Thursday, March 01, 2018

mathematical thinking

The fourth graders are sometimes given a "problem of the week," which this week asked them how many more minutes there are with at least one 5 in them than minutes with at least one 6 in them in a 12 hour period (using a digital clock with no seconds). They are allowed to have an adult help them work through the problem.

One notion I've been trying to work with Anders on is that for a problem like this, figuring out the answer is only part of the solution—you also need to be able to explain your reasoning. Anders quickly figured out that there are "matching" minutes for 5s and 6s. That is, just as there is a 1:05, there is a 1:06. Then we explored the 5 o'clock and 6 o'clock hours, where every minute has a 5 in one, and every minute has a 6 in the other. Finally, we talked about the minutes from :50 to :59, where every minute has a 5, but only one (:56) has a six.

After all of that, we figured out the answer (there are 99 more minutes with at least one 5 than with at least one 6)—in fact, we figured it out three times, using slightly different techniques (two of which are on the left page below). Finally, we worked out a way to express the solution (right page). Once we had hashed that out, Anders wrote up the answer himself.

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