My wife has taken on the challenge of homeschooling our children this year. My main participation in this is a weekly math session with the kids in the evening on any subject of my choosing!
Tonight was our first session. I decided to do partitions with them. I am priming them to be able to help me with my research on Q1 graphs.
We pulled out cubical blocks and I told the kids to make partitions with them. The hardest part about this is keeping my mouth shut and staying out of their way.
B invented Ferrers diagrams. Meanwhile I set A to work on making all partitions of the small numbers. She found 1 partition of 1, 2 partitions of 2 and 3 partitions of 3. She started working on 4 and found 4 partitions. Then B chimed in with a 5th partition of 4. This upset A and she refused to accept it as a partition, because it didn’t follow the pattern that she had seen. She stormed off, but came back and was ready to accept the 5th partition of 4.
I tried to get them thinking about how we could know that we had got all of them. They haven’t come up with anything along those lines yet. B (of his own volition) started working on an algorithm to generate all of the partitions of a given number. The algorithm needs work, so far only generating the n partitions of n: (1,1,…,1), (2,1,1,..,1), (3,1,1,..,1),…,(n-1,1), (n). He was also working on an algorithm for getting partitions of n+1 from partitions of n. I think that one was pretty incomplete too.
Their minds were still going, but it was getting late, so I sent them to bed. It was a good evening of math.