Three versions of the same problem

My younger son and I have been studying angles for the last week. I decided to run through a few clock problems for a review. The secret about this exercise is that all three problems are pretty much the same problem in a slightly different form.

Question 1: How many degrees does the hour hand move in 10 minutes. I love the way he talks through this problem.

Question 2: What acute angle do the hour and minute hand make at 2:10?

I really didn’t know how he’d approach this problem. He got a little confused in the beginning thinking that the hour hand would move 1/3 of an hour in 10 minutes. Eventually he found that it moved 1/6th of the way through and that observation got him to the answer. I was a little surprised that he didn’t notice a connection between this problem and the first problem.

Question 3: What acute angle do the hour and minute hand make at 9:50?

The interesting thing here is that he does pick up on the fact that this one is similar to the previous problem. That observation allows him to get to the answer quickly. It was nice to see him also notice at the end that all of the answers were the same. Fun little project.

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