I used to think frequency trees were naffmaths. No real mathematical stuff in there. A place mathematical reasoning goes to die. Internally, I’d be convinced I needed to grit my teeth and get through it before returning to something proper. No more!

The resources linked at the top of this post deal with two aspects of reasoning with frequency trees.

Different frequency trees representing the same data.

The gif below demonstrates the animations in the example section of the slides.

This is then followed by a series of questions that expose these relationships.

Following this, pupils are asked to identify which of the following frequency trees is not showing the same information as the other three. Having focused on frequency trees being the same as partitioning models, this then broadens pupils reading and interpreting.

The difference is subtle but vital. The aim of this task is to explicitly train pupils in seeing and noticing.

2. Identifying fractions of amounts from frequency trees.

The gifs below demonstrate the two examples shown in the slides.

The rationale behind these examples and the tasks below are to explicitly link the language with the numerators and denominators of the resulting fractions.

In the tasks, there is a bit of simplifying much later, but the focus is on identifying language.

(For example, in the third one, explicitly bringing to pupils’ attention that ‘What fraction of circles are green?’ and ‘What fraction of greens are circles?’ are not going to be the same.)

The final couple of pages of questions are a bit more involved. The final question uses only one quarter as the fraction and one value to focus pupil attention on the language.

All resources are in the powerpoint file at the top of the post, including solutions.