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This reports on students’ responses to a mathematical problem from the NRICH website. In particular, we were interested in students’ responses to a question that provided an unusual challenge. We have used the findings to suggest mediation strategies that could be offered on a website to meet the needs of all learners. These mediation strategies take into account the strategies used by teachers in classrooms.

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view of the purposes and skills of visualising.

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?