicole |$350,000 |$60,000 |

Which equation can be used to find the total annual salary for any salesperson?

( A. [pic]

( B. [pic]

( C. [pic]

( D. [pic]

24. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15.

Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?

( A t + m = 2.10

2t + 2m = 5.15

( B. t + m = 2.10

3t + 3m = 5.15

( C. t + m = 2.10

3t + 2m = 5.15

( D. t + m = 2.10

2t + 3m = 5.15

25. Russell hits a golf ball, the path of which can be approximated (a number close to the exact number) by the equation shown below.

| |

|[pic] |

|y = height of the ball, in yards |

|x = horizontal distance, in yards |

Which is the approximate height of a golf ball when it has traveled a horizontal distance

of 100 yards?

( A. 65 yards

( B. 53 yards

( C. 45 yards

( D. 33 yards

Show your work using words, numbers and/or diagrams.

26. Which graph best represents the line passing through the point (0, 4) and perpendicular (intersects at right angles) to the line [pic]? (Perpendicular lines have negative reciprocal slopes.)

( A. ( C.

( B. ( D.

27. An ornithologist observed a bird’s travel over a period of one minute. She used the data to construct (create) this graph.

[pic]

Which statement describes the slope of the graph between points P and Q?

( A. It is the number of seconds the bird took to travel from point P to point Q.

( B. It is the bird’s rate of speed between points P and Q.

( C. It is the bird’s rise in height from point P to point Q.

( D. It is the distance between points P and Q.

28. Tonja and Edward are participating in a jog-a-thon to raise money for charity. Tonja will raise $20, plus $2 for each lap she jogs. Edward will raise $30, plus $1.50 for each lap he jogs. The total amount of money each will raise can be calculated using the following expressions where n represents the number of laps run:

Tonja: 20 + 2n

Edward: 30 + 1.50n

After how many laps will Tonja and Edward have raised the same amount of money?

← A. 3.0

← B. 6.5

← C. 14.5

← D 20.0

Show your work using words, numbers and/or diagrams.

-----------------------

In part a, if a student doubles the table value for 7 weeks there answer will be $200.00 more than the correct answer…They doubled the initial $200.00 by using this method. For part b they would be off by $600.00 or 3($200.00).

The point of this question is to begin helping students understand that trend line models are useful but not for all independent values. Good judgment must be used when interpreting where the trend line is valid.

[pic]

[pic]

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