I am rather shocked that it’s taken me so long to blog about the mathematical value of cones. They are a wonderful resource yet are often overshadowed by the sleekness of sticks and the smoothness of stones. So this post is written in honour of the cone and its mathematical versatility and diversity. I am grateful for the gifts of intrigue and interest provided by these remarkable seed keepers.

Cones can be collected sustainably from woods – just gather a few at a time and double check that it’s okay to do so if it’s a nature reserve or special place. Watch out for Sitka Spruce (Picea sitchensis) which has very sharp needles. This is tree that is often planted in commercial plantations. Cones are also easy to find online and in flower shops. Cosy have several packs including a place value pack, huge sugar cone pines and a cone maths pack which has a good variety of different species.

Estimate the number of cones in a bag

When collecting cones, challenge children to estimate how many have been collected. Tip them out and check. If children are ready, you can model counting in twos, threes or other clumps or they can show you how to do this.

Give children time to investigate cones

Children find the variety of shapes and sizes fascinating. It is worth ensuring they have plenty of opportunities to play with cones. Talk about what they are, where they have come from and any stories you know about cones such as the Douglas Fir Tree and the Mice. You may even wish to have conifer tree identification charts so that children can work out which cone comes from which tree and their classification.

Encourage children to discuss the similarities and differences between the cones as this is the precursor to discussion concepts such as equivalence and transformation.

Invent games which use cones

Cones can be used as counters. However many simple games can be made up by children. For example, try:

• Throwing cones through a hoop that has been hung up. Talk about the likehood of this happening and the investigate the effect of how far away you stand from the hoop.
• Play boules (Petanque). Use the biggest cones you can find as the boules. Mark them so that each person can identify their pair of cones. Use a tiny European larch (Larix decidua) cone as the jack. The jack is tossed  from a line or marker. The aim of the game is to get one of your cones closest to the jack. Use a measuring tape to work the distance of the winning cone to the jack. Usually several rounds are played.
• Have a target on the ground – such as a hoop or circle of leaves. The children throw five cones at the hoop and work out how many have landed inside the hoop and how many outside the hoop. This is useful for practising number bonds. It also makes a good team game where children are on the same team rather than competing against each other, when learning number bonds from 10 to 20.

Create arrays that you see around you

When developing children understanding of arrays, cones work well as they fit nicely into egg boxes, baking tins and other fixed array shapes. So are easy to use in this context. They are also a hand resource to get children to quickly represent arrays seen outside on the ground. For example a child may spot a 2 x 3 array of windows on the side of a building and  create the same pattern using cones.

Spot the Fibonacci spiral

I spent ages working out how this worked. Most cones sport a double helix, that is to say the spirals go both clockwise and anticlockwise. You can count the number of spirals you can find. The spirals radiate from the base of the cone where it was attached to its tree.

Make one-metre

This is a brilliantly simple yet challenging task .Ask your children to lay cones in a line until they are one-metre in length. It will let you know exactly who understands the concept of one-metre. It’s a good opportunity to hear the maths conversations which happen.

Measure your height in cones

Children can take turns to lie on the ground whilst others build a line of cones which matches their height. These can then be counted. Young children enjoy this activity.

Is it true that the larger the cone is the more it weighs?

This is a good investigation for older children who are learning to read weighing scales accurately. Also an agreement has to be sought beforehand over the definition of size – is it the length, width, horizontal or vertical circumference of the cone that will be used?

Order cones according to length and then width… is there a difference in the sequence of the layout?

This is also surprisingly tricky. How do you measure the size of a cone? It’s a good way of demonstrating the need for accuracy when using a tape measure and introducing the concept of millimetres.

Use cones to teach place value

In role play and games, set up an exchange system. 10 tiny cones such as larch (Larix decidua), can be swapped for one medium-sized cone such as a Scots Pine (Pinus sylvestris). 10 Scots Pine cones can be swapped for one Sugar Pine cone (Pinus lambertiana). This can work well for games that involve collecting points and also games where cones are laid out and children have to guess the value.