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Maths problem-solving – Activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

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Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…

Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.

But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.

Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.

The non-statutory  Development Matters Guidance , as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:

• thinking of ideas;
• finding ways to solve problems;
• finding new ways to do things;
• making links and noticing patterns in their experience;
• making predictions;
• testing their ideas;
• developing ideas of grouping, sequences, cause and effect;
• planning, making decisions about how to approach a task, solve a problem and reach a goal;
• checking how well their activities are going;
• changing strategy as needed;
• reviewing how well the approach worked.

All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.

Role of the adult

Maths problem-solving for young children involves them understanding and using two kinds of maths:

• Maths knowledge – learning and applying an aspect of maths such as counting, calculating or measuring.
• Maths thinking skills – reasoning, predicting, talking the problem through, making connections, generalising, identifying patterns and finding solutions.

The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.

Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.

One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.

Supporting maths problem-solving

You can effectively support children’s developing maths problem-solving strategies through:

• Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical vocabulary in context. You can promote discussion through the use of comments, enabling statements and open-ended questions.
• Providing hands-on maths problem-solving activities across all areas of the setting. Children learn maths through all their experiences and need frequent opportunities to take part in creative and engaging experiences. Maths doesn’t just happen in the maths learning zone!
• Identifying potential maths learning indoors and outdoors. Provide rich and diverse open-ended resources that children can use in a number of different ways to support their own learning. It is important to include natural and everyday objects and items that have captured children’s imaginations, including popular culture.

Maths problem-solving possibilities

Spell it out.

This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.

What you need to provide:

• Assorted containers filled with natural materials. This includes leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud and sand. Include some ‘treasure’ – sequins, gold nuggets, jewels and glitter.
• Bottles and jugs of water, large mixing bowls, cups, a ‘cauldron’, small bottles, spoons and ladles.
• Cloaks and wizard hats.
• Laminated ‘spells’ – e.g. “To make a disappearing spell, mix 2 smooth pebbles, 2 gold nuggets, 4 fir cones, a pinch of sparkle dust, 3 cups of water”.
• Writing frameworks for children’s own spell recipes and a shiny ‘Spell Book’ to stick these in.
• Temporary mark-making opportunities such as chalk on slate.

The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.

So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.

When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.

Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…

Going, going, gone

We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks , consider introducing maths problem-solving opportunities that extend this interest.

This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.

• Some unfamiliar trucks and cars and some old favourites. Ensure these include metal, plastic and wooden vehicles that can be sorted in different ways.
• Masking tape and scissors.
• Sticky labels and markers.

Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.

Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.

When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.

Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.

What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.

Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.

Observe children’s strategies

It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.

If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.

Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?

Camping out

Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.

• Materials to construct a tent or den such as sheets, curtains, poles, clips and string.
• Rucksacks, water bottles, compasses and maps.
• Oven shelf and bricks to build a campfire or barbecue.
• Buckets and bowls and water for washing up.

Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.

Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.

Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.

Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.

Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”

If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.

Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.

This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.

• A ‘building site’ in the outdoor area. Include hard hats, builders’ buckets, small buckets, shovels, spades, water, sand, pebbles, gravel, guttering, building blocks, huge cardboard boxes and fabric (this could be on a tarpaulin).
• Some distance away, builders’ buckets filled with damp sand and large gravel.
• Bucket balances and bathroom scales.

With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.

Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?

Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?

Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.

Extend children’s learning by modelling the language of weight:

• heavy/heavier than/heaviest
• light/lighter than/lightest
• about the same weight as/as heavy as
• balance/weigh

Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of  Foundations of Mathematics – An active approach to number, shape and measures in the Early Years .

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10 fun maths activities and games for the EYFS

With Famly since

Maths in the early years is a crucial stepping stone for developing children, which is why it’s so important that the little ones can explore and experience it in an enjoyable way. We’ve carefully chosen some fun maths games and resources to promote early learning of numbers through play.

Want to see how it’s done? Click here to watch the video of our five favourite activities ⏯

1. Combine mathematical skills with fine-motor skills.

Number Hunt in Jelly by Hazeldene Family Centre

This fun maths activity:

First, spread out some plastic numbers in jelly layers. When it’s all set, give out some tongs to children and show them how to pick up the numbers from the wiggly substance ( and practice their fine motor skills along the way! ). This sensory play is a great way of sneaking in number recognition into some sensory play.

