Back to Learning and development

Numbers, shapes and problem solving

Print this page



You can support children’s mathematical development in your childcare setting in many different ways. The information on this page 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 practise 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, 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 lamp posts.

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.

Want to know more? Continue your learning about Numbers, shapes and problem solving with this download.

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.

Planning and recording 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.

#DoOneThing

PACEY has developed a tool for you to record your reflections of the CPD you are undertaking. Whether that is attending a PACEY Live Webinar, reading an article in Childcare Professional, reading our webpages and downloads or an external piece of CPD, completing the Certification of Reflection means you have taken the time to think about why you are doing the CPD, what you have learned from it, what you are going to do with the learning, how will it enhance your practice, what is your #DoOneThing and most importantly what has been the impact of the changes you have made to your practice for those children in your care.

#SignPosts

Early years foundation stage statutory frameworks DfE publications

Development Matters: Non-statutory curriculum for the early years foundation stage DfE publications

Welsh Government Curriculum for funded non-maintained nursery settings

Welsh Government National Minimum Standards for Regulated Child Care for children up to 12 years of age

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 website@pacey.org.uk with details of your request.

Whilst every effort has been taken to ensure that the information provided is accurate and up to date, PACEY will not be held responsible for any loss, damage or inconvenience caused as a result of any inaccuracy, error or omission.

Information provided in PACEY's materials is not a substitute for professional advice tailored to specific requirements

We authorise users to view and download PACEY's materials only for personal and educational use to inform best practice. You must keep the copyright, trademark or other notices contained in the original material on anything that you download and these should not be altered in any way.

Materials should not be reproduced without the prior written consent of PACEY. Materials should not be altered or used in a misleading context.