Problem of the Day” - Calculations and Calculators – Whole ...



Problem of the Day” – Applied Math

Math Focus Topic - April 2014

To increase student thinking and rigor, problems have been revised to reflect CCS of Mathematical Practice.

Use the “Problem of the Day” in any way that works for integrating this content with similar content found in your program area. Please note that the solutions are immediately adjacent to the problem. Additional problems of the same type are available upon request.

Suggestions for use: ATB or Sponge Activity; write on board and have students copy problem into a journal / notebook / notes; hold students accountable by checking the work for completeness and accuracy; review errors and procedures to improve students’ skills and confidence.

Problems for April, 2014

April 1

You work at a fruit market. Bananas cost 50¢ a pound. A customer hands you a bunch of bananas that weighs 3.75 pounds and a five dollar bill. Explain how you rounded to find the cost of the bananas. You only have a box with money in it and there are other customers in line. How much change should the customer get? What is the best way to return change to be sure it is correct?

April 2

Your employer, an interior decorator, has been commissioned by a repeat customer to provide curtains for a living room window. You need to figure the estimated cost. You believe the work time will be 4 hours. Your minimum labor charge is $100 which includes 2 hours of work; anything over that is an additional hourly charge. The project needs three pieces of fabric in the following lengths: 3 feet, 3 feet, and 5 feet plus an additional yard of fabric for pattern matching. What is the estimate for the curtains if the fabric is $49.00 per yard? Explain how you calculated this estimate.

April 3

You make and sell pies at a farmers' market for $12.50 each. A group of five people want to pitch in equally and purchase a pie. They ask you how much each of them will need to pay to buy a whole pie together. What do you tell them? They are skeptical of your answer – seems like too much! How do you prove you are correct?

April 5

You are a receptionist at a doctor's office. A patient's bill for a checkup totals $85.00. The patient's health insurance requires the patient to pay 20% of the total bill. Your office collects payments at the time of service. How much should the patient pay before they leave? How much will be paid by the insurance company? Explain an easy way to calculate 20% using mental math.

April 7

At R&R Distribution the products are sent out daily. Business is increasing and you are scheduling a new delivery route to improve efficiency. You need to find out how long it will take a driver to complete the route. You drive it yourself and start the route at 9:50 A.M. and finish at 2:05 P.M. How long does it take to drive the route? What factors might influence the route times on a day to day basis? Which factors can be controlled? Which cannot be controlled? How might these factors be accounted for in creating the schedule?

April 8

As a bowling instructor at Knock’em Down Lanes, you figure your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. Two weeks later at the Spring Fling Tournament the same bowler had the following scores: 148, 158, 176, 139, and 155. Find the averages for both tournaments. Did your instruction improve this bowler’s skill level? Give reasons for your answer.

April 9

At Future Labs you are employed as laboratory assistant. You measure chemicals using the metric system and, according to lab protocol, calculate to the nearest hundredth. For your current research, you need to measure out 45 grams of sodium chloride. The bottle you are using lists the amount in ounces. About how many ounces of sodium chloride will you need to measure? (1 Ounce = 28.3495231 Grams) How do the rounding protocols affect the measurements? What would happen if the protocols were not in place?

April 10

You are making a welding fixture and must cut down a length of steel tubing from 193/8 inches to 119/16 inches. When you cut the tubing, you will waste 1/16 inch of it because of the width of the saw cut. If the leftover piece is long enough, you will use it in another fixture. How long will this leftover piece be? Explain how you subtracted the fractions.

April 11

A current trend in the food industry is local or regional manufacturers with specialty products. There are seasonal, holiday, and combination products that are marketed for a limited time. You are doing marketing research to find out the purchasing potential of students in the community before you introduce a new product. Based on the latest census, there are 9,860 students in a population of 62,400 people. Students make up what percent of the total population? Why would this information be helpful to you?

