This is a problem that I wrote for my statistics class. The objectives for this problem are as follows:

This is a problem that I wrote for my statistics class. The objectives for this problem are as follows:

1. Compute percentages.

2. Compute the arithmetic mean.

3. Critically think about whether or not Joe had enough tacos to meet the ‘average’ demand.

What I found was some students had a hard time computing the percentages and some also had a hard time keeping straight how many beef and how many chicken tacos Joe ordered on each day.

So, my whole recent obsession with Scotch Tape sort of began a few weeks ago when the following problem popped into my mind…

Suppose your boss wants you to buy six 1/2 in x 450 in rolls of Scotch tape at the dollar store (remember the 6% Michigan sales tax). Your boss wants you to use the tape to enclose an area of 3,225.8 square cm, but has only given you a budget of $7.00 to do so, including the amount of gas to drive back and forth to the dollar store, which is exactly 1.5 miles away from work. Your car gets 0.0735 liters per kilometer city (you will not be taking the highway), gas is $4.09 per gallon, and your boss does not care about the gas that it takes to actually start your car. Do you have enough tape to enclose the area that your boss asked to have enclosed? If you do have enough tape, explain why. If you do not have enough tape, do you at least have enough money to buy another roll of tape? If you need to buy another roll of tape, but cannot afford to, how much short would you be? If this is the case, would it be worth it to pay the amount out of your own pocket, or would you rather call your boss and explain the situation?

I totally meant to share these problems a few weeks ago, but I wanted to try it out with my classes first. However, I got so distracted with doing my Capture & Recapture Lab that we never got to the worksheet. Yes, I did a Capture & Recapture lab for my Beginning Algebra Classes to help demonstrate how proportions might be used as part of a method of estimation. Several students told me that without the lab, they wouldn’t have really understood exactly why we even needed proportions. That made me happy. So, here we are after the semester has already ended and I never used these problems. But I thought that I would share them anyway.

I am teaching a Finite Math class this semester and the majority of students in the class are business majors. I’m trying to make the class as relevant to them as possible, so I’ve been reading magazines such as INC, and Entrepreneur to try to get ideas for things that I can talk about in class. Well, here is one problem I came up with for my lesson on multiplying matrices. And by the way, I put a copy of the pie chart from the magazine on the Document Camera before even starting (I brought the magazine to class, actually).

According to INC Magazine (March 2011), 54% of workers describe their workplaces coffee as tolerable, 30% great, 10% terrible, and 6% other. Use matrices to answer the following questions:

1. If a company has 5040 employees, how many fall in each category?

2. Within this company, there are 3000 people in sales and 2040 people in marketing, how many from each department fall in each category?

3. Using the results from part 2, how many employees in marketing thought that the coffee was terrible?

4. Use matrix multiplication to verify that the row totals in part 2 match your answer from part 1.

Yesterday I came across this problem while planning a lesson on ratio and proportion:

"When I woke up this morning, I hit the snooze button and got 10 extra minutes to sleep. Every time I hit the button, I get 10 extra minutes. At this rate, if my alarm first goes off at 5:30 and I hit the snooze button 4 times before I actually get up, what time do I get up?"

After careful thinking, it turns out that I wasn't actually interested in this problem at all. I was actually interested in asking questions such as:

Personally, I would love an alarm clock that gives me 10 minutes on the first hit, 8 minutes on the second hit, 6.4 minutes on the third hit, etc. Then I could use this situation to talk about the limit of the time approaching zero.

This problem came about because I was talking about solving the equation 4x + y = – 14 for y and there was a little confusion about how I could subtract 4x from – 14. Although this was really a problem with combining like terms, I figured that now was as good of a time as ever to reinforce the idea of combining like terms.

“Yaletta bought an unknown number of tomatoes at $4 each, but when she got home, she found out that all of the tomatoes were rotten. In addition, she checked her receipt and realized that the store had charged $14 to carry the tomatoes to the car. Write an equation to model Yaletta’s total losses.” (as a signed number)

Then I asked these questions as well:

- What does y represent?
- What does x represent?
- What does -4 mean?
- What does -14 mean?
- How much would Yaletta lose if she bought 25 tomatoes? (as a signed number)

What’s even more interesting about this problem for me is that later in the day I was talking about ratio and proportion and so I used this same problem to ask questions such as:

- Do you think that it’s fair that the $14 dollar charge is fair? Why or why not?
- Would it be more appropriate to have a charge proportional to the number of bags of tomatoes carried to the car?
- What additional information would we need to know in order to make this change to the charge?

1. Clyde owed 8 different people $4 each for some doughnuts that he bought to eat on his birthday. Then when he wasn’t looking, Hellman’s stole $4 from Clyde’s wallet. In order to reclaim his debt, Clyde needed to split up his total losses over a period of nine months. How much debt will he recover over each of the nine months?

2. Clyde went to the store and he bought seven nuclear weapons, but he doesn’t know the price of them yet. He had to return four of the weapons because they were defective. Then Clyde had to pay $9 in order to bribe a government official into letting him keep the weapons. Finally, when buying the weapons, Clyde had a $4 off coupon. How much did Clyde pay since he did not yet know the price per weapon?

3. The hypotenuse of a right triangle is the median of {0.52, 0.69, 0.71, 0.34, 0.54} and one of the legs is the median of {0.26, 0.12, 0.35, 0.43, 0.28}. Find the length of the missing side.

4. The length of a boat is the mean of {11, 32, 21, 74, 32, 25, 29} ft. Convert the length of the boat to meters.

5. The diameter of a doughnut is the average of {3.6, 7.4, 3.9, 6.2, 7.6} cm. Convert the diameter to millimeters.

Here are three new application problems that I came up with **while** teaching signed numbers this morning. Remember, I came up with these on the spot, during class. So, just imagine that the entire class is paying attention to each of these problems as I am writing them, trying to figure out what is going to happen next to Clyde in each of the problems. I hope you enjoy these!

1. Clyde was walking down the street and he lost 1/3 of his vodka. A little later down the street Clyde encountered a zombie who wanted to steal another 2/5 of his vodka. The zombie agreed not to kill him if he told him the total loss that he incurred, as a signed number.

2. Clyde was running another scam where he collected $6.20 from people to buy an invisible potion of life. The local ghostbuster caught wind of this scam and blackmailed Clyde with a $3.30 charge. How much money does Clyde still have from this scam?

3. Clyde was in debt $12 to the local spy shop for some new night vision goggles that he needed to monitor paranormal activity coming out of the bottom of his shoes. When Clyde informed the spy shop that they forgot to include the complimentary antenna that comes with his goggles, they subtracted $4 off of his debt. How much does Clyde still owe, as a signed number?

In my Basic Mathematics class we just finished discussing the order of operations, and students always seem to have a problem with it, especially when division comes before multiplication (Sally has always told them otherwise). Today we discussed finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM), another topic that students sometimes seem to have a problem with. I came up with the following problem, which sparked quite a lot of discussion in the classroom. But more than that, I think it is the type of problem that continues to reiterate the Order of Operations, and doesn’t back students into the hole of forgetting what they have learned from one chapter to the next.

Sometimes as an instructor I struggle to get students to see the relevance of mathematics. Although mathematics isn't in the news nearly as often as I think it should be, here are links to a few websites that do document real-time mathematics news, along with a website with some interesting videos that might help to get some of the most stubborn students to possibly look at mathematics from a different perspective.