Why use this resource?

This is a problem about Egyptian fractions presented from a different angle. By working on the problem, students may get lots of practice at manipulating fractions, and they can also start to explain patterns they have noticed by exploring algebraic structure.


The resource has cards which can be printed and cut out.

Possible approach

The bullet points in the Problem section provide a structure for supporting students as they explore the unit fractions.

For a more investigative approach, the question about probability could be posed by itself.

Possible support

The questions in the Suggestion section, such as “How do you subtract two fractions with different denominators?” could be used to provide extra support.

If students are struggling with the probability part of the problem, you could suggest they draw a sample space diagram or ask them how they could use the diagram from the Solution section.

Possible extension

Encourage students to explain and try to generalise any patterns they have noticed.

For further work exploring fractions, including algebraic fractions, students could try Which is bigger? at the Thinking about algebra station.

If students would like to explore the importance of highest common factors in what they have noticed, they could try to make links with Buckets and ponds or Picture this! at the Divisibility and induction station.