Pricing Mistakes Challenge

I challenged my students this week to find pricing mistakes. For example, mistakes such as .11¢ instead of \$0.11 or 11¢.  I found two of my own this week.  Here they are:

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…

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 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?

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 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.

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 \$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?