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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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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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• EYFS Activity

12 EYFS Maths activities to count on

EYFS Maths plays a vital role in the seven areas of learning and development in the early years. Early mathematical knowledge is thought to directly predict reading, academic ability, and social confidence ( Duncan et al, 2007 ).

Spreading far wider than just numbers, early years maths activities help children recognise patterns, develop comparison skills, and think scientifically. This is why it’s important to offer a variety of EYFS Maths activities for the children to enjoy.

Read on to learn how pirate treasure maps are helping children’s mathematical skills.

Early years maths: What does the EYFS framework say?

The EYFS statutory framework recognises the need for variety and frequency when planning maths activities in your nursery. Early years settings should develop relationships with numbers up to 10 and spotting patterns.

The practical use of manipulatives is encouraged to support children in exploring the concepts of number, shape, space, measure, and spatial reasoning.

The main takeaway from the guidance for nurseries about early mathematics is that children should develop positive attitudes, genuine interest and enjoy exploring mathematical concepts through play.

12 Early Years Maths activities to try

If you are looking for fun but varied EYFS Maths activities to try, look no further. We share 12 of our favourite maths activities EYFS children will love, and that’s not even the best part.

Most of these activities can be enjoyed with existing or minimal resources yet still develop their mathematical skills.

Counting copycat

This maths game is great for toddlers, it can be played between two children or you can get involved! The gist of the game is to copy the objects player one picks up. You may wish to focus on copying the number of objects and the object’s colour, size or weight.

Sock pairing

Hear us out with this one. You know all of the ugly socks you have lying around at home? They have a recycled calling as a maths manipulative.

A big basket of odd socks will not only keep children entertained, but it can also improve their pattern-spotting skills, as well as their fine and gross motor skills, for a physical development win .

We aren’t sure of the age at which this task stops being fun, but for toddlers, it’s a blast!

'Eye' can see you

Who doesn’t love animals? Play pattern-spotting games with animals to develop observational skills (it also doubles up as a communication and language activity). If you’re fortunate enough to have access to different animals or can find virtual alternatives to the real thing, children can play counting games.

For example, on a trip to the zoo, you might ask the children to find another animal with four legs.

Share this activity with your nursery parents to try at home. They can upload images, videos, and comments to the Parent App using home observations .

Sing it out

It’s surprising that so many songs include numbers and counting. The children in your nursery will be too young to appreciate a rendition of Steps’ “5,6,7,8”, but alternative songs are available.

Here are a few of our favourite number-related rhymes:

• 1, 2, 3, 4, 5, once I caught a fish alive
• 1, 2, buckle my shoe
• Ten in the bed
• Hickory Dickory Dock
• Three blind mice
• Ten green bottles sitting on the wall

Real-life Maths activities

When thinking of EYFS Maths activities, you may not even need to alter your nursery routines. Applying mathematical counting, estimation and measure to everyday activities in the early years is simple.

For example, if the children line up to leave the nursery room, they could count the number of children (up to 10), walk as tall as they can, as wide as they can and even walk in pairs.

A tasty maths calculation

Food and maths activities, tell me more! During snack time, get creative with counting activities. The children can help to hand out snacks to others (five grapes, two slices of banana etc) – do be mindful of hygiene and any food allergies you should be aware of from their online Child Profile .

If you feel even more creative, you can make pizzas with children using wraps. Encourage the children to count the toppings they place on their pizza.

Let's go shopping

Understanding money should be a mathematical concept introduced at an early age. To clarify, we don’t mean expecting your toddlers to count the correct coins or give change (wait until key stage 1 for that!), but the concept that items are bought by ‘spending’ money can be understood by all ages.

In your role-play area, set up a shop. The children can be given counters, tokens, or even pieces of pasta to ‘spend’ in the shop. A simple key showing how many pieces of pasta an item is worth can be helpful.

Outdoor shape explorer

During your next outdoor walk, encourage the children to notice shapes. You can print or draw some simple shapes to take with you for reference (a circle, square, or triangle are good starting points).

Or, bring outdoor maths opportunities to the nursery with a selection of different-sized sticks. Using the drawn shapes as a template, the children can create their own 2D shapes.

Maths-related books for early years

Combine early maths and early reading for the best of both worlds. So many EYFS books have number themes running through them.

Here are a few popular maths-related EYFS books to try in your nursery:

• The Very Hungry Caterpillar (a firm favourite) by Eric Carle
• How Many Legs by Kes Gray
• Simon Sock by Sue Hendra and Paul Linnet (a great one for your odd sock basket)
• One to Ten and Back Again by Nick Sharratt and Sue Heap

Estimation at work

Your nursery rooms are likely to have tuff trays and water play stations. Water play is an excellent vehicle for developing estimation and measuring skills. Give the children a small container, access to water and a measuring jug. The challenge is to fill the container with the measuring jug just to the brim without overspilling.

The perfect place for adult prompts, such as:

• Do you have enough water to fill it with one jug?
• Is the container bigger or smaller than the measuring jug?
• Can you find another container the same size as the measuring jug?

A little to the left

Finding treasure on a pirate map is the type of maths we’re here for! Co-ordinates and direction are introduced into maths during primary school.

Following simple-step instructions not only strengthens speaking and listening skills but also sets the foundations for some seriously talented mathematicians (and pirates).

Pattern spotting

Patterns can be found anywhere. A traffic light has three circles, multi-link cubes can be made into reoccurring patterns, and hopscotch follows a pattern. Help your nursery children find patterns and continue them. They can use crafts, natural materials or Maths manipulatives.

Did you know that continuing a colour pattern using multi-link or Lego is actually the beginning of algebra?

For more brilliant EYFS activities, check out our Ultimate guide to EYFS activities blog post and easily cover the seven areas of learning!

