##### Stage: 3

Published March 2013.

The tree diagram is fundamental to our approach to learning probability.  Right from the start, we expect students to:
1. Collect data, which is then represented on a tree diagram and a 2-way table.
3. Test their impressions about what the data is saying against results aggregated across the whole class.
4. Move from counts to proportions.
5. Consider what the proportions will settle down to as we do more experiments.
6. Compare their experimental results with what we would expect to happen - working from a tree diagram and 2-way table completed with the expected number of each outcome at each stage, using simple probabilities (eg. chance of getting a blue face on a die with four yellow and two blue faces) to find expected results in whole numbers (natural frequencies).
The branches of the tree diagram provide a complete set of mutually exclusive narratives, each leading uniquely to one particular outcome, with no possible outcome omitted.

In Which Team Will Win? students are asked to record their results in a table, then tally, and then transfer them as whole numbers to a tree diagram, a process which 10 and 11 year-old students were able to do quite easily in the lessons I observed.

In one lesson, the teacher then put the aggregated results from the whole class on a tree diagram on the board, which he then used for a football-style commentary in a dialogue between him and the class:

What's the story for these branches?
The Yetis scored, then scored again!  A win to the Yetis!
And how about these branches?  What's the story here?
The Yetis scored, but then the Beavers fought back.  It's a draw!