Classwork to Practice

1) Bruce added 5 boxes of a dozen eggs to 2 boxes of a dozen eggs. How many eggs are being shipped?
Choose the expression that represents the facts of the problem.

a-5 + 2 (12)
b-5 (12) + 2
c-5 (12) + 2(12)5
d-(12) (2)


2) The Giants added 3 three-point field goals to 4 seven-point touchdowns.
What is the score of the Giants?
Choose the expression that represents the facts of the problem.

a-3 + 7 (7)
b-3 + 7 (3)
c-3 + 3 + 4 + 7
d-4 (7) + 3 (3)



3) Find the average of 5 test grades: 87, 78, 92, 75, and 81. Choose the expression that represents the facts of the problem.

a-87 + 78 + 92 + 75 + 81/58
b-7 (78) (92) (75) (81/5)
c-(87 + 78 + 92 + 75 + 81)/5
d-5/(87 + 78 + 92 + 75 + 81)

4) Astro Paving Co. plans to resurface 10,560 ft of highway in 16 equal sections.
How many feet will be resurfaced in each section?
a-660 ft
b-168,960 ft
c-660 sections
d-102.76 ft



5) Ken sold 95 shares of stock for $42.17 per share and 300 shares of another stock for $28.92.
How much did he receive from the stock sale?

a-$4,006.15
b-$12,682.15
c-$71.09
d-$395

Answers:

1.c
2.d
3.c
4.c
5.b

Solve applied problems using problem-solving strategies:

Six-Step Problem-Solving Plan

1. Identify the unknown facts or the question to be answered.
2. Identify the known facts.
3. Determine the relationship between the known and unknown facts.
4. Estimate the answer or the characteristics of a reasonable answer.
5. Perform the calculations.
6. Interpret the results of the calculations within the context of the problem.

A retailer buys 75 cases of computer paper at $15.35 per case. If each case sells for $20.99, what is his gross profit?

Unknown facts:
Total revenue from sale of paper
Gross profit

Known facts:
75 cases of paper
Cost of $15.35 per case
Selling price of $20.99 per case

Relationships:
Cost = number of cases × cost per case
Total Revenue = number of cases × selling price per case
Gross Profit = Total Revenue – Total Cost

Estimation:
The profit per case is more than $5 per case. $5 (80) = $400. The gross profit should be approximately $400.

Calculation:
Total Cost = number of cases × cost per case
Total Cost = 75 ($15.35)
Total Cost = $1,151.25

Total Revenue = number of cases × selling price per case
Total Revenue = 75 × $20.99
Total Revenue = $1,574.25

Gross Profit = Total Revenue – Total Cost
Gross Profit = $1,574.25 – $1,151.25
Gross Profit = $

Interpretation
The gross profit for the computer paper is $423.

Earning Money - Taxi Driver
Percentages

1.After taking a taxi, Mackenzie's fare was $11.37. If Mackenzie also gave the taxi driver a tip of 12% then how much tip was received? _______________

2.After taking a taxi, Andrew's fare was $26.25. If Andrew also gave the taxi driver a tip of 10% then how much in total was paid? _______________

3.Logen works 6 hours per day as a taxi driver. Last week, Logen worked 3 days and earned $237. How much did Logen earn per hour? _______________

4.After taking a taxi, Olivia's fare was $42.46. If Olivia also gave the taxi driver a tip of 13% then how much in total was paid? _______________

5.Madison's taxi service charges a fare of $1.60 per mile. What is the cost to travel 11 miles? _______________

6.Matthew works 6 hours per day as a taxi driver. Last week, Matthew worked 3 days and earned $311. How much did Matthew earn per hour? _______________

http://www.moneyinstructor.com/ws/ws0167.asp

ANSWERS

1. $1.36     2. $28.87     3. $13.17    
4. $47.98     5. $17.60     6. $17.28

ANSWERS

1. $8.86    2. $17.31    3. $13.64    4. $160.67      5. $12.10
6. $6.10    7. $2.68      8. $1.08      9. $21.00      10. $3.83

ANSWERS

1. $30.00     2. $65.00     3. $535.00     4. $64.00          5. $375.00
6. $12.00     7 $871.29    8. $640.00     9. $1,698.50    10. $1,080.00

Create your own business:

GOOD DECISIONS THROUGH TEAMWORK
Choose a home business in your team’s target career field and investigate the cost of starting the business. Decide whether
the home business will market products, such as sports memorabilia, or services, such as desktop publishing. Once your
team agrees on the product or service, investigate the required equipment, materials, and other items and their cost. For
example, you might search business and trade magazines and interview a professional in the chosen business. Some items
to consider purchasing are telephones, supplies, furniture, a computer system, fax capability, subscription to an on-line service, and, if necessary, the product inventory.