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EYFS Numeracy Activities: 10 Fun Ways to Boost Early Maths Skills

Maths in the early year’s foundation stage is a vital stepping stone for children and it forms one of the seven key areas for learning. Therefore it is so important to make sure that your little ones can explore and learn it in an enjoyable way. In this blog we share 10 of our favourite EYFS numeracy activities for you to try out with your little ones and support a love of learning maths!

1. Counting Songs

Resources required (optional):

• Puppets or props
• Audio or instruments

Activity details:

• Start by playing the chosen songs a few times with your children for them to become familiar with it (if they aren’t already)
• Next, start by introducing counting elements such as encouraging children to count on their fingers “1, 2, 3, 4, 5” alongside the song 1, 2, 3, 4, 5 Once I caught a fish alive for example
• Elevate this by introducing puppets or props as a further visual aid
• Depending on your child’s development, now you might want to consider additional challenges such as pausing the song after 1, 2, 3__ and seeing if they can correctly name the following two numbers

2. Numicon Shape Matching

Resources required:

• Numicon shapes
• Numicon picture baseboards (you can draw these on white paper as an alternative)
• Challenge your little learners to match the Numicon with the coloured shapes on the baseboards
• They will need to be careful to use the pieces with the correct colours and numbers to make them fit correctly!
• Test their understanding by prompting them to count the numbers of each piece or the shape as a whole!

3. Snakes and Ladders

Snakes and ladders board game, OR:

• Tuff Tray or Paper

This game is as old as time and the rules simple: roll the dice to determine how many steps your piece can move forward. If you land on a ladder you travel upwards and if you land on a snake you travel down! Whilst this is a fun game for all, it is also a great way for children to practice their counting as they roll the dice and move forward to win the game.

4. Lolly Stick Maths

• Lolly sticks

This is a great activity to teach maths on a budget. Start by writing a number line 1-10 on a lolly stick. Then add the individual numbers 1-10 on pegs (you can add a number to each side)

All your little ones will need to do is match the numbers and add he correct peg over the matching number. Your little ones will develop their fine motor skills whilst also improving their number recognition

5. Colour Sorting

• Tuff tray colour mat (optional)
• A selection of different colour resources

A simple yet effective activity to help children to develop early maths concepts. The objective is simple, children will need to select an object from the pile of resources provided, correctly identify a key characteristic, in this case, its colour and then add it to the corresponding coloured section.

This activity can be adjusted depending on your objective, for example can objects be classified by size or shape instead? Tailor the activity to support your individual child’s area of development.

6. Numicon City

• Tuff tray paper pad
• Counting cubes (optional)

Numicon is a brilliant early maths resource as it allows children to visualize the concept of addition, subtraction and other maths challenges

• Start by building your numicon “towers” flat on the tuff tray paper pad
• Then trace around the towers with your pen leaving an outline behind
• Your children will then be challenged to rebuild the towers to fit inside the outlines
• You can further supplement this activity with counting cubes. Why not try building towers that stand up independently?

Why not prompt your children with some questions:

• How many pieces do you use?
• What do the pieces add up to?

7. Sand Writing

• Number prompts (we used number tiles)
• This is a great activity to encourage children to practice their number mark making, understanding the shape of the numbers and generally become more familiar.
• By using sand, there is the added bonus that any mistakes can easily be brushed away and it provides children with a fun tactile and sensory experience with which to enjoy maths!
• Simply provide your little ones with a number – this could be presented visually or verbally depending on your child’s development level – then they will need to write this in the sand using their hands!

8. Target Tuff Tray

• Target tuff tray mat
• Encourage children to practice their hand-eye coordination and gross motor skills by throwing the bean bags onto the target mat to hit a number
• Why not encourage children to hit a particular number to make this more challenging? For example, try asking them “what number is missing, 1, 2, 4, 5” and see if they can correctly identify 3 and then hit it on the target
• Alternatively why not encourage children to complete a particular task depending on the number that they hit, for example, when a 1 is hit see if they can do a star jump, if a 2 is hit why not ask them to pat their head twice.

9. Shopkeeper Role Play

• Role play baskets, cash register, dressing up clothes, panels (optional)
• Set up a designated “shop” area. Children can be encouraged to use their imaginations for the items in their shop or various different resources can be gathered to be “sold” in the shop
• Talk your little ones through the different coins and their values – these can be made up depending on your child’s level of development
• During role play, guide the children in using the correct amount of money and counting out the change
• You could also engage your children in conversations about prices, quantities and costs. For example, “how much are these two items”, “do I have enough money for that toy?”

10. Pattern Practice

• Introduce your child to patterns and discuss what a pattern is by showing different examples
• Next create a basic pattern in front of the children for their reference and get them to identify what comes next in the sequence
• Then provide children with materials to start creating their own patterns using objects of different types, colour, shapes and sizes!

We hope you try some of these EYFS Numeracy Activities and enjoy them! If you have any activities you would like to share with the community then tag us in your posts on social media or use the hashtag #ExplorewithEYR to start the conversation!

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Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Early Years Foundation Stage Activities

Explanation of Our EYFS Format

Here you can find out more about how we structure our EYFS activities.

Early Years Activities - Number

Early Years Activities - Measures

Early Years Activities - Shape and Space

Early Years Activities - Pattern

Early Years Guide

Introduction.

The first few years of a child’s life are especially important for mathematics development . For many education experts, no other group represents a greater opportunity to improve mathematical standards than children in the early years.

The more grounded in mathematical concepts young children become, the better their later outcomes. Conversely, research shows that children who start behind in mathematics tend to stay behind throughout their educational journey.

On this page, we’ll examine:

• What do we mean by Early Years?
• What does learning look like in the Early Years?
• Why is Cognitive Load Theory so important?
• What mastery strategies are available for Early Years?

What do we mean when we talk about Early Years?

The UK government published the Statutory Framework for the early years foundation stage in March 2017. It sets standards for the learning, development and care of children from birth to five years old.

