# Thinking 3D

The NRICH team develop problems for the whole site collaboratively, choosing themes that can be explored by children from 5 to 19. When the team are faced with the topics such as "3D geometry" we often need to pause and think about what this might mean for younger pupils. When thinking of 3-D, our initial thoughts ranged around planes and intersecting lines, three dimensional coordinate geometry and all sorts of 'hard and scary' maths. How could we begin to introduce these ideas to young children? Where do they start? What are the key concepts that we could introduce so that young children can gain some insight into this challenging area of maths? How could we lay the foundations for a later enthusiasm for working in three dimensions?

We thought for a while and then realised that the starting point for very young children is the language that we use to describe positional relationships of objects in space. Behind, beside, in front, to the left, to the right are all important in the development of children's understanding of objects in three dimensions. From this idea we developed the Building Blocks problem.

Our problem Chain of Eight Polyhedra also focuses on the properties of 3D shapes, and in particular on the characteristics of their faces. Analysing the polyhedra in this way and getting to grips with the associated vocabulary will equip children with the confidence to talk clearly and easily about three dimensional problems.

Triangles to Tetrahedra combines all of the above skills and concepts, and draws too on the notion of combinations. In tackling this problem, knowledge of the properties of a tetrahedron is essential, but almost immediately other questions come to mind. How is the length of the sides of the triangular faces important? Can it simply be a matter of combinations? What other factors do I need to consider? In answering these questions, children will be using positional language, visualising and applying what they know about properties of shapes. And of course they will be describing, reasoning, hypothesising, justifying and explaining, which are all key mathematical skills.

And so, in conclusion, we are now convinced that 3D geometry for younger children is not 'hard and scary'. If we create problems like these to give our pupils a good grounding in this topic, equipping them with complementary knowledge and skills, then perhaps three dimensional problems will never become 'hard and scary' at all.