Friday, 16 September 2016

Patterns / Relationships with Multiples of 3 and 6

The PYP key concepts are a brilliant tool to help children dig deeper in their investigations into mathematical thinking.

We did a think-pair-share routine to come up with key concept questions we felt we should find out to gain a deep understanding of our central idea.

Here are those we felt would best help us which now form our maths unit. Student-created maths units are far more engaging and powerful than teacher created ones:






To help us discover how amazing our number system is when it comes to patterns, we began looking at the multiples of 3 on a hundred grid. Again we used the think-pair-share routine and discovered some amazing patterns and number relationships:





Asking another number with a close connection with 3, we chose the multiples of 6 and repeated:






To help us investigate patterns / relationships / connections further, we then created a 'museum of the multiples of 3 and 6'. 

Partners used cuisenaire rods and/or counters to explore what these multiples could look like visually.

There was lots of trail and error as the children tried to solve patterns they first thought might continue only to discover they mightn't.  We discussed how those moments can be very powerful as we really need to think why they aren't working to then see if we could find a creative way of making them work.


We wrote small museum-style explanation cards for when others in the class would come to visit their display.

A lot of creative ideas emerged:









We liked the idea this student had of creating a key for the viewer to understand:
























Comparing the multiples of 3 and 6:






Multiples of 3 growing:









Tension is a good thing. I showed this pattern I was making to show the multiples of 3. I faced a problem though when adding the next multiple of 3 using the white counters. I explained how I wanted a symmetrical pattern to continue and so need to think how I could make this happen.  Modelling our own thinking and tensions in maths, I think, helps children see what we should be valuing and what they should do to as mathematicians. 
















Children really appreciated this representation when they visited it. Discussions about why you could keep adding one colour each as the multiples of 3 continued intrigued many:


In our class oral reflection, we felt this helped us to deepen our understanding that numbers do have connections and that mathematical thinking does involve creative thinking. We also reflected how visualising can helps us a lot as mathematicians.






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