Areas of learning

The EYFS framework outlines seven areas of learning :

• Communication and language
• Physical development
• Personal, social and emotional development
• Mathematics
• Understanding the world
• Expressive art and design

Mathematics in EYFS

In the context of mathematics, the framework says children must be given opportunities to develop their skills in the following areas:

• Understanding and using numbers
• Calculating simple addition and subtraction problems
• Describing shapes, spaces, and measure

Revised guidance

The DfE published revised guidance in March 2021 to take effect in September 2021.

The mathematics component now incorporates many elements of the mastery approach.

Specifically, the revised framework says:

Children should be able to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers.

By providing frequent and varied opportunities to build and apply this understanding — such as using manipulatives, including small pebbles and tens frames for organising counting — children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built.

In addition, it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures.

It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

Early Learning Goals

The latest framework has the following early learning goals for mathematics:

Children at the expected level of development will:

• Have a deep understanding of number to 10, including the composition of each number
• Subitise (recognise quantities without counting) up to five
• Automatically recall (without reference to rhymes, counting or other aids) number bonds up to five (including subtraction facts) and some number bonds to 10, including double facts

Numerical patterns

• Verbally count beyond 20, recognising the pattern of the counting system
• Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity
• Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally

Reception class is the first year at primary school in England, generally for children ages four to five. Unlike every other school year, it’s not compulsory for children to attend Reception, though it’s a good way to introduce them to life at school.

Multi-academy trusts

Looking for impactful maths provision across your multi-academy trust?

Learning in the early years

The first few years of a child’s life are especially important for mathematics development , says the National Center for Excellence in the Teaching of Mathematics.

Research shows that early mathematical knowledge predicts later reading ability and general education and social progress.

As young as eight months old, children are developing an awareness of number names , and include these in their speech, as soon as they begin to talk. As children listen to the talk around them, they are introduced to numbers through opportunities that occur in everyday life, and experience a variety of number rhymes. This supports their growing knowledge of number names.

According to the NCETM, there are:

Six key areas of mathematical learning

Cardinality and counting, composition.

• Shape and Space

Looking briefly at each in turn:

When children understand the cardinality of numbers , they know what the numbers mean in terms of knowing how many things they refer to.

Comparing numbers involves knowing which numbers are worth more or less than each other.

Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding.

Developing an awareness of pattern helps young children to notice and understand mathematical relationships.

Shape and space

Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes

Measuring in mathematics is based on the idea of using numbers of units in order to compare attributes , such as length or capacity.

Learning to count in the early years is a fundamental skill and key to mastering mathematical concepts in the future, but there’s more to it than you might think, says Sabrina Pinnock, a primary school teacher in Yorkshire.

According to researchers Rochel Gelman and C.R. Gallistel, these are the steps needed to successfully count :

• The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted
• The stable order principle: children must know how to count in the right order
• The cardinal principle: children need to understand the last number in the set is the total amount
• Counting anything: children need to realise that anything can be counted, not just objects that can be touched, but also things like claps and jumps
• Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount

Assessing children to find out which step they are struggling with is key to helping them overcome difficulties and become confident counters.

How do children develop counting skills?

Very young children start to count spontaneously and later begin to refine their skills by pointing their finger at the objects they are counting.

They will often try to get all the names of the numbers they know into their count as they pass their finger along the objects. They also reuse numbers. If they have not finished and they have used up all their known numbers, they will begin using the same numbers again. For example, a child might decide to count eight shells she collects at the beach. She might line them up carefully, tag numbers to them by pointing as she slides her finger along the shells, quickly counting out loud, “one, two, three, four, five, one, two, three, four, five, one, two, three.”

In their drive to make meaning, children are eager to experiment as they acquire new small bits of mathematical knowledge. It is extremely important to respect their developing understanding and not expect “perfect” counting sequences.

By valuing children’s partial understanding, children will develop enthusiasm for numbers and become confident mathematicians.

Activities to boost number sense in Reception Year

Children need lots of opportunities to develop number sense and deepen their conceptual understanding. Here are some simple activities to get your Reception Year learners counting:

Crowd control

Display the number of children allowed in each area using pictorial representations of cubes on a 10 frame. Once the children begin to realise how many are allowed in the area, they start to discuss the meaning of more and less. For example, “no more children are allowed in,” or “you can come in because one more than three is four.”

Encourage children to show numbers using their fingers above their head. “Bunny ears six” means they place their fingers above their head to show six. They may decide to use three fingers on each hand. As they become more confident, you could introduce swapping, where they show the same number but with a different configuration of fingers, in this case two and four, or five and one.

Grouping straws

Each morning, drop different amounts of art straws all over the carpet. Say something like, “oh no class, I can’t believe it. I’ve dropped all my straws again. They were all in 10s. Can you help me?” This activity helps children consolidate counting objects and gets them to think about stopping after they have made 10. Providing elastic bands helps them to keep track of their groups of 10.

Fastest 10 frames

This game can help distinguish between those who have developed a good understanding of number sense and those who need further support. Give each child their own frame and cubes. Tell them a number and observe how they place the cubes on the frame. If the children are working with the number eight, do they say each number name as they place the cube on the frame, or do they realise eight is two less than 10? If so, they should be able to place the cubes down faster than other children.

What do they do when you say the next number? For example, for the number five, do they automatically remove three cubes, or do they remove all of the cubes and start over counting from one to five?

Everyday questions to develop number sense

These questions for children aged five to six help develop their number sense and let them practice using mathematical terms.

When prepping lunch or a snack, count out the different types of food with your child, and as you lay the table, count out the different items. Ask your child questions like:

• How many grapes are there?
• How many tomatoes are there?
• How many plates are there?

Practice using the terms more than, fewer than and as many as by asking:

• Are there more grapes than tomatoes?
• Are there fewer tomatoes than grapes?
• Are there as many plates as people eating?

