Defining a rhombus

[First paragraph] Is “telling” the only way to teach definitions in mathematics? How can pupils possibly know what something like a rhombus is, unless we tell them explicitly? We would suggest there is another way. We have recently been working on a guidance report on mathematics teaching for the Education Endowment Foundation, entitled Improving mathematics in key stages two and three, which makes eight recommendations. Recommendation 6 is to, “Use tasks and resources to challenge and support pupils’ mathematics.” One way to do this is to explore examples and non-examples of concepts. The task below shows how this strategy might be used to engage pupils in defining a rhombus, without the teacher having to present a definition at the start.