Now find the total cost to start your home business. 
Will you need a loan or are other sources of funds available? 
If the budget is tight, can you eliminate or trim any nonessential expenses? 
Setting priorities early in the planning process is an important part of developing a realistic start-up budget.

How often do you see fractions?

Over the course of one week, note each time you see a fraction or percent used outside the classroom. Describe the situation and the use made of the fraction or percent. For instance, a computer store advertises a half-off sale on selected peripherals, your bank charges interest on 60-month car loans, or
a painter adds ounces of TSP to a solution to clean a wall before painting it.
With your team, make a master list of situations, eliminating duplications. For each situation on your master list, discuss
why a fraction or a percent is used rather than a whole number or a decimal. Also discuss why a fraction is used rather than
a percent. On the basis of your discussion, identify major categories for the use of fractions and percents. How many of
these categories apply to technical settings, such as in science or industry? Give a technology-related example for each category your team judges to be related to a technical setting. Choose a team member to share the results of your discussion with the class.

Metric Observations

Think about what would happen if the metric system completely replaced the US customary system in the United States.
Would people still refer to an inchworm or the 50 yard line? Would they still use sayings like, “An ounce of prevention is
worth a pound of cure”? What about Robert Frost’s poem “Stopping by Woods on a Snowy Evening,” which ends with “And miles to go before I sleep”?
Spend a week observing examples of both systems of measurement in everyday use. Look for things like product packaging, tools, hardware items, sporting events, clothing sizes, language use (like Frost’s poem), and so on. Record examples
of the measures and the situations in which they are used. Then investigate the advantages and disadvantages of each system in different situations. You might investigate library sources or interview instructors and other professionals in contrasting fields like physical science and social science, or English and engineering.
With your team members, discuss the advantages and disadvantages of each type of measurement you have observed or
investigated. Also discuss the status of the gradual conversion to the metric system in the United States and what impact
this conversion is having on the way people speak, work, play, and so on. Choose a team member to present the team’s findings to your class.

Research Project

Your team has been hired to conduct market research for a major consumer magazine. Your assignment is to choose an area
of interest, conduct a survey, and prepare a report of your findings. Pay careful attention to the content of your survey: How
long should it be? Should the questions be formatted to give yes or no answers, or do you want the respondents to rate the
product or opinion topic? Two examples of suitable multiple-choice survey questions are: “Which long-distance telephone
company do you prefer?” “What single piece of exercise equipment would you most want to purchase?” Then identify 5–10
possible responses, including “None of the above.”
Next, determine your team’s survey methods. How many responses do you feel would be adequate to make the results
reliable? When and where will you survey people? On campus? At a mall? Through the mail? Discuss how the time of day
and location can affect survey results.
Conduct the survey and record the responses. Then tabulate the total number of respondents and the number choosing
each possible response. Use a circle, a bar, and a line graph to plot your findings.
Write a report documenting your methods, results, and conclusions. Include the tabulation of responses and the summary graphs. Keep in mind that a high-quality report could mean another high-paying market research project for your team.

Similar Triangles

The proportionality of the sides of similar triangles gives rise to the classic problem of finding the unknown height of an object, such as a building, if the building casts a shadow and a nearby object whose height is known also casts a shadow.
Your team is to find the height of a measurable object, such as a post holding a stop sign, using the similar triangles formed by a team member and his or her shadow and by the object and its shadow. Measure the length of the team member’s shadow or use a yardstick or other rule and compare to the length of the object’s shadow whose height is unknown.
Solve the similar triangles. What did you find for the height of the object? Now measure the object to verify your findings. How close is your computed height to the actual height? Is there a difference? Why or why not? If there is a difference, what is the percent of difference?
Repeat the process with two other objects that are easily measured. Find the percent of difference between the calculated and measured heights. Next, find the height of an object that you cannot measure directly. Establish a reasonable range of values that your team expects the actual height to be.
Present your team’s findings to the class. Include a demonstration of the method you used and the solutions of the similar right triangles. Make a chart or transparency to aid in the presentation. Defend your estimate of the unmeasurable object.

Earning Money - Taxi Driver
No percentages

Earning Money - Taxi Driver

1.After taking a taxi, Isabella's fare was $31.14. If Isabella gave the taxi driver $40.00 then how much in change was returned? _______________

2.Jennifer works 7 hours per day as a taxi driver. Last week, Jennifer worked 7 days and earned $848. How much did Jennifer earn per hour? _______________

3.Michael's taxi service charges a fare of $3.41 per mile. What is the cost to travel 4 miles? _______________

4.Last week, Christopher worked 3 days and earned $482. How much did Christopher earn per day? _______________

5.After taking a taxi, Paige gave the taxi driver $20.00. If $7.90 was returned, then what was the fare? _______________

6.After taking a taxi, Dylan's fare was $13.90. If Dylan gave the taxi driver $20.00 then how much in change was returned? _______________

7.Michael took a taxi for 4 miles and the fare was $10.72. What was the charge per mile? _______________

8.Nicholas took a taxi for 3 miles and the fare was $3.24. What was the charge per mile? _______________

9.Christopher works 7 hours per day as a taxi driver. Last week, Christopher worked 5 days and earned $735. How much did Christopher earn per hour? _______________

10.Isabella took a taxi for 5 miles and the fare was $19.15. What was the charge per mile? _______________

1.Ryan's hourly salary is $15. If Ryan normally works 9 hours, but today works for only 2 hours, then how much money will Ryan make today?

