Authenticinquirymaths.blogspot.com Website Review

I was interested in exploring how we might represent the addition operation as a pattern. We had been playing with the addition So I took it way back and asked how we might make a pattern to represent adding 5. I was underwhelmed. Surely we could come up with more than simple lines getting bigger by 5 each time. And was it a coincidence that just about every student had represented adding 5 in exactly the same way? So, I drew a long breath and asked our favourite question: Several representations looked at groups of 5 being stacked up on top of each other. An interesting idea - take it into another dimension - Two different students looked at representing the idea of adding 5 as an array.  Then we had a few interesting ideas. Here, the student has decided to start at 3 (the central group of light blue lids) and then adding This was a rather unusual idea. I can see the 5 blue lids. I can see several rows that have 5 yellow lids. But I could also see lots with 6 Well, you can start at any lid, and then count 5 in any direction. And then keep going. Well, that certainly took it to places I wasn't expecting. So, this student decided to reinvent numbers, place value, the counting system - everything. Each group of lids represents a number in the counting by 5s pattern (5, 10, 15, 20, 25 etc) but the number of lids is not relevant. Each group has a unique arrangement, demonstrating an understanding that all numbers are unique and represent unique values.  I was honoured yesterday by the Australian Mathematical Sciences Institute (AMSI) along with 9 other outstanding Australian teachers This is me with BHP Principal, Inclusion and Diversity Fiona Vines. The Canberra Times, our local newspaper, did a very sympathetic write up about me, though I'm not sure about the rockstar bit: I would like to thank everyone who has supported me in my mathematical journey, starting with my inspirational and extremely patient wife, my family, my colleagues, you - the readers of this blog - and ultimately my students who challenge me to think clearly and to be creative every