This is the kind of post Maggie encouraged me to make on Saturday, so here it goes.
We have been working on factors and multiples. After working together to find all the factor pairs for 100, the students were asked to figure out the factor pairs for 200, 300 etc. What I knew from observing the kids was that some (a few) intuitively knew the factor pairs for 100 and, perhaps one or two of those few would know how to use what they knew about 100 to figure out the pairs for the next groups of 100. What was really bothering me was that I knew most of the students did not have nearly enough experience "playing" with materials to see, let alone, discover the relationships between the groups of 100. So, I stopped the paper and pencil work for two days and had the students build the factor pairs for the 200s, 300s. What happened was great - the kids started seeing the "groups of" that made up the multiples and discovered they could figure out all the factor pairs and consequently discovered the patterns involved in seeing the relationships among the multiples. This is really hard to explain without feeling that it sounds silly and simplistic, but it wasn't and I am a happy that I dropped where the program was sending me and took the time to serve some mangos.
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2 comments:
I had the same experiences with my kiddos. Some students were counting by ones, or skip counting to 100, while others responded to my questions, "How does knowing which numbers are factors of 100 help you find the factors of 200? 300? Why are some of the factors of 200 not factors of 300? What number would have the same factors as 200?" Once we found those I challenged them to find a number that included all the factors of 200 and 300. It was exciting to see the thinking going on.
I am impressed by the idea that your kids can come up with factors of 200 and 300, but am unsure what the reasoning behind it is. What I think is that it helps them to see/understand that multiplication is groups of..... We are working on how multiplication and division are related. the kids had made lots of arrays and groups of things at the start of the year, but I have to insert using play/manipulatives into my program because it much more paper/pencil oriented. My students didn't have the same program last year and I wonder if the third grade program used more hands on work. I'll have to check it out.
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