2.Dereck's hourly salary is $13. If Dereck works 5 hours a day, then how much will be earned in a day?

3.Sarah's hourly salary is $10. If Sarah works more than 40 hours a week, then Sarah gets overtime pay at 1 and 1/2 times the regular hourly rate for each hour worked over 40 hours. Last week, Sarah worked 49 hours. What was the total pay last week?

4.Gabriel's hourly salary is $16. If Gabriel gets to work in the morning at 9 has lunch from 12 to 1, and then works until 2, then how much did Gabriel make that day?

5.Connor earns 75.00 in a day. If a normal work week is 5 days, then what is Connor's weekly pay?

6.Alexander earned $72.00 for 6 hours of work. How much was earned per hour?

7.Christopher was hired for $45,307.00 per year. How much does Christopher receive per week?

8.Jaden's hourly salary is $16. If Jaden normally works a 40 hour week, then how much is normally earned in a week?

9.Elijah was hired for $20,382.00 per year. How much does Elijah receive per month?

10.Jacob earns 54.00 in a day. If a month has 20 work days, then what is Jacob's monthly pay?


http://www.moneyinstructor.com/ws/ws0095.asp

Raises?

You work in a department that has 6 members, and you are to distribute annual raises that must average 4% per department.
No employee can get exactly 4%, and the raise must be at least 2% and no more than 6%. You may establish your own criteria for distributing the raises, but you have also been given the years of experience and the annual performance review ratings for each member. A performance rating of 1 is the lowest rating possible and a rating of 5 is the highest. Each member should assume the role of one of the following employees for purposes of this project: Employee 1 has 4 years experience, a performance rating of 4, and a salary of $28,500; employee 2 has 3 years experience, a performance rating of 3, and
a salary of $22,800; employee 3 has 10 years experience, a performance rating of 4, and a salary of $32,700; employee 4
has 7 years experience, a performance rating of 3, and a salary of $31,400; employee 5 has 15 years experience, a performance rating of 3, and a salary of $34,600; employee 6 has 12 years experience, a performance rating of 5, and a salary
of $32,400.
As a team, decide the amount of increase each of you will recommend to your supervisor. Prepare a report for your
supervisor that justifies your recommendations; a table showing the original salary, the amount of increase, the new salary,
and the percent of increase for each employee; and calculations to verify that the total increase is exactly 4% of the total
original salaries except for rounding discrepancies. Will the percents of change also average 4%? Why or why not?

Build a House and Sell it

You and your team are designing options for placing a single-family home on a lot your customer has purchased. The subdivision covenant where the lot is located requires that permanent structures be located no closer than 25 feet from the front
curb and 10 feet from the side and back property lines. The minimum living space must be 2,800 square feet, with at least
1,800 square feet on the ground level. The lot measures
Make three different scale drawings of the lot and a house, as viewed from above, that meet the subdivision covenants.
Prepare a written document for your customer that presents the strengths and weaknesses of each option.
Pair with another team and have each team alternately play the role of the customer. In an open discussion, the customer
team will decide which, if any, of the options is suitable for its needs. If no option presented meets the needs of the customer, construct a new scale drawing that will meet the needs of the customer, or show the customer why his or her needs
cannot be accommodated within the requirements of the subdivision covenants.

No signs

We use symbols in everyday life to overcome language barriers and to understand concepts. Pictures and symbols are easily associated with concepts. Even preschool children can distinguish between the symbols indicating male and female restroom facilities. A symbol is processed much more quickly than words. Our brains process much faster than they process
the words “no left turn.”
In your teams use a flip chart or board to write the words and draw the nonmathematical symbols that any team member can recall. Have one team member be the recorder and another the reporter. Discuss the components of effective symbolic representation. Next, design signs that contain no words to distinguish a walking path from a bicycle path, to direct
people to the information office on your campus, to direct people to keep off the grass. In addition, identify one additional
communication need on your campus and design a “no words” sign to meet this need.
Compare your team’s signs with those of the other teams in your class. Share the “no words” sign you designed to meet
the additional communication need on your campus and measure its effectiveness by asking classmates to interpret it.
Extend this activity by researching international symbols for signs and investigate the history of this means of communication.