The Beef Taco Dilemma

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. ...

Scotch Tape and Gas Prices Dilemma

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...

Thought-Provoking Proportion Challenge Problems

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. Proportion.pdf Download this file ...

I Use Matrices in Everyday Life, Do You?

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...

The Snooze Button is Now a Math Problem

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:Does it make since to get 10 extra minutes every time you hit the button, or would it make more sense for the number of minutes to be related to the number of times that the button is hit? Personally, I would love an alarm clock that gives me 10 minutes on the first hit, 8 minutes on the second...

Rotten Tomatoes, Linear Equations, Ratio and Proportion

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) The students seemed to come to the consensus that an appropriate answer would be y = - 4x - 14. Then I asked these questions as well: What does y represent? What does x represent? What does -4 mean? What...

New Application Problems from the Classroom

Here are few more problems that I came up with during today's class: 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...

Teaching Signed Numbers with Zombies, Ghostbusters, and Night Vision Goggles

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...

GCF, LCM, and Order of Operations

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. ...

Mathematics in the News

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.Related Links:Science Daily:  Mathematics NewsMath Real-Time News Index The Futures Channel ...