What you need:

• Plastic Numbers

2. How do you make maths activities fun? Add Lego!

DIY Lego Pattern Cards by A Crafty Living

This fun maths game:

Lego. Useful in so many different ways , including making mathematics exciting. Prepare some cards with colourful blocks on them and let children discover colour patterns and reproduce them with LEGO bricks. Consider leaving the colouring part to your little learners so they can form their own patterns and include some EAD in the mix too. It's a win-win!

• Paper Cards
• Coloured Pencils
• LEGO Blocks

3. Challenge the children's maths skills to solve a missing number mystery

Missing Number Math Activity by Planning Playtime

This Early Years maths game:

Write number sequences on craft sticks and remember to leave some blanks in between. Next, you write the missing numbers on some clothes pins and give them out to the players. Now the children use their fine-motor skills and clip the pins on sticks and complete the sequence. The best thing about this fun and inexpensive maths game is that you only create the props once and they’re ready to be used as many times as you like.

• Craft Sticks (colour or plain)
• Clothes Pins

4. A simple game of swat the number.

Smack the Number Counting Game by Fun Learning for Kids

Prepare some sticky notes with various numbers and place them in front of the children armed with fly swatters. Roll the dice to get your target number. The goal of this simple yet fun game is for the little ones to identify the number on the dice and match it with the ones written on sticky notes by smacking the correct answer with a fly swatter!

• One or two dice
• Fly swatter
• Sticky notes

5. Playing with pom-poms to promote problem-solving skills

Straw and Pom Poms Counting Game by Nurture Store

Label small containers with some numbers that you’d like your learners to practice and prepare some straws and pom poms. For this fun maths activity, the kids simply put the straw on a pom-pom and suck in, to try and pick it up. Then they drop it over the containers until they’ve got the right number in each one.

• Shallow containers
• Labelled stickers (or any paper, glue and marker)

Get 50 free EYFS activities

6. A fun maths game to drive you dotty!

Number Dots and Easy Touch And Count Activity by Busy Toddler

Tape some paper to the wall and write several numbers, each decorated with dots, to match the quantity the number represents e.g. 4 dots on the number 4. Now, the players can touch each dot with a marker and see the number and the quantity altogether! You can also put the paper on the floor but holding a marker up and out makes this not only a fun game for early years maths but also a good way to strengthen those little arm muscles.

7. A magnetic, mathematical, magical fishing game

Magnetic fishing number game by Messy Little Monster

This Early Years maths activity:

First, you or the children need to cut your paper into fish shapes and add a paperclip. Next, write the numbers on the fish using a pen. For the fishing rod, tie some string (with a magnet on the end) to your stick! Now the whole class can 'fish' for numbers!

• Card/ Paper (or old pieces of artwork) to cut into fish shapes
• Paper clips
• Magnets, preferably some too large to be swallowed.
• Stick or long piece of wood

N.B. Always supervise children very carefully with magnets.

8. Fun maths activities are eggs-actly what we're looking for!

Egg Cracking Counting Activity by Modern Preschool

Looking to 'hatch' a plan for some fun maths games? Create ‘eggs’ by cutting out oval shapes from cardboard and writing different numbers on them. Students identify the numbers and 'crack the eggs' by punching the corresponding number of holes in them - you could always make one first, as an example. This exercise can also help develop muscles in those minute hands.

9. More fun in maths? Make it musical!

Top 10 Counting Songs by Super Simple Songs – Kids Songs

According to the BBC “When children are singing they are taking in information and training the brain but they don’t think they are, they think they are just having fun. Singing is an aerobic activity that boosts oxygenation in the bloodstream, increasing mental alertness”. We agree! Check out these 10 lovely songs to give it a go.

• A way to play music
• Your voice!

10. Matching with maths - a classic game with a mathematical twist.

Valentine Math Activity – Broken Heart Numbers by Fun a Day

Sometimes the most fun games are the classics. A simple matching game for one player, two players, or the whole classroom! Simply cut out some hearts and cut each in half using different zigzags, squiggles and other connecting shapes. Then write a number on one side and draw a corresponding number of hearts on the other. Well done, you’ve just created puzzles! Challenge the children to see who can find the matching hearts card to their number cards.

• Paper or card

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Please note: here at Famly we love sharing creative activities for you to try with the children at your setting, but you know them best. Take the time to consider adaptions you might need to make so these activities are accessible and developmentally appropriate for the children you work with. Just as you ordinarily would, conduct risk assessments for your children and your setting before undertaking new activities, and ensure you and your staff are following your own health and safety guidelines.