Remember to practice each sentence:

• There are more grapes than tomatoes
• There are fewer tomatoes than grapes
• There are as many plates as family members eating

When counting, make sure that you count one number for one item to strengthen your child’s sense of one-to-one correspondence.

Number Rhymes

Carefully select number rhymes to include those that children are familiar with from home. Make sure the rhymes include:

• Counting back and counting forward
• “No” or “none” (Five little ducks went swimming one day)
• Counting in pairs (two, four, six, eight, Mary at the cottage gate)
• Counting to five, 10 and beyond

Problem solving, reasoning and numeracy

The EYFS requires children to be supported in developing their understanding of problem solving, reasoning and numeracy in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. They must be provided with opportunities to practise these skills and gain confidence.

Young children learn best through play. For their learning to be effective, they need sensitive and informed support from adults.

All children can be successful with mathematics, provided they have opportunities to explore ideas in ways that make personal sense to them and opportunities to develop concepts and understanding. Children need to know that practitioners are interested in their thinking and respect their ideas.

Foundations

Maths — No Problem! Foundations is designed with all the theory and rigor that underpins a true mastery approach. It meets all the requirements of the national curriculum’s Early Years Foundation Stage. But Maths — No Problem! Foundations doesn’t shy away from embedding learning through play in Reception.

Genuine learning through play in the early years is something the team at Maths — No Problem! gets very excited about. What may appear to be simple games are actually carefully designed activities that have a deep maths mastery focus.

Maths — No Problem! Foundations is a complete Reception programme that includes Workbook Journals, Picture Books, and online Teacher Guides with printable resource sheets, all in one package.

The Maths — No Problem! suite of products — including textbooks, workbooks, a revolutionary online assessment tool, world-class teacher training, and much more — is based on the Singapore method, which combines 30 years of international research with painstaking craftsmanship and constant refinement.

Mark making

Research from Carruthers and Worthington into children’s mathematical graphics reveals young children use their own marks and representations to explore and communicate their mathematical thinking. These graphics include:

• Scribble-marks
• Tally-type marks
• Invented and standard symbols including numerals

Young children’s graphical exploration “builds on what they already know about marks and symbols and lays the foundations for understanding mathematical symbols and later use of standard forms of written mathematics,” the researchers said.

In a 2009 publication, the UK Department for Children, Schools and Families, says practitioners should: “Value children’s own graphic and practical explorations of problem solving” and observe “the context in which young children use their own graphics.”

Developing understanding with careful questioning

When children play and interact with other children, there are always opportunities for maths talk to help them develop a deep understanding, says Sabinra Pinnock.

For instance:

• I have made a pattern. What’s your pattern?
• How many blocks taller is my model compared to yours?
• How do we know this area is full?
• I have three cars, how many do you have?
• Do you have more?
• How do you know?

Give learners long enough to think about their answer and give their response, but not so long that it disrupts the flow of play.

Adding maths talk activities to your daily routine

Developing maths talk in your daily routine gives learners a chance to understand concepts while using real-life concepts. It also means that children can consolidate what they have learned.

The following activities can get you started:

How many children are at school?

Get your class to work out how many children are at school by placing a picture of themselves or a counter representation on large 10 frames. Ask them questions like:

• How do we know this 10 frame is full?
• How many children are absent?
• What can you tell me about number seven?

Sorting and grouping objects as a class

Sorting and grouping objects as a class helps children learn to reason and look for patterns. Give them a variety of buttons each day and ask open-ended questions like, “how can we sort the buttons?” They can use critical-thinking skills to come up with a range of ideas like sorting by size, colour, pattern, and shape.

Vote for a story

First, ask a child to pick two books. Everyone in the class gets to vote (using a piece of lego, for instance) on which of the books should be read. Tally the votes at the end of the day to determine the winner. This can lead to questions such as:

• How many more votes did one book have than the other?

The key to introducing mastery in the early years is to keep activities fun and part of your daily routine. The more learners explore maths through play, the more engaged they become.

Pattern Awareness

Dr. Sue Gifford, emeritus fellow at University of Roehampton, says recent research shows a child’s ability to spot mathematical patterns can predict later mathematical achievement, more so than other abilities such as counting. It also shows pattern awareness can vary a great deal between individuals.

Australian researchers, Papic, Mulligan and Mitchelmore have found pattern awareness can be taught effectively to preschoolers, with positive effects on their later number understanding.

Explicitly teaching pattern awareness links to encouraging “pattern sniffing” with older children in order to develop mathematical understanding and thinking.

What is mathematical pattern awareness?

Patterns are basically relationships with some kind of regularity between the elements. In the early years, Papic et al suggest there are three main kinds:

• Shapes with regular features, such as a square or triangles with equal sides and angles, and shapes made with some equally spaced dots
• A repeated sequence: the most common examples are AB sequences, like a red, blue, red blue pattern with cubes. More challenging are ABC or ABB patterns with repeating units like red, green, blue or red, blue, blue
• a growing pattern, such as a staircase with equal steps

Children who are highly pattern aware can spot this kind of regularity: they can reproduce patterns and predict how they will continue.

Why is pattern awareness important?

Spotting underlying patterns is important for identifying many different kinds of mathematical relationships. It underpins memorization of the counting sequence and understanding number operations, for instance recognizing that if you add numbers in a different order their total stays the same.

Pattern awareness has been described as early algebraic thinking, which involves:

• Noticing mathematical features
• Identifying the relationship between elements
• Observing regularities

The activity Pattern Making focuses on repeating patterns and suggests some engaging ways of developing pattern awareness, with prompts for considering children’s responses. Children can make trains with assorted toys, make patterns with twigs and leaves outside or create printing and sticking patterns in design activities.

Repeating Patterns

It is important to introduce children to a variety of repeating patterns, progressing from ABC and ABB to ABBC.

