## Wednesday, September 4, 2013

### Why We Need Puzzles in Maths

Now that September has come again, I realise that I have spent a fair amount of my summer 'off' doing maths. In July I finished off a Calculus course that was part of the Masters in Mathematics Teaching I'm doing at the University of Waterloo. I was also at Waterloo for a four-day Summer Conference for teachers which was well worth it. In between, I took Jo Boaler's excellent How to Learn Math online course and also started reading Alex Bellos's fascinating book Alex's Adventures in Numberland as part of an online Maths bookclub http://mathsbookclub.wordpress.com/.
More importantly, my daughter (who is 9) completed her first Sudoku on her own. Now it wasn't a Sudoku with numbers (it had Disney characters!) but it still required a fair amount of puzzling and struggling on her part.
And I liked it that she struggled.

And so did she.

It got me thinking about how we should use puzzles on a regular basis with our students. Now I'm not as fond of Sudoku as I am of some other puzzles like Kakuro and KenKens; not only do these require problem solving and resilience but they also require good number sense.
I first came across Kakuros in the Toronto Star:
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The idea is to fill this in using the numbers 1 to 9 that add to give the values shown in the row to the left or the column above with the restriction being that you cannot use a number more than once in any sum. So with a little thought, I can fill in the following as a start:
What I also do is look for certain rows that have triangle numbers (e.g. 15=1+2+3+4+5) or what I call 'frustrum numbers' (e.g. 24=7+8+9) as these will give me some clues as to what numbers must be used.

With a bit of puzzling (OK, sometimes a lot) the numbers topple like dominoes.
KenKens are a bit like Sudoku in that they are based on a Latin Square (i.e. a grid in which no row or column can have the same symbol appear more than once). The wonderful website http://www.kenken.com/ allows you to vary the size and level of difficulty of the puzzle but you basically start with a square like this which needs to be filled with the numbers 1 to 4:
The single squares can be filled straight away:
Now I can work on some of the blocks:
This allows me to complete the bottom row, then the third column, then complete the third row and the second column:

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For more of a challange, all four operations can be used with bigger squares:

And if you are teaching complex numbers, how about a complex KenKen (courtesy of The College Mathematics Journal):

Part of being a good problem solver is tenacity, the ability to stick-at-it. It strikes me that this is a quality that is positively encouraged through puzzles such at these.
As such, why should they not be a regular part of any Maths classroom?
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