## Wednesday, December 20, 2017

### A Nice Number Sense Building Puzzle

Today I was at a school and before going to work with some kindergarten classes, I had a spare 20 minutes to fill. I went into a Grade 4 class to challenge them with this puzzle that we shared on our @DCDSBMath Twitter feed from a few weeks ago:
The students were given whiteboards and told to get cracking!
And get cracking they did. What I found interesting at first was that they all worked from the top down: they split the 20 into two numbers and worked from there. When I have given this puzzle to adults, I have seen them work from the bottom row upwards. I'm not sure what to make of this!
Initially, some students hadn't noticed that they need to use four different numbers on the bottom row:

A quick reminder of what was required on the bottom row got them back on track. Excitement was evident as the students eagerly showed me a solution. I often found myself saying "Great! I've not seen that one yet. Now find a different one."

There were some mistakes on the way, but these were mainly caught by the students and, because we were using the whiteboards, these were corrected with minimum fuss. I was particularly impressed with these solutions:

I wasn't expecting to see negative numbers being used without prompting!
What I liked about this task is how quickly the students took to it and how much it provoked their thinking. At the same time it got them to use their number sense especially to decompose numbers in different ways. Next time, I would use a larger target value in the top brick to allow them to practice their mental arithmetic for adding and subtracting two-digit numbers.