Focusing on alternating AB patterns can result in some young children thinking that ‘blue, red, red’ can’t make a pattern. They say things like, “That’s not a pattern, because you can’t have two of the same colour next to each other.”

Cognitive Load Theory

Cognitive Load Theory has gained a lot of traction in recent years as educators embrace evidence-based research to inform their evolving practice, says Ross Deans, a KS2 teacher and maths lead in Bournemouth, England.

What is Cognitive Load Theory and why is it important?

Why are new teachers so overwhelmed by tasks that more experienced teachers can juggle alongside multiple other responsibilities?

The answer is simple — new skills demand more attention.

This logic can be applied to any situation. When learning to drive, for example, you focus carefully on every small detail. That mental exertion can be very demanding. Compare that to the feeling of driving after you’ve been doing it for years; you may barely remember the drive, the process is so familiar.

Now put yourself in the shoes of your pupils. Each lesson provides fresh learning and new skills to master. Consider what happens inside your learners’ heads when they encounter new information, new skills and new vocabulary.

Working memory

Cognitive Load Theory , originated by John Sweller, acknowledges that working memory is very limited.

Working memory is the information we hold in our minds while we’re learning. The number of things that we can keep in working memory at one time is approximately four, plus or minus one, and perhaps even less for children.

It’s important to keep this in mind when planning and delivering lessons. If our learners cannot balance more than four things in their working memory, then we need to be very careful about the information we choose to present to them.

Intrinsic versus extraneous load

Intrinsic load includes anything that is necessary to learn a desired skill. In other words, the essential stuff.

Extraneous load is anything that will detract from desired learning. In other words, the stuff that should be reduced as much as possible.

It can be tempting while teaching to embellish lessons with child-friendly imagery and gimmicks. While It’s important to foster enjoyment, we should avoid distracting learners from the essential components of a lesson.

Supporting the transition to long-term memory

While acknowledging the impact of Cognitive Load Theory, we can consider the following to support our learners:

Focused learning objective

First and foremost, we must have a very clear idea of what we want our learners to achieve. Keep the limitations of the working memory in mind and let this guide the content you choose to include in a lesson.

Activate prior learning

At the start of the lesson, you may choose to design a task that encourages learners to retrieve essential skills. This means their working memory can hold on to new learning during the lesson.

Present information clearly

Take time when designing lessons to make sure information is presented clearly. Avoid unnecessary extras which may detract from the learning goal. Keep slides clean and similar in style.

Avoid cognitive overload

In maths, problems are often detailed and complex. Consider breaking questions up into chunks so that learners can digest each part separately. By taking away the final question, you can make a maths problem goal-free.

Maths mastery for Early Years

Given the importance of developing sound mathematical understanding in the early years, the maths mastery approach can be especially useful, considering its focus on problem solving and whole-class learning.

Early Years and CPA

If you’re teaching the Concrete, Pictorial, Abstract (CPA) approach in the early years, it’s best to focus on C and P. Here’s how to use concrete and pictorial representations effectively.

The CPA model works brilliantly in the primary years but for the youngest learners, moving onto abstract concepts too soon causes difficulties. Spending as much time as possible with concrete objects and pictorial representations helps children master number skills.

By the time they reach Key Stage 2, children need to develop their understanding of numbers by being able to visualise what the concrete looks like in their heads. Therefore, it’s positive that the revised EYFS framework focuses on numbers just to 10, from 20 previously.

If learners develop a deep understanding of numbers to 10, their chances of understanding larger numbers increases significantly.

C is for concrete

Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects.

Spending time with real-life objects

The theorist Jerome Bruner stresses the importance of children spending time learning maths through tangible items. Spending lots of time using real-life objects, solving real-life problems, and manipulating abstract concrete objects (when ready) such as cubes and counters is essential in the early years.

Ideas include counting out fruit for snack time, comparing, sorting and counting a range of different buttons, pasta, and even ‘magic beans’ linked to specific topics.

Early years and number bonds

By mastering number bonds early on, pupils build the foundations needed for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can decide what action to take when trying to solve problems in their head.

How to teach number bonds

Children are usually introduced to number bonds through the Concrete, Pictorial, Abstract approach . Here’s just one way to introduce and teach number bonds.

Concrete step

Children start out by counting familiar real-world objects that they can interact with. They then use counters to represent the real-world objects. From here, they progress to grouping counters into two groups.

By putting five counters into two groups, children learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration, children work out other ways to break numbers into two groups.

Pictorial step

Now that they understand the concept with hands-on objects and experience, children progress to writing number bonds in workbooks or on whiteboards. Early number bond explorations might simply reflect the two groups of counters that they created during the concrete step, along with other combinations.

Abstract step

With the concrete and pictorial steps done and dusted, children progress to representing abstract problems using mathematical notation (for example, 3 + 2 = 5).

Early Years and place value

Number and place value are foundational concepts for all mathematics learning. This means we need to address how to teach place value as early as possible so that pupils can secure their knowledge of the concept.

How do you develop an early understanding of place value in the primary school classroom? Let’s start by defining place value. It is a system for writing numerals where the position of each digit determines its value. Each value is a multiple of a common base of 10 in our decimal system.

Here are some teaching strategies I’ve found useful when helping learners develop an early understanding of place value.

Progress through concepts systematically

Developing an understanding of place value requires systematic progression. Each new concept should build on previous learning experiences so that pupils can gain deeper, relational understanding as they go.

This approach ensures knowledge is developed, refined and applied correctly as numbers become meaningful tools for solving problems rather than just a series of symbols on a page. Most importantly, this starts our learners on the path to becoming confident problem solvers and pattern spotters.

Use the CPA approach to establish meaning

The CPA ( Concrete, Pictorial, Abstract ) approach helps pupils connect a physical representation of a number (concrete manipulatives) to that same quantity as shown in drawings or graphics (pictorial), and finally to the actual written name and symbol for that number (abstract).

