A bit of a struggle with estimation

My wife was running a few errands with my older son this morning, so I decided to do today’s Family Math with just my younger son. The topic today was estimation and the specific problem we were thinking about was this:

If we drive from the Museum of Science in Boston to the Exploratorium in San Francisco, how many time will the wheels in our car turn around?

Fun question, and we began by talking about the different pieces of the puzzle we’d need to solve this problem (with a little help from the math cat):

After talking through the problem, we went outside to see if we could measure the circumference of our car wheel. We were unable to find a wheel of the same size (we tried a garbage can, a christmas tree stand, and a bike wheel) so we had to measure the diameter. I wanted to also make a chalk mark on the tire and measure the distance along the ground when it made one rotation, but I accidentally left my keys in my wife’s car. Oh well . . .

Next we came back inside to tackle the problem. In this segment my son was having trouble estimating some of the numbers we’d encounter in the problem, so instead of proceeding straight to the solution we went back outside.

We went back outside to take a closer look at some of the numbers in our problem. I thought it would be helpful for him to see what 88 inches looked like in relation to the length of our driveway, for example. That seemed to help him get a better estimate of how many times one of the car wheels would turn leaving our driveway.

The second trip outside seemed to help him get a better understanding of some of the distances involved in the problem, but he still had a tough time getting a good estimate of the number of times the wheel would turn going from Boston to California. He now understood that his estimate of 500 from before was too low, but he wasn’t sure how much to increase that estimate. We did a series of simple approximations and arrived at an estimate of 2 million.

Finally we get to the point where we plug in some numbers. We haven’t done much with unit conversions, so I had to help him through that a little bit. Eventually we arrived at a number of roughly 2.2 million for the number of times the wheel would turn.

So, a little bit more of a struggle with this one than I’d intended, but still a lot of fun. The lesson for me on this one is that I need to do a few more exercises that involve estimation and unit conversion. Hopefully I’ll remember to incorporate an exercise with those characteristics as least once per month.

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