April 14

This is the last day that You’ve Got Class Pictures is photographing students. You are a school photographer taking individual and class pictures for the remaining 2 classes of 21 students each. On average, each individual picture takes 3 minutes and a class picture takes 10 minutes. The students leave at 3:30 PM so you have got to be finished by then. About how long should it take you to get all of the pictures? What is the latest time you can start taking pictures if you get back from lunch at 12:30 PM? Explain why you chose this time.

April 15

The Local University employs four full-time groundskeepers to keep their sports fields in top playing condition. You are applying fertilizer to a football field in preparation for the spring growing season. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1,000 square feet. The fertilizer comes in 50-pound bags. How many bags of fertilizer will you need to load on the tractor trailer to complete the job? What formula do you need to use to solve this problem and how did you know that?

April 16

At Appliance City you sold a refrigerator to a customer for $369.00. Appliance City advertises that if a customer finds the same refrigerator anywhere else for a lower price you will give a refund equal to 150% of the price difference. The customer returns with a Kitchen Stuff Inc. ad that shows the same refrigerator for $335.00. After you give the advertised refund to the customer, what is the customer's final cost? Explain how you can use mental math to calculate the refund.

April 22

The mayor of the city wants information to apply for a national grant to bring money in for street improvements. You are an urban planner assessing the growth of the city to determine if there is data to support the grant proposal. Ten years ago, the city's population was 249,583. Its current population is 318,270. By about what percentage has the city grown over the past ten years? What would you expect the population to be in 10 more years if the city continues to grow at the same rate? Do you think the city should be awarded the grant?

April 23

As the office manager at Acme Co., you are responsible for purchasing supplies. You have a budget and need to justify all purchases to your boss. You are comparing prices from 2 office supply stores. Your office needs 5 cases of blue paper. Home & Office Headquarters lists a case of paper at $25.85 with a 10% discount on an order of 5 cases or more. Office Supplies R Us lists a case of paper at $27.36 with a 15% discount on 5 cases or more. Delivery costs from Home & Office Headquarters are $2.50 per case. Office Supplies R Us will deliver for $10 an order. What is the least amount that you would have to spend for the paper? How much money will you save since you took the time to comparison shop?

April 24

To complete bookshelves, a customer at your store needs to purchase vertical brackets to attach to the wall. The customer wants the shelving to be 9 feet high (vertically) and 10 feet long (horizontally). The wall brackets come in 48-inch and 60-inch sections. The 48-inch sections cost $12.95; the 60-inch sections cost $16.95. The brackets should be placed 1 foot from each end and no more than 24 inches apart. Before tax is added, what will be the total cost of the brackets the customer will need? How did you decide which brackets were needed?

April 25

Charles owns a toy store and stores his inventory of collectable toys at his home office. He keeps them in plastic containers to keep the packaging clean and undamaged. Each container holds 12 toy boxes and he has 278 toy boxes to store and is expecting a shipment of an additional 150 toy boxes. He has 20 containers already. What will be the cost to purchase additional containers at $3.50 each to hold his entire inventory? Explain why multiplication is the operation that is needed to solve this problem.

April 28

Todd wants to order the newest video game for his store. His cost is $21.15 and he will sell the game for double the price, plus an additional 15% of the doubled price. He wants to keep the cost of games at about $50 including the additional 8.5% sales tax. Will the customer cost of this game fit those criteria? What is the final customer cost for the game? Explain why you think Todd wants to keep the customer cost below $50.

April 29

Stan walks 10 miles a day on his delivery route. He works five days per week. He has 15 vacation days, 10 holidays, and 10 sick days per year. He usually uses only 20% of his sick days and banks the rest. About how many sick days does Stan usually use each year? About how many miles does he walk each year while on the job? If Stan had a knee replacement and needed to use his yearly sick leave and last 5 years’ worth of banked leave, about how many total days would he have to recover and still get paid?

April 30

You are employed as a nurse at a local hospital. One of your duties is to administer medication. A physician orders a drug at a dosage rate of 60 mg/kg/6hr. For a patient who weighs 185 lb, how many grams should be administered every 6 hours? What makes this problem more difficult? What do you have to know to administer the correct dosage?

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