This job takes two brains to handle the thoughts of these students.
In class on Friday, one student made the comment that he didn’t really like adding fractions on the clock because it could only be used for certain fractions. When I asked him to expand on that, he explained he could only do halves, 3rd, 4ths, 6ths, 12ths and 60ths easily and what if he wanted to do other fractions like 1/8 or 1/24? He said he couldn’t do that without breaking the minutes up. I am excited at this comment especially because this student is one whose parents have taken him to Kumon math for years for “extra help” and he is most comfortable memorizing procedures over thinking about the math. He thinks changing to “common denominators by multiplying the numerator and denominator by the same number” is faster and easier than this clock.
Upon reflection, I think it is interesting that he stayed with fractions of the fractions we were working…why not pull out 1/9 or 1/11? But my first train of thought in the moment was changing the whole. I wanted to see if he could put the clock in terms of a whole day, 24 hours, 2 rotations around the clock being the whole instead of one. That way 8ths and 24ths would be more apparent.
So I asked him if he could think of a way we could change the clock to do 1/8 or 1/24 without breaking up minutes? His first reaction was no, so I said “That is interesting because there are 24 hours in a day, so I feel like this should work.” Possibly leading him too much but at that point I could see the glazed look in some of the students eyes and I felt like I was losing the class’ attention. I told him that during math workshop that day he could chat with me about it or he could take that thought and work with some more for Monday. He said he wanted to think about it over the weekend…I think mainly because he didn’t want to miss the Math Workshop activities, so we will see what he has for me tomorrow.
After school, I am recapping this lesson for Nancy and saying how difficult I thought it would be for them to grasp two rotations of the clock as the whole for the 24 hours that would allow for 8ths and 24ths more easily. After listening to me ramble for about 5 minutes about this idea, she casually says, “What about military time?” UMMMmmm…DUH. Where was she during that class period?? This job really does take two brains.
So needless to say, I have amended my lesson for tomorrow. I am handing them this military clock and letting them talk about what fractions we can work with easily that are the same as our first clock and which one’s are different. Design addition equations we can solve with this clock that we couldn’t do on the other clock without breaking minutes.
Don’t get me wrong, I still want to get to changing the whole on our original clock, but I think after working with this clock, it may be more accessible for more of the students. I will post later to update on this lesson to show how it went…but good or bad, the questions and thinking that led to this lesson are so worth it!