Matt Arnerich

Matt Arnerich is Famly's Director of Brand & Comms. He looks after the story of what makes Famly different, helping us to get closer to our mission.

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• Teaching & Learning
• Early Years

Problem-solving in early maths: 3 simple teaching tips

E d has made an enclosure for dinosaurs using four wooden blocks. He wants to make sure the dinosaurs can’t escape.

“Interesting, I can see the dinosaurs are all locked inside the enclosure,” says Ed’s teacher, “but the tyrannosaurus rex is very tall. I think it would be able to climb out? Is there something you could do to stop him escaping?”

Ed fetches four more blocks and stacks them on top of his enclosure, making it taller.

“Good thinking, Ed,” says the teacher, “but we can still see his head, so it might need to be taller. There are no more long blocks for you to use. I wonder what you could use instead?”

“I think lots of these shorter ones might fit on the top,” says Ed.

• What would “phonics for maths” look like?
• Is this the “right” way to teach early maths?
• How to develop number sense

There are frequent opportunities for mathematical problem-solving throughout a typical day in an early years setting. But how can we ensure that we maximise their impact when they arise?

The Education Endowment Foundation’s Early Years Evidence Store identifies approaches that educators can use to support young children’s early maths learning and development, while providing a summary of the evidence behind each approach.

Created as part of the EEF’s work supporting the Department for Education’s Stronger Practice Hubs, the store has been co-developed by researchers and educators.

The newly published Early Mathematics theme recommends five approaches for supporting children’s maths development:

• Teaching the association between number and quantity.
• Promoting fluency with numbers and sequences.
• Teaching problem-solving skills for maths.
• Teaching and modelling how to make comparisons and connections.
• Facilitating mathematical language.

If we look at the third approach, teaching problem-solving skills for maths, this covers how we teach children to apply purposeful thinking, communicate their ideas and use manipulatives to solve problems.

Strategies for teaching early mathematical problem-solving skills

Evidence and experience tell us that explicitly teaching problem-solving skills can be effective when combined with other approaches, especially when matched to children’s level of development.

A multi-pronged approach is particularly important for children from lower-income families or those at greater risk of not meeting expected levels of development. Sequencing learning and breaking tasks down, as well as modelling problem-solving strategies, can also help to improve outcomes.

But what does that look like in practice?

1. Thinking aloud

In the example at the start of this article, Ed’s teacher models her mathematical thinking aloud, encouraging Ed to do the same. Deliberate modelling, meanwhile, provides opportunities for the teacher to suggest additional challenges for Ed’s play in manageable chunks.

2. Modelling using representations to solve a mathematical problem

Educators can encourage children to use representations in different contexts to scaffold understanding.

This could be through using drawings, fingers or objects, such as pinecones or cubes. For example:

Ben is playing with a friend in the mud kitchen. They plan to make “fir cakes” for the teddy bears they have set up on the picnic bench.

Their teacher asks them how many cakes they will make. Ben tells her, “Four, so there is one each.” Andrea encourages Ben to use his fingers to check this, as she points to each teddy.

The teacher counts aloud as Ben lifts each finger, stopping at five.

“I need five cakes then,” Ben says.

“Yes,” the teacher agrees, “you need one more cake, and then there is one for each teddy”.

3. Reminding

Educators can prompt children to remember and apply a previous strategy to solve a mathematical problem. For example:

During welcome time, the teacher asks the class how they can find out how many children are here today, using their self-registration board.

“We can count them,” says Amrita.

“Yes, you are right; we can count the children. Is there a way we can do it that helps us count them correctly?”

The children aren’t sure, so the teacher reminds them: “If we move the photos one by one into the basket as we count, it’ll make sure we only count each photo once.”

Amrita then moves the photos one at a time into the basket as the children count in chorus to work out how many children are at nursery today.

Lauren Grocott is an early years specialist for the Education Endowment Foundation (EEF)

For more examples of how to teach problem-solving, including narration and using mistakes as teaching and learning opportunities, visit the Early Maths theme of the Early Years Evidence Store

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topics in this article

7 EYFS maths activities for kids

Check out these 7 indoor and outdoor EYFS maths activities for ages 4 and 5. 

