The 12 days of Pascal’s triangular Christmas

For the recreational mathematicians amongst us, some Christmas fun! The 12 days of Pascal’s triangular Christmas.



Tackling the Big Questions in Mathematics

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I ran the holiday session sampling our Big Questions in Mathematics course  yesterday. This was a lot of fun!

The morning session was all about map colouring and the four colour problem. The children colour maps and drew their own, and discovered the secrets of making a two-colourable map. My personal highlight was the giant map collaboratively coloured on my window with window crayons. It’s a shame that we can’t get a good photo of it.

Lunch break and then back to work – using and making wonderful finite state machines. I loved watching the giant automata take shape on the floor.


Most of all, I love the questions they ask! That’s what it is all about. 🙂

Investigating Patterns


Patterns are a big deal in the curriculum for younger children. It seems to fade in importance later, which is a shame because it’s underneath so much higher level mathematics. Even without explicit teaching, noticing, playing with, and creating patterns is a stage a lot of children seem to go through. After all, noticing and responding to patterns is what our brains are supposed to do.

And so they do it. Without a worksheet in sight, I am watching my children develop and refine his ideas about patterns. I am glad I get to observe and record.

But because I am a teacher, I know parents want to know how to respond and encourage to this development of patterns. For younger children, in this early phase, I would suggest providing a variety of hands on pattern making materials. Some examples might include:

  • Popsticks
  • pattern blocks
  • wooden blocks
  • toys – cars, dolls, you name it!
  • art materials such as pencils, markers and paint.

Don’t force it, children will make patterns of their own accord. If you are home educating, you might want to keep the camera on hand to record these spontaneous patterns to help at review time. If you are not, record anyway! You will love looking back on them later!