Numbers, shapes and problem solving

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This factsheet introduces how you can support children’s mathematical development in your childcare setting and is suitable for all early years and childcare professionals in England and Wales.

Key points

  • Maths is not just about number recognition and adding and taking away. It’s also about shape, pattern, space, measurements and solving real-life problems.
  • Songs and rhymes help with mathematical concepts of beat, meter, duration of sounds, tempo and rhythmic patterns as well as counting.
  • It’s important to talk about the characteristics of different shapes rather than just naming them. That includes regular, irregular, 2D and 3D shapes.
  • Estimating, guessing, and solving real-life mathematical problems help children’s confidence as well as consolidating their knowledge of mathematical concepts.

What does this mean for me?

So much of our everyday lives include maths on some level, whether that’s shopping, telling the time, cooking, doing crafts, budgeting and solving problems, for example, how much to increase the ingredients if the recipe is for four people and we’re planning a meal for six.

It’s important to practice skills in number, shape and problem solving from the beginning of a child’s life. A baby can understand shape and size from stacking bricks and can understand the concept of all gone or nothing left when they’ve eaten all the food on their plate.

Think out loud

Being confident with numbers and thinking aloud when counting or working out a maths problem such as how much something costs in a shop will help the children’s understanding of numbers. When you can, use mathematical words such as longest, shortest, longer than, more than, fewer than, all gone, and none, heavier, lighter. This is a good opportunity to use Welsh language too, if you live in Wales.

Also, allow children time and space to work things out themselves when you pose them a problem, and ask them to show you how they worked it out. This will help with their confidence and mathematical development.

Value mathematical graphics

Provide resources for imaginative play that encourage making mathematical graphics, for example, calendars, cheque books, birthday cards, petty cash receipts, raffle tickets, recipes, and maps. Taking a register and looking at clocks also include number recognition.

Out and about

An outdoor space at your setting or going out and about on a walk provides lots of opportunities to explore patterns and collections, and the space to actively explore shapes and numbers.

Take a look at all the different patterns in nature, or take pre-school children on a shape walk, encouraging them to point out all the shapes they can see. Look at paving stones, road signs, drain covers, brick walls, park benches, and lamposts.

Junk modelling

Empty food boxes and containers provide a great opportunity to experiment with how shapes fit together. Give the children some flattened boxes so that they can see the relationship between 2D and 3D. Providing a big pile of materials and encouraging the children to sort them into categories that they decide upon also helps with maths, as grouping and matching is an important skill.

Songs and rhyme

Listening to music, clapping and tapping along, dancing and joining in with action counting rhymes such as 1, 2, 3, 4, 5 Once I Caught a Fish Alive or Ten Green Bottles all help with mathematical development as they become familiar with rhythm, whether a song is fast or slow and whether the sound is long or short.

Reflective task

Plan a series of activities exploring numbers, shapes and problem solving for the children in your setting, taking into account their ages, stages of development and current interests. Experiment with encouraging children to solve mathematical problems, giving them time and space to collaborate and come back to them if they don’t solve them straight away.

Reflecting on your learning

Did you know that reading and reflecting on factsheets and practice guides, and the resources mentioned in them, all contribute to your continuous professional development (CPD)?

It is helpful to keep a CPD log evidencing what you have done, when you did it, why you did it, what you learnt, and the impact it has had on your work and the well-being, learning and development of the children in your care. Think about how you would explain the impact the CPD has had for you to a parent, a student, an inspector, or a visitor to your setting.

Remember CPD is not just about attending a training course. It can be visiting another setting, reading a relevant book, publication, or blog; attending a webinar; researching a relevant topic; taking part in discussions with peers or taking part in on line learning.  

PACEY Professional Standards


Planning activities to support numbers, shapes and problem solving will help you meet this standard: C1.1 Organise activities, routines and experiences to promote children’s development by showing that you have ideas for activities and experiences and that you can adapt them to suit children’s needs and interests as required.


Planning a wide range of enjoyable and stimulating maths (including numbers, shapes and problem solving) activities and experiences will help you meet this standard: C1.2 Organise activities, routines and experiences to promote children’s development by taking into account each child’s interest and individual learning, play and development needs as well as taking into account the expectations of parents and carers.

Frameworks and Legislation


Early Years Foundation Stage Framework, Department for Education (2017)

Early Years Outcomes, Department for Education (2013)


Foundation Phase Framework, Welsh Government (2015)

National Literacy and Numeracy Framework, Welsh Government (2013)

Additional resources

Numbers, Shapes, and Problem-Solving Practice Guide, PACEY

NRICH Enriching mathematics – lots of mathematical games, problems and resources set up by Cambridge University.

This information is provided by the Professional Association for Childcare and Early Years (PACEY) as guidance only. The content may have been personalised to reflect the requirements of your home country. If you believe you need to see a different version of this content, please email with details of your request.

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