Author Sam Layng

Updated April 2024

Key takeaways

• Playtime is where children develop motor and language skills, creativity, and social abilities.
• Children retain and recall information they’ve learned from games they engage in.
• EYFS maths activities are a great way to supplement any young child’s learning experience.

Table of contents

• Key Takeaways
• Why EYFS maths activites?
• Indoor EYFS maths activities

Outdoor EYFS maths activities

If you were to link anything with young children, it’s more than likely that ‘play’ would be one of the first things to come to mind. In fact, ‘play’ is more than just a fun activity: it also serves an important purpose, with explorative play forming a key component in young children’s overall development!

Luckily, there are plenty of EYFS maths activities out there to supplement a young child’s learning experience. Below, we explore some of the more notable activities that anyone can try.

The importance of EYFS maths activites

Children in EYFS span up to the age of five, which – as you might imagine – is an extremely formative period. It’s the stage where we come to discover how the world works and familiarise ourselves with communication, socialising, and motor skills. Then school comes along, and we take our first steps into the world of education.

However, maths can seem like a particularly intimidating area for many young learners. While we all encounter maths during our daily lives in one way or another, some may find it to be an abstract concept. If not approached in the right way, it can seem completely alien.

But luckily, as we’ve touched upon, kids love to play. It’s the perfect way for children to develop their language skills, their creativity, and their intellectual and social abilities. While adults may have to help with some more complex games, most young children find play to be organic and spontaneous, increasing their engagement and interest in the activities.

So, introducing a new subject under the guise of play isn’t just a great way to help children be more open and receptive. They’ll also find it easier to retain and recall the information they’ve picked up from the games they’ve engaged in!

Therefore, EYFS maths activities are a great way to supplement any young child’s learning experience. And as kids have been playing for thousands of years, it’s no surprise that teachers have meticulously crafted engaging games that can draw children in, while also producing some significant learning outcomes. For young learners, EYFS maths activities are the ideal introduction to their learning journey!

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Select a year group

• Early Years

Shape, space and measure

Number and place value, addition and subtraction, multiplication and division, operations (asmd), shape/geometry, ratio and proportion, probability, sample questions, indoor eyfs activities.

To make this clearer, let’s break up the activities into two sections: indoor and outdoor. Dynamic learning is important, and this includes the environments that children learn within too. When inside of the classroom – or anywhere indoors, for that matter – there are some great games that you can have a go at, such as:

Choose two: LEGO maths game

To set up this LEGO maths game, simply find any container and fill it with LEGO pieces. Try your best to grab as many different shapes and sizes as possible. If you want, find a LEGO base plate to make organisation easier. Otherwise, all you’ll need is a pencil and a piece of paper.

Now, have children close their eyes and grab two LEGO bricks from the container. For example, they may pull out a brick with four studs and a brick with two studs. Then, have them add or subtract the studs on their piece of paper. This activity is simple but effective, as kids love any chance to play with LEGO, regardless of the activity!

Doodle scavenger hunt

It’s a fact: children love fun, interactive activities. And whether it’s moving shapes around a screen or tapping colourful icons, our award-winning DoodleMaths app has you covered!

This activity is ideal for four and five-year-olds. To get started, download DoodleMaths onto a tablet or phone, or visit  students.doodlelearning.com  on a laptop. Then, ask each child to find a specific number of items (e.g. ‘Find four pencils’). Once they’ve found them, ask them to complete the same number of activities in DoodleMaths.

With engaging exercises and games to choose from, they’ll complete their activities in no time at all – and they can even use the stars they earn for their hard work to build their very own robot!

DoodleMaths is ideal for EYFS children, with audio dictation and hints available for every question. And best of all, you can try it for  absolutely free .

DoodleMaths  is an award-winning app that’s filled with thousands of questions and games exploring multiplication, division and more!

Designed by teachers, it creates each child a unique work programme tailored to their needs, doubling their progression with just 10 minutes of use a day. Try it for free!

Find the missing number

For this EYFS maths activity, you’ll need craft sticks, felt tip pens, and clothes pegs. Write number sequences on the sticks, remembering to leave some blank spaces at various points. Now, write any missing numbers on the pegs and distribute them out to the participating children.

Then, the kids are able to pin the pegs on the blank spaces of the craft sticks! This is not only great for sequencing and number recognition, but it’ll help tune their fine motor skills as well.

Splat the number!

