**And it was.**(Click link to see details about the lesson.) We made them on paper, and we made them in Geogebra. And people noticed things! The same pattern was repeating with different numbers. And the pattern of repeats was interesting.

To give them another way of looking at the pattern of repeats, I showed them a multiplication square. We looked at the last digits in the multiples of 4 and how they are the same as the ones of 6 but backwards.

There seemed to be so much noticing going on, that the next day I gave them an image of what we'd discovered with the stars and also a blank multiplication square, and asked them to write about, and illustrate, what they'd noticed about one or both of these. I wanted to do this because I thought I would get a variety of responses, and get away from the idea that there was one thing I expected, towards the idea of their own individual directions being important. And they were able to describe and illustrate lots of noticings:

Today T's claim went up. I wondered whether they might be able to justify it - especially if they'd had some concrete experience fresh in their minds. So we borrowed the Numicon, which because it's lined up in two rows is great for odds and evens. We represented some multiplications and saw whether T's claim held true.

It was interesting that there were more things observed when we looked at T's claim together:

These could be followed up, but I sense it's time to move on, and perhaps return to the whole thing later, before anyone gets boggled.

At first I didn't see what the times table had to do with the stars, but I kept looking and reading what your students wrote and finally got it! Fascinating! What your students are doing is looking at these stars and number table in ways that they are able to see relationships and harvest new information. As far as I can tell, this is exactly the work of mathematicians, to organize observations around defining relationships so that other relationships are illuminated.

ReplyDeletePaula

Thanks Paula - and thanks for taking the time to puzzle it out when perhaps I hadn't spelt out the progression clearly enough! I've now added another picture to the post, and also emphasised the link to more about the lesson.

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