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

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 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.

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?