I was scratching around last night trying to find something interesting for class today to introduce tree diagrams. I was very grateful for the worksheet/puzzles from Bron that I printed out – more as extension work for the class (these may be the probability tree puzzles from mathfour.com that I have some hard copies of on my desk?). I did refer to them throughout the lesson with some students in discussions about outcomes with different probabilities, which are not part of the curriculum for them at the moment.

Anyhow, the activity I thought of seemed to work well, get a good level of engagement and was fun… we’ll see about how well the concept was learnt later!

First up, I asked for 6 volunteers. It just so happened that we go three boys and three girls, which worked perfectly for framing this question:

Are the boys more ‘unique’ than the girls?

This certainly sparked from frantic discussion around the room… which I then reined back in a bit by explaining the particular scenario/context for the question today – as follows:

- I had three different coloured lollies behind my back (in a bag might have been better?). Three was a good number as it took it beyond the tables used in the previous lesson where there was two choices mostly.
- One boy could choose a side to reveal – the lolly pulled out was recorded on the board and he got to eat it
- Next boys went in order, choosing a lolly, recording it and then eating the lolly
- When it got to the girls turn, the first girl chose but then I kept the lolly! I put it back behind my back (ie. ‘replaced’ it) and then asked the next girl to choose and so on until all three had made their choice. (I then gave the girls a lolly each :))

This seemed to lead nicely into putting the heading ‘tree diagrams’ on the board and starting to show them how we could use the diagram to work out probabilities. I asked for observations about what the difference was between the boys and girls task (reinforcing the concept of with and without replacement) and we worked on the tree diagrams. Once this was done we could then answer the question! – which combination of lolly choices was more unique?

Again, there was good opportunity here for discussion around whether order mattered or not, and my ‘extension’ question was to ask if they could come up with two scenarios under these conditions that had relatively similar probabilities (e.g. boys in a particular order 1/6, girls in any order 2/9).

After all this, I set them some textbook questions – yay!?