This is a simple but engaging game that’s bound to get EYFS children excited. What you’ll need is a die or two, post-it notes, and a fly swatter. Arrange the post-it notes labelled with various numbers in front of the participating children. Have them roll the die (or dice) and then swat the number in front of them.

If your kids love a bit of competition (and can handle the excitement) have them play against each other, seeing who can swat the number first. This simple game is a great way to have children test their reaction times in relation to numbers, which will prove handy in their later academic years.

When outside, young children are naturally going to be more stimulated and excited about the task at hand. Skittles is a great EYFS outdoor activity that can help improve number recognition and motor skills at the same time. After buying a set similar to this, you’ll be able to set up a variety of dynamic maths activities.

For example, set up the skittles, then have participating children take turns to knock as many down as they can. If the number 2 and 4 fell down, have them add or subtract the numbers that toppled over. For even younger kids, only use smaller numbers, then work your way up based on their level of readiness.

Number line hopscotch

This one’s easy to do and plenty of fun. Simply go outside, grab a piece of chalk, and draw a number line on the asphalt. Begin with 0, then go upwards as far as you think is necessary. You could even make use of large foam dice to add another level to it.

Encourage activities such as hopping over numbers, then adding up what they missed, or seeing how far they can jump, then after two jumps adding or subtracting the amount. There are plenty of ways to take advantage of the humble chalk and concrete!

Squirt the numbers!

What you’ll need here is access to a hose or some water pistols, some empty cans or kitchen roll tubes, and a felt tip pen. It’s no secret that kids love spraying water, and this game leverages that to the fullest extent. Simply arrange the cans or tubes somewhere elevated (such as a table) ensuring that each one has been labelled with a number.

Now, have the children step up and spray them! Try to encourage them not to knock every single one down at once. Then, organise some sums or subtractions that the child can tackle with the fallen cans or tubes. You could even have two participants trying to reach a total, taking it in turns to spray numbers until reaching their goal!

In summary…

Ultimately, younger children love dynamic, engaging play. Using a combination of the activities we’ve gone over – and searching for even more out there – you’ll gain the most out of everything that EYFS maths activities have to offer. This explorative fun is the perfect introduction for young children, so take full advantage of it!

For even more ways to explore EYFS maths, be sure to give DoodleMaths a try. Created by our team of teachers and education specialists, it’s filled with engaging exercises covering all core curriculum areas, making it the perfect way to introduce young learners to the subject! Try it for free today.

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

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Ten of our favourite early years problem-solving activities

A lot of the time when we hear the term ‘problem-solving’, our brain jumps back to the tricky maths teasers from our school days, and we immediately recoil a little. However, problem-solving is much more than number conundrums.   

Problem-solving is a key part of early years development and can support learning across many of the My First Five Years streams. The skill of problem-solving starts developing very early in a child's life and stems from the knowledge of the world that they are constantly building.[1]. For instance, your baby may cry when hungry as they know that crying gets the attention of an adult who can feed them.   

Problem-solving is a part of everyday life for children, from being a baby through to their future adulthood. When children learn how to solve problems, it can support them in building resilience, self-confidence and self-esteem. Taking part in problem-solving activities with others can also help children develop social skills, communication and relationships.[2]   

Psychologist Jean Piaget’s theory of cognitive development also focuses on the importance of problem-solving for early childhood development. In each developmental stage of his theory, the psychologist emphasised the importance of play-based learning for young children when it comes to problem-solving, and in turn building skills across the spectrum.[3]    

Supporting problem-solving  

When thinking about problem-solving activities for your child, it can be difficult to know where to begin.   

To keep children engaged, enabling them to take the lead and follow their interests, is key. Play-based, hands-on learning makes acquiring new skills more interesting and memorable for young children.[4]    

Many activities can support children when developing their problem-solving abilities – the possibilities are wide open. When considering which problem-solving activities are the most effective, it is also important to consider how they can be adapted to multiple interests, abilities and how accessible they are when it comes to using resources and materials.   

To help you out, here are ten of My First Five Years’ favourite problem-solving activities that you can try with your child.   

1) Den-building

Den-building is brilliant for problem-solving as it requires creative and critical-thinking, foresight, and planning. It is also a wonderful way to promote sustained shared thinking with your child. Sustained shared thinking is a way of working together that encourages individuals to evaluate the problem that they are working on and is focused on collaboration, using experiences and prior knowledge.[5]  

When building a den with your child, encourage your child to take the lead. You could provide materials such as boxes and blankets, or you could even ask your child to decide what materials you need before starting, encouraging them to plan out their work. Den-building can also be done both indoors and outdoors and with children from a young age. You may find that people have already started creating these in your local woodland that you can add to, adapt, or just enjoy!  

