My school uses Connected Math for it’s 6th grade math curriculum; it’s pretty bad in many ways, but on the other hand, it is much better than all the other 6th grade math curricula I’ve seen, which are complete and unadulterated junk (I’m looking directly at you, Go Math!!) The 6th grade unit on rates and ratios has some pretty good activities in it, but I think the use of gummy worms is pretty lame, because, well, I am a believer in the separation between crappy food and educational matters. Yes, it may seem like fun to play games with M & M’s, that is, until one gets shoved up your nose and explodes.
This activity is designed to expand your students understanding of what a “rate” is by using the example of a tamale eating contest that has been held during the past 11 years in Lewisville, Texas. The contest sounds kind of awesome, and you really should look it up on the web to find cool photos, as well as the latest results.
The official rules of the contest are to see how many tamales a single person can eat in 12 minutes. To make things interesting, I scrambled up the ratios so that not all were out of 12 minutes. For example, competitor Brent Ricord ate 13 tamales in 6 minutes, which works out to 26 tamales in 12 minutes, which makes a rate of 1.3 tamales per minute. I also alphabetized the rankings, so that the students would have to order the decimals from smallest to greatest after calculating the rates, which is how we judge who was the winner.
Student should definitely use calculators as well as work in pairs of two to complete this activity, and one of the things you should be looking out for is that they know when to perform different operations based on the missing data. For example, to calculate the “unit rate,” you have to know how many tamales were eaten in a specific number of minutes. By turning all the results into unit rates, it is easy to figure out who was the winner of the contest, as well as put them into the correct order.
This activity connects to thinking about rates as relationships between three factors: the speed at which something is done, the length of time it is done, and the resulting total of that rate. Thus, it is closely related to the "distance formula" of Distance = Rate x Time, but the context is a lot more fun.