Concrete resources are meaning makers. They add meaning to abstract representations of numbers so that when learners progress to the abstract phase, they know what those numbers stand for, what they mean, and how they relate to each other.

If a pupil can identify the meaning of each component in a problem, they are far more confident in how they work to solve it.

Teach the ‘10-ness of 10’

At an early level, spend as much time as possible studying the numbers from 0 to 10, as understanding the 10-ness of 10 is crucial for maths attainment, and it cannot be rushed.

Once this understanding is locked-in, follow this with an introduction to number bonds. Start with the additive relationships between numbers less than 10, then progress to adding and subtracting up to 10. This ensures that learners see 10 as an important ‘base’ number in all of their future maths applications.

Progress to 20, then to 40

I make sure to take my time teaching 10 and teen numbers so that a solid understanding of place value with numbers up to 20 is properly established.

I then extend the place value concept by working with numbers up to 40 — followed by addition and subtraction to 40.

Because pupils have learned to make 10 and use number bonds, they are ready to begin working with multi-digit numbers and regrouping. Focusing on numbers to 40 while developing the concept of place value also allows learners to associate numbers with easily-managed, physical quantities (meaning makers).

Use base 10 blocks for 100 and 1000

The work we’ve done building a gradual understanding of place value will have prepared pupils to progress to three-digit numbers. So we can now move on to studying up to 100.

We start here by developing an understanding of numbers in multiple place value representations. For example, one thousand five hundred is 15 hundreds or 150 tens.

Once they get the hang of that, learners then sharpen their counting, reading, and writing skills for numbers up to 1,000. Moving into addition and subtraction with numbers up to 1,000 — with and without regrouping — is the next step.

Here is where our work establishing an early understanding of place value is key, because pupils will intrinsically know why these algorithms work for three and four-digit numbers. Base 10 blocks are a great tool to help solidify those earlier place value ideas when working with numbers up to the thousands.

Approach larger numbers the same way

The CPA approach is once again our answer to learning place value in larger numbers. Apply those skills and always be on the lookout for chances to extend number and place value concepts.

For example, you can identify and complete number patterns or find missing digits on a number line.

From there you can explore strategies for mental mathematics as well as addition and subtraction for numbers up to 10,000. Take learners even deeper by having them explore place value with an emphasis on multiplication, division, and decimals.

Mastering maths concepts like place value in the early years is not just key to success in the classroom. It prepares learners for a lifetime of deep mathematical understanding by giving them invaluable real-world tools like resilience and problem-solving ability.

And a confident problem solver in maths is a confident problem solver in life.

Well done on making it to the end of our Ultimate Guide to Early Years.

We’ve looked at the definition of Early Years and what the government recommends in its revised guidance, and we’ve taken a deep dive into some of the most-effective strategies for teaching mathematics mastery in the Early Years.

We’ve also discussed Cognitive Load Theory and what it means for teachers in the Early Years classroom.

If you’d like to learn more about Early Years, we recommend checking out the following links:

• NCETM: How Early Years children develop mathematical thinking (Podcast)
• NRICH: Early Years Foundation Stage Homepage
• The School of School: Episode 17 Play and early years (Podcast)
• Maths — No Problem! CPA approach

Also, don’t miss our other Ultimate Guides:

• The Maths — No Problem! Ultimate Guide to Maths Mastery
• The Maths — No Problem! Ultimate Guide to Assessment

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EYFS best practice - All about ... problem-solving

Mathematics in the EYFS is called Problem Solving, Reasoning and Numeracy. It's an odd title, probably chosen because it has a rhythmic assonance with Knowledge and Understanding of the World and Communication, Language and Literacy. It's odd, first because problem-solving and reasoning are applicable across all learning, not just maths, and second, because maths is about more than numeracy.

My dictionary defines being 'numerate' as 'able to perform arithmetical operations'. But 'mathematics' has a much wider definition: 'the science dealing with measurements, numbers, quantities, and shapes'. That's a gripe of mine, but let's focus on problem-solving and reasoning. Each of the areas of learning could have had 'problem solving, reasoning and ...' added to their titles.

UNPICKING THE EYFS

The Early Years Foundation Stage has a mixture of very clear, brief descriptions of learning development and more complex general ones.

Simple and brief:

'Continue a rhyming string'; 'respond to simple instructions'; 'handle books carefully'; 'recognise numerals 1 to 5'; 'say the number that is one more than a given number'; 'select a particular named shape'; 'use simple tools competently and effectively'; 'notice and comment on patterns'; 'sing a few familiar songs'; 'go backwards and forwards as well as sideways'.

Complex and general:

'Have an awareness and pride in self and as having own identity and abilities'; 'question why things happen, and give explanations'; 'use language for an increasing range of purposes'; 'use talk to connect ideas, explain what is happening and anticipate what might happen next'; 'use writing as a means of recording and communicating'; 'use developing mathematical ideas and methods to solve practical problems'; 'describe solutions to practical problems, drawing on experience, talking about own ideas, methods and choices'; 'explain own knowledge and understanding, and ask appropriate questions of others'; 'collaborate in devising and sharing tasks, including those which involve accepting rules'; 'talk about personal intentions, describing what they were about to do'; 'work creatively on a large or small scale'.

It is easy to allocate the simple descriptions to particular curriculum areas, and these are recognisable discrete skills that we know we have to teach. 'Continue a rhyming string' is language and 'recognise numerals 1 to 5' is maths.

The general descriptions are harder to allocate, unless there are clues like 'mathematical' and 'writing'. These complex statements have embedded in them a problem-solving approach. How do you teach 'question ...', 'collaborate ...', 'pride ...', 'personal intentions ...'? Well, you don't. You have to set up the environment and the ethos that will encourage these things, and support the children with planned interventions.

