So, I was driving around with my son Maxwell (Max) and we were discussing giant pumpkins. The whole family loves carving pumpkins each year and we had just seen a television show about the giant squash species. So, he posed the question:
“How big do you think the largest pumpkin in the world is?”
Well, that made me think of many math problems, from the obvious relationship between the diameter or circumference and the weight. to estimating how many giant pumpkins would fill the Arlington Auditorium (a truly huge structure). I settled on just trying to predict this year’s world record pumpkin weight by looking at past trends. Here’s the problem in both MS Word and Pdf:
I give data for the last six years of world record pumpkin weights, which progressively are getting larger. Students then need to mathematically model the problem to predict the world record weight this year (getting near 2,500 pounds!).
I like this problem because the data is messy, yet approachable by students in both Algebra I and Algebra II. It is a real problem that has no clear correct answer as that has yet to happen. Clearly, students can use a regression approach and both linear and exponential are pretty good (r-values in the .95 range). But they could also just look at the average increase in weight per year.
I love extending this problem in both courses by collecting predictions by the entire class and then doing the statistics on them. Really neat to then finally see what the record is this year and how close the predictions are.
The whole problem lends itself two two of the primary Mathematical Practices from the Common Core:
Mathematical Practice #4: Model with Mathematics
Mathematical Practices #5: Use Appropriate Tools Strategically
Have a great Halloween season! Enjoy the fall before the darkness of winter spreads over us (hey, what can I say? not a fan).