In what's turned out to be a hectic week I've decided to write an account of my S1 lesson yesterday quite simply because I enjoyed it and want to remind myself of it in the future.
I was ready to begin examining Factors with my S1 class. In the past, I would have referred to this as 'doing Factors', 'teaching Factors' or something to that ilk, and would have relied heavily on direct instruction followed by what may be perceived by pupils as a boring exercise which no clear aim. However, I decided we were going to 'examine' Factors using various discussion points together. I started off by asking the class who knew what a factor was. It should be noted at this point that this is a group of pupils who are moving at a fast pace and their pre-requisite knowledge of the basics of number appear strong. Various definitions were offered, all of which told me they knew what a factor was. I checked this using statements like 7 is a factor of 35, 10 is a factor of 96, 3 is a factor of 81. For each, they told me on their mini whiteboards if the statement was true or false, and on asking them how they knew, I was met with a variety of answers (I didn't have the chance to take photos as the lesson was moving fast): Q: 10 is a factor of 96 A: 96 isn't an answer in the 10 times table A: Numbers end in a zero if 10 is a factor A: 0 in units column A: 96/10 = 9 r 6 so it can't be a factor During this, the girls in the class had to leave for an assembly but I decided to continue with the lesson. We then went on to list the factors of a numbers. Examples were 6, 24, 11 and 21. On reflection during the lesson, I hadn't thought these numbers through as well as I could have, although I could see what I had been thinking: 6 - even, 24 - larger even, 11 - odd and prime, 21 - odd. We found the factors of each and I asked the pupils if they agreed with the following statement: the larger the number the more factors there are. As they thought, I reordered the numbers on the board and they told me I was wrong but one pupil said 'Well maybe you're not completely wrong. Maybe the larger the even number, the more factors it has.'. So before I could even tell them we would explore this conjecture, another pupil asked if we could try a larger number to see if Xpupil was right. We had listed the factors of 6 and 24 and added 36 and 48 to our list. At this point, the conjecture was holding true, so I asked them to list the factors of 50 and when they realised the conjecture wasn't true some were surprised. It was a nice moment as they wanted to find out and prove it was true but then realised it wasn't. We then went through all of the numbers we had used and I asked them if they noticed anything about the number of factors. Someone said most of them had an even number of factors. Someone else said they all had an even number of factors apart from 36. I nodded just before someone shouted out that 36 is a square number followed by various reactions of agreement. So we found the factors of other square numbers and found that all square numbers have an odd number of factors. We then examined the factors of prime numbers and 1. This may be the sequence which most peoples' Factors lessons may take, but the important thing for me was that I was changing how I approached a lesson like this: less jotter work - I didn't feel like finding the factors of various different numbers in an exercise would have been productive time spent for these pupils; more discussion - I know from pupil reactions that they were getting something from this. The most significant moment for me was the conjecture which one child made and the 'noticing' which took place by all...being mathematical at its best?
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AuthorS McKenna Archives
March 2021
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