It's difficult working with such a mix of complex concepts. You know how to approach 'begin to form recognisable letters' and 'select a particular named shape'. You show children how to form letters. You teach them the names of the shapes. But how do you ensure that this develops into 'use writing as a means of recording and communicating' and 'use developing mathematical ideas and methods to solve practical problems'?

What are the children learning?

Clearly, children are learning about shapes and how they move and fit together; about how to manipulate large objects; about relative heights; about hollow and solid shapes; about filling spaces; about the properties of materials. But they are also learning about collaboration and working to a common goal, and about perseverance; and above all, they are setting themselves problems that they have to solve.

The work in the case study below involved a problem-solving chain, each one with its own goal to be set, obstacles to be overcome, and the solution to be found. One goal is to build a tower with tyres, but the problem is how to lift and place the tyres.

Another goal is to fetch the tyres to add to the tower, but the problem is how to get the tyres to the tower. Another goal is to make the tower as tall as possible, but the problem is how to reach the top of the growing tower - and so on.

Seeking solutions to the problems involves analytical reasoning, conscious or unconscious. How do I move the tyre? Turn it into a wheel by putting it on its edge and rolling it.

Later, during circle time, the children talked about their play with the tyres. Although there was not a lot of talk during the activity, just brief and necessary instructions and comments, the children were able to put into words what they had been doing.

THE NATURE OF PROBLEM-SOLVING

Problem-solving is an integral part of everyday provision, an expectation rather than an added extra, and it relies on a 'have a go' ethos. Successful problem solvers have these kinds of strategies:

- setting themselves a goal - recognising there are obstacles in the way of the goal - getting a feel for the nature of the obstacles - having a sense of possible ways of overcoming the obstacles - planning ahead, and predicting what will happen - checking progress as they go - trying out different possibilities in a systematic way - trying different approaches to see which will work best - looking for even better solutions.

Children who feel confident and secure in their surroundings, and free to make choices, are better able to solve problems, both on their own and collaboratively.

Problems can be minor and arise incidentally, or they can be major projects. But the most important thing is for children to set themselves a challenge, or to engage with the challenge that is there, and then to know that they can choose their own ways of solving it. If children are told the problem and then told the method to use to solve it, they are not problem-solving.

To become confident, proficient problem solvers, it stands to reason that children must have access to a wide range of appropriate resources they can use independently.

The ethos of the setting must support their investigations and allow them to move resources between areas of provision. For example, the children working with the tyres knew with confidence that they could move the tyres around, they could fetch a chair, and they could empty into the tower a range of objects at their disposal, without adult intervention. One of the important things about problem-solving is that it involves choice and that children have opportunities to reason and make decisions.

WHY IS PROBLEM-SOLVING IMPORTANT?

Two highly influential thinkers have stressed the importance of problem-solving as a vehicle for learning: Piaget and Vygotsky.

Piaget thought that children under seven saw the world differently from older children and adults, and they need time to explore the world in their own way. These are some of Piaget's key ideas:

- Children need to be in charge of their own learning by choosing their own activities and taking their own time in that exploration.

- We should provide children with materials to explore, such as block play, role-play materials, small-world toys, and so on. We should involve children in planning the uses of these resources, such as setting up a shoe shop or organising a picnic.

- We need to observe children to find out what they are focusing on and what their interests are, and respond to them if they ask for it. Our role as an adult is as a facilitator in their play.

- We should be aware of the stages of learning that children go through so that we can offer appropriate materials and activities for each stage, and note when children become 'ready' for the next stage.

- We should value each child as an individual.

Vygotsky emphasised collaborative and guided problem-solving. He focused on the social aspect of children's learning, and how they develop their thinking skills through shared experiences. This meant that language is a vital tool for thinking and for sharing ideas. He also looked at the roles of older children and adults in influencing learning. These are some of Vygotsky's key ideas:

- Children learn best through active self-directed play.

- Children learn more effectively in collaboration with other children and with adults.

- Our role is to offer help and support in helping children learn how to do things they cannot quite do on their own. Language is very important here.

- We need to observe children to find out where they are on their own learning trajectory.

- We must focus on language, as this is vital in helping children make sense of the world.

- We must be sensitive in how we take part in children's learning. Sometimes we can take the lead and instruct, at other times we will have minimal engagement.

The EPPE (Effective Provision of Pre-School Education) project corroborated Vygotsky's ideas, by finding that quality conversations between adults and children, and children and other children, enhanced children's problem-solving and reasoning skills. The work of the nursery settings in Reggio Emilia also puts into practice Vygotsky's ideas, with children and adults working collaboratively on long and complex projects.

Children's thinking will only develop well if they can spend their time solving problems. As they solve problems, their confidence and self-esteem increases. However, their self-esteem will decline if they fail too often to solve a problem. The role of the adult is so important in providing appropriate help, support, knowledge and skills.

Problem-solving involves reflection and thought. The adult can help by modelling strategies and encouraging children to talk about their methods. Children can develop a range of methods by collaborating with adults and with other children, and by discussing the range of methods.

HELPING CHILDREN BECOME PROBLEM-SOLVERS

- Create an atmosphere where exploration and having a go are more important than getting the right answer or doing the expected thing to please an adult.

- Provide a rich and stimulating environment, with plenty and varied activities, and don't make things too easy for the children.

- Be an opportunist and look for problem-solving possibilities in everyday activities, such as parties, picnics, tidying-up, arriving and leaving, charity events, a new baby, children's own interests.

- Approach everyday activities as problem-solving opportunities. In adult-led guided learning sessions, make sure children have choices within the framework of the objectives of the session. For example, if children are focusing on counting, play an interesting game that involves choices.

- If children ask you to be involved in their problem-solving, prompt them with comments or questions that will help them to continue to grapple with the problem themselves, or supply further resources that will keep the problem with them. A comment or a look can be as effective as questioning. Certainly, asking questions should not be an inquisition, but a collaborative conversation.