2) Cooking and baking

Cooking and baking are not only fun activities, but they also focus on mathematical problem-solving. To bring problem-solving into a cooking and baking activity, you can ask your child to count out simple measurements, for instance, cups of flour or sugar. Activities like cooking or baking are great for children to be able to take ownership of what is happening; encourage them to choose what you will make and allow them to do all the elements themselves.   

What’s great about cooking is it really doesn't matter how it turns out! Problems can arise often in cooking or baking, for example, the mixture may turn out too dry, you may be an ingredient short, or your cakes might not rise how you expected them to. If this is the case, talk to your child about what might have gone wrong and how you can rectify it next time! Then when they come to do it again, they can use their prior knowledge to help them.   

3) Playing with patterns

Patterns are a great activity for mathematical problem-solving. You can create patterns of any objects that you can find! For example, with pieces of fruit, pebbles from the garden, building blocks or even snacks! You could encourage your child to continue patterns, fill in the missing pieces or even create their own for you to solve problems with as they grow more confident. 

4) Sorting and categorising

Sorting and categorising objects is an activity that supports children in mathematical problem - solving and can be easily adapted to individual children’s abilities . You could encourage your child to sort by shape, size, colour, or better yet , their interests . For example, if they are a dinosaur enthusiast, they could classify them by wh ich is their favourite or least favourite , or order them by the size of their feet. They may even find enjoyment in helping you with daily sorting such as recycling or washing!  

Puzzles are a fun resource that can be used with children from a very young age. There are a wide variety of puzzles for children to access , such as chunky wooden puzzles or traditional shape sorters. When playing with puzzles, children will have to use their prior knowledge and experience of shape, space and measure whil e also experimenting with different angles and placements. They will use trial and error to find the best way to complete the puzzle and then will use this knowledge in future attempts.  

6) Ice rescue

As well as being a great problem-solving activity, ice rescue enables children to explore seasonal changes, temperatures and develop their fine and gross motor skills using tools. To play ice rescue, freeze toys inside ice overnight. This could be in cake moulds or small bowls. Use toys that will motivate your child, for instance, their favourite small figurines.   

Once frozen, place your blocks of ice in a big bowl or tray, and encourage your child to think about how they can get the items out. You could provide tools, or even get your child to find tools themselves.  

7) Obstacle courses

Obstacle courses are versatile and can be made with a wide variety of resources. When setting up an obstacle course for your child, try to include sections where your child will have to stop and think about how they will have to adapt their body to move through it , for example, something that they must climb over or under, or a section where they have to move differently. You could even include them in trying to create the obstacle course and allow them to make it the most challenging they can.  

8) Filling, emptying and investigation

Many children enjoy filling and emptying during play. Investigating this way helps children to get a sense of size, capacity and explore predicting and estimation. For instance, if your child likes playing with sand, you could ask them to guess how many scoops they will need to fill a container, or if they like water play you could challenge them to find a way to move the water between two containers as quickly as possible , or from one tray to another.  

9) Story problems

Stories are an effective way of introducing problem-solving and they can be a highly engaging way to promote creative and critical-thinking. You could use familiar or traditional stories to help scaffold play opportunities for your child. For example, you could try building a house for the three little pigs that cannot be knocked over. You could test out different methods using materials that you can find around your home.   

If you are feeling creative, you could also make up a little story using your child’s favourite toys. An example of this could be figuring out how to share food between their favourite teddies during a picnic and making sure that everyone gets enough.   

10) Playing with loose parts or open-ended resources

Natural materials such as leaves, conkers, sticks, acorns, and pinecones are all brilliant open-ended play opportunities (if supervised). You can also use household objects like bottle caps, curtain rings, tubes, tins, boxes, buttons etcetera in this sort of play. All it requires is a tray of different objects that you've collected and time to explore them. Your child will have to think creatively about how to utilise the objects and in doing so will be challenging their cognitive capacity by problem-solving to achieve the desired outcomes.   

References 

[1]  Rachel Keen. (2011). The Development of Problem Solving in Young Children: A Critical Cognitive Skill. Available: https://www.annualreviews.org/doi/full/10.1146/annurev.psych.031809.130730#_i22 .  

