A couple of days ago, Dan Meyer posted this new 3-Act problem about boxes of Girl Scout cookies being packed into the back of a Nissan Rogue. It came at exactly the right time for my 3D Geometry class. We’re entering the last couple of weeks, so I’ve been posing review problems each day to help them remember all of the topics we’ve tackled. As I was considering the plan for Wednesday, one dropped right into my inbox.
We watched the Act 1 video. I asked for questions:
- How many boxes are there?
- How many different shapes?
- How many cookies?
- How much do all those boxes weigh?
- How much would that cost?
- Could they have fit more?
- Could they have packed them more efficiently?
I asked for estimates, including guesses that they thought were too low and too high: The too low & too high estimates ranged from 1 to 1,000,000 and the guesses ranged from 206-3000.
I asked for the information they would need:
- How big are the boxes?
- What is the cargo space?
- How much do the boxes weigh?
- What’s the maximum payload?
I knew that Dan would provide some of this information in Act 2, but my students are very inquisitive and quite resourceful. They wanted to figure these things out for themselves. And as luck would have it, our principal drives a Nissan Rogue. We also had Girl Scout cookie experts who were quick to point out that not all cookie boxes are created equally. We sent a group out to measure the cargo space while two other groups worked on the problems of cookie box sizes, cookie box weights, and Rogue payload capacity.
In researching the payload, the group found that Nissan noted that the Rogue had a cargo capacity of 32 cubic feet, not the 39.3 cubic feet noted in the video. Guess we need to work on those research skills – clearly. The payload capacity was about 1,000 lbs.
Measured cargo space came out to be about 25.8 cubic feet (or approximately 44,600 cubic inches).
The group researching the cookie boxes decided to take a sample and find some average measurements. As a result, our boxes measured 2″ x 7.2″ x 3.5″ and weighed an average of 9.3 oz (or 0.58 lbs).
Final calculations showed that the Nissan we measured could fit about 885 boxes, which would weigh a little more than 500 lbs. But that was a pure volume calculation and the students knew from previous packing problems that we had done, that the reality would be less than that, and that there would be empty space.
Finally, we watched Act 3 (this is the Nissan version). We noted that the Rogue in the video was a different model year than the one that we measured. The measuring team also noted that the Rogue in the driveway had a floor at the level of the lift gate – it didn’t have the same depth as the model in the video.
So thanks, Dan, for the great set-up and giving my students the opportunity to revisit some of the work they’d done earlier in the term.