What do you think would help you to reach up there?

Mmm ... I don't know ... What have you tried so far?

Why didn't that work? I wonder if there is another way of doing it.

I wonder if we need anything else here to help us.

How does it look now?

I'm not sure I can do it either! Let's have another go.

- In group sessions, encourage children to describe their play, and the problems they tackled and overcame. Invite them to share ideas and thinking to show what they have done.

- If children are becoming frustrated, or if you feel they are on the cusp of new learning, introduce them to a technique or strategy for taking them on to the next step of learning. You can suggest breaking the problem down into smaller steps, or draw their attention to key features or clues.

- On the other hand, also allow children to get into a muddle so they can see that they need to think things through and develop systematic strategies. Don't take the problem away from the children. Healthy confusion is a good starting point for trying to sort things out.

- Make sure that children have long, uninterrupted periods of time at their own self-directed play.

- Observe children regularly to gain insights into their learning. Analyse and interpret these observations to help understand how to support them in their further learning.

For children to engage in and learn from problem-solving, they need to solve problems that they understand, in familiar contexts, where the outcomes matter to them, either on their own or in collaboration with others. They need to have control over the problem-solving process, and the problems should involve knowledge and skills they are confident with. They should have the opportunity to talk about the process, and have adult help to scaffold smaller steps in the process where they need it.

Two boys are playing with the tyres in the outdoor area of the setting. Their play leads them to start piling one tyre on top of the other. There are lots of tyres lying around the grassy area, and gradually they collect them and add them to their growing cylindrical tower.

Two more children join them, but in a different activity. They each find a container - one a bucket and spade and the other a dustpan and brush - and they gather up leaves and twigs and stones and empty them into the growing tyre cylinder.

The children building the tower have difficulty manipulating the tyres, as they are big and unwieldy. They have to turn each one on its edge and try to roll the tyre along. Sometimes another child sees this going on and volunteers to help.

Lifting the tyres increasingly higher is also difficult and reqiures two children, at least. As the tower grows, one child runs off and fetches a chair, puts it up against the tower, and lifts each tyre up on top. Meanwhile, the fillers continue to collect material to put into the central cavity.

Now that the hole is deeper, they add larger items such as lumps of wood and bark from the digging area. There are eight or nine tyres, one on top of the other. The children work at this activity for an hour and a half with no adult intervention. There is an adult observing from time to time and making notes.

Early Years Practitioner

Hampstead, London

Putney, London

Notting Hill, London

Nursery Deputy Manager

Finchley, London

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EYFS best practice - All about ... problem-solving

Sheila Ebbutt, a freelance consultant and was formerly managing director of BEAM (Be A Mathematician) Tuesday, July 7, 2009

Responding to challenges and finding solutions is not confined to mathematics but arises in all areas of learning, says Sheila Ebbutt.

Mathematics in the EYFS is called Problem Solving, Reasoning and Numeracy. It's an odd title, probably chosen because it has a rhythmic assonance with Knowledge and Understanding of the World and Communication, Language and Literacy. It's odd, first because problem-solving and reasoning are applicable across all learning, not just maths, and second, because maths is about more than numeracy.

My dictionary defines being 'numerate' as 'able to perform arithmetical operations'. But 'mathematics' has a much wider definition: 'the science dealing with measurements, numbers, quantities, and shapes'. That's a gripe of mine, but let's focus on problem-solving and reasoning. Each of the areas of learning could have had 'problem solving, reasoning and ...' added to their titles.

UNPICKING THE EYFS

The Early Years Foundation Stage has a mixture of very clear, brief descriptions of learning development and more complex general ones.

Simple and brief:

'Continue a rhyming string'; 'respond to simple instructions'; 'handle books carefully'; 'recognise numerals 1 to 5'; 'say the number that is one more than a given number'; 'select a particular named shape'; 'use simple tools competently and effectively'; 'notice and comment on patterns'; 'sing a few familiar songs'; 'go backwards and forwards as well as sideways'.

Complex and general:

'Have an awareness and pride in self and as having own identity and abilities'; 'question why things happen, and give explanations'; 'use language for an increasing range of purposes'; 'use talk to connect ideas, explain what is happening and anticipate what might happen next'; 'use writing as a means of recording and communicating'; 'use developing mathematical ideas and methods to solve practical problems'; 'describe solutions to practical problems, drawing on experience, talking about own ideas, methods and choices'; 'explain own knowledge and understanding, and ask appropriate questions of others'; 'collaborate in devising and sharing tasks, including those which involve accepting rules'; 'talk about personal intentions, describing what they were about to do'; 'work creatively on a large or small scale'.

It is easy to allocate the simple descriptions to particular curriculum areas, and these are recognisable discrete skills that we know we have to teach. 'Continue a rhyming string' is language and 'recognise numerals 1 to 5' is maths.

The general descriptions are harder to allocate, unless there are clues like 'mathematical' and 'writing'. These complex statements have embedded in them a problem-solving approach. How do you teach 'question ...', 'collaborate ...', 'pride ...', 'personal intentions ...'? Well, you don't. You have to set up the environment and the ethos that will encourage these things, and support the children with planned interventions.

It's difficult working with such a mix of complex concepts. You know how to approach 'begin to form recognisable letters' and 'select a particular named shape'. You show children how to form letters. You teach them the names of the shapes. But how do you ensure that this develops into 'use writing as a means of recording and communicating' and 'use developing mathematical ideas and methods to solve practical problems'?

What are the children learning?

Clearly, children are learning about shapes and how they move and fit together; about how to manipulate large objects; about relative heights; about hollow and solid shapes; about filling spaces; about the properties of materials. But they are also learning about collaboration and working to a common goal, and about perseverance; and above all, they are setting themselves problems that they have to solve.

The work in the case study below involved a problem-solving chain, each one with its own goal to be set, obstacles to be overcome, and the solution