Carroll Diagrams

Why do this problem?

This problem gives children a way of sorting numbers according to different properties and also provides a situation in which they need to consider more than one attribute at once. In addition, it gives children the chance to explain their placing of the numbers, using appropriate language.

Possible approach

• What do you notice?
• What do you wonder?

This could then lead on to pairs of children completing the Carroll diagram itself, either using the interactivity on a tablet/computer, or on paper. When you bring everyone back together again, you might like to ask which numbers were easier to place and why. 

Depending on their experience, you can then offer the second interactivity and/or you could create your own Carroll diagram for completion using the Settings menu (purple cog). You can include some examples of Carroll diagrams which have lost their labels. Here is a printable example but you could also do this in the Settings by leaving the label text blank and just inputting the numbers. You can then drag the numbers to the correct positions yourself and invite the class to decide what the labels are. (You could present the class with all the numbers in the correct places, or you could add numbers one by one as they watch and see how long it takes them to work out the labels.) There are many different approaches to a 'no labels' version of the problem, and sharing some of their ideas with the whole group would be beneficial. Try to focus on the clarity of their arguments, thereby encouraging well-reasoned solutions.

Key questions

Possible extension

Possible support

You could suggest a particular way of starting, for example, looking at all the odd numbers first and deciding whether each is less than 10 or not. The interactivity allows users to change their mind about the positioning of a number, so learners who do not like committing ideas to paper might benefit.