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Younger children: just play with the shapes and water. Use a washing up bowl to capture the water and then play. Alternatively you can go outdoors and play with the resources outside. Let children pick up on the number of times you can fill a cylinder from the cone. At this age it is more about interacting with the shape. These are an excellent resource for nursery schools to have as part of a set of games and activities to develop numeracy.

Formal lesson:

Allow students time to play with the shapes and then give a set of questions to be asked if the students haven’t generated the outcomes themselves. This can be followed up with exploring further to formalise the outcomes. Colleen Young has some examples on her website.

This would be followed with applying the formulae. At this stage I would not be attempting to prove any of the formulae but I would introduce this in later years.  

3D Shapes

Exploring mathematics is a key part to learning and engaging with the subject. 3D shapes can be used in play to explore at a younger age and later in a formal maths lesson.

These resources relate the formulae for different shapes. Take a cylinder and a cone with the same base. The volume of the cylinder will be a third of the volume of the cone.