Plastic cubes used to represent data on a two-way table
Using cubes to represent data in a two-way table

Two-way tables

Two-way tables are another useful way of recording data, and you may well have used one with plastic cubes to gather data from your own ‘Dog ate my homework’ experiment. We will now describe how we use these tables in the classroom.

We set up a large two-way table as shown above, positioned in a convenient location in the classroom so that students can gather around it. As groups of students complete their individual experiments and tally their frequencies, we ask them to bring their connected cubes and place them in the appropriate position on the table.

Using physical data on large displays is an alternative to averaging groups’ data to see the effect of gathering more data. Once the data has been collected, we ask some key questions:

  • How many students in total were telling the truth?
  • How many students in total were accused?
  • How many were truthful but wrongly accused?
  • Are you surprised? Why (not)?

Students will probably be surprised to see that the number of students who are wrongly accused is similar to the number who are correctly accused when all groups’ cubes are displayed together, even if that did not happen in individual groups’ results.


It might be simpler to record numbers in the two-way table, rather than assembling physical data as we have described.

  • What are the likely benefits of our approach?
  • Do you agree that these benefits make the additional effort and organisation worthwhile?

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This article is from the free online course:

Teaching Probability

Cambridge University Press