[2] Sheila Ebbutt. (2009). EYFS best practice - All about ... problem-solving . Available: https://www.nurseryworld.co.uk/features/article/eyfs-best-practice-all-about-problem-solving .  

[3] Piaget, J. (1983). Piaget's Theory. In P. Mussen (ed). Handbook of Child Psychology. 4th edition. Vol. 1. New York: Wiley.  

[4] Unicef. (2018). Learning Through Play. Available: https://www.unicef.org/sites/default/files/2018-12/UNICEF-Lego-Foundation-Learning-through-Play.pd .  

[5] Kathy Sylva, Edward Melhuish, Pam Sammons, Iram Siraj-Blatchford and Brenda Taggar. (2004). The Effective Provision of Pre-School Education (EPPE) Project: Findings from Pre-school to end of Key Stage1. Available: https://dera.ioe.ac.uk/8543/7/SSU-SF-2004-01.pdf .  

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Reception Maths: Open-ended Investigations Mathematical Problem-solving

Problem-solving tasks develop mathematical skills and problem-solving tactics. These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside.

Session 1 Shape

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Shape Hunt By looking for and finding shapes, children gain an awareness of similarities of shapes in the environment. They match shapes by recognising similarities and orientation, show curiosity and observation by talking about shapes and begin to use mathematical names for shapes.

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Sorting While playing with and arranging twigs, stones, leaves, etc., children can be encouraged to take an interest in shape and space. They can talk about similarity and difference, while sorting objects. Developing mathematical ideas and methods can be used to solve practical problems.

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Trails Remember… just about anything you do indoors in maths can be done outside. Some children ‘come alive’ once out of the classroom and may just surprise you with the observations they make or the learning behaviours they show.

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Milk the Maths: Wellies Encourage children to use everyday language to talk about position whatever they are doing! Putting wellies away is a colourful opportunity.

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Session 3 Number and Shape

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The Mud Kitchen Ask children questions about shape, space and measure while exploring mud. Consider similarities and differences.

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Session 4 Number and the Language of Addition/Subtraction

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Exploring Problem-Solving in Early Years Mathematics | EYFS/KS1

This webinar will provide headteachers, mathematics leads, teachers and teaching assistants with practical guidance and methods they can use to nurture and develop pupils’ problem-solving skills in early years and KS1 mathematics.

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• Learning Outcomes
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Webinar Duration: 46 minutes (approx.)

This webinar will provide headteachers, mathematics leads, teachers and teaching assistants with practical guidance and methods they can use to nurture and develop pupils’ problem-solving skills in maths.

Problem-solving has long been at the heart of the mathematics curriculum. Teaching children how to problem solve in mathematics can support children’s ability to critically evaluate, encourage independence and develop their skills in reasoning and creativity. It is also an essential part of developing mastery of the subject.

In this webinar the Association of Teachers of Mathematics (ATM), who aim to support the teaching and learning of mathematics in the UK, will explore strategies that schools can use to approach problem-solving in maths with the youngest pupils which are creative and engaging and reflect a better understanding of the needs of the learner.

• Understanding how to introduce learning and problem solving in mathematics which supports children’s ability to problem solve and improve critical thinking skills.
• Recognising successful techniques that can be used in the classroom which improve reasoning in mathematics.
• Appreciating the importance of making maths problem-solving learning tailored towards the needs of children and ensuring continuous sharing and evaluation of different methods used.
• Understanding what is meant by ‘problem-solving skills’ and how to nurture an environment which encourages curiosity and positive attitudes.
• Building a culture which supports teaching and learning through playing and exploring, active learning and creative and critical thinking.

Since 1994, Helen has been an independent educational consultant specialising in developing the teaching and learning of primary mathematics. In July 2014, she completed her doctorate with the University of Roehampton, London. She is interested in engaging all learners mathematically, and how we might nurture effective and supportive learning communities in classrooms in a current educational climate geared to high-stakes testing. Helen is passionate about all children being given opportunities to become confident mathematical thinkers, through the establishment of a classroom culture that nurtures curious learners.

Helen has taught children across the full primary range and has a particular interest and expertise in early years and KS1 mathematics. Her work involves researching and teaching mathematics alongside colleagues in school and contributing to in-service training courses and conferences. Helen is a long-term, active member of the Association of Teachers of Mathematics (ATM).

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