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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Paths

**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!'.
**Describing**

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 ... ?
**Reasoning**

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?
**Recording**

Would you like to show your path on paper?
**Development and Variation**

Children could:
**Resources**

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.

Or search by topic

Age 3 to 5

Talking about positions and shape properties

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 ... )?

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

**Number:**

- 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

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.

Download a PDF of this resource.

nrich.maths.org/early-years

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© University of Cambridge