NRICH: Paths

By making ‘paths’ out of different materials and discussing these, children will develop their shape and space language in this activity.

Age 3 to 5

Children often enjoy putting objects in lines wiggling all over the place.

Adults could build on this by providing an environment that will give good opportunities for language work and discoveries.


The Activity
Gather together a selection of flat shapes of different colours and sizes, with sufficient room to create paths in and around the surroundings. This could be indoors or outdoors using man-made or natural shapes. The children are asked to ‘make paths!’.

Encouraging mathematical thinking and reasoning:


Tell me about your paths.
Let’s look at what everyone has made.
I wonder where this path is going.
I wonder who/what could be going along your path. How do you know what to put next?
Who used more shapes, you or … ?


Why did you put … next to the … ?
Is there a pattern to your path? What could you put after the … ?
Can you make your paths go (under the … , round the … , by the … )?


Opening Out
How many teddies/lorries can use your path?
Can you put more lorries on your path?


Would you like to show your path on paper?

The Mathematical Journey

Comparing and describing:
• using everyday language to describe geometric ideas
• using mathematical language to describe shape, moving from informal such as wiggly, to more specific such as straight or curved

• counting and knowing that the last number in the path tells the total

Adding and subtracting:
• increasing or decreasing the number of shapes in the path

Properties of shapes:
• selecting shapes to add to the path by analysing their properties
• using shapes to solve problems about the route of the path


Development and Variation
Children could:
• Collect all kinds of objects, both natural and man-made, and stack them up into towers.
• Fit different objects into big boxes or drawers.
• Choose things to build with outside.

Small flat shapes that could be used as stepping stones or put together to make a continuous path.
Outside, look for larger flat shapes that are able to be carried safely, both man-made and natural.

Math Topics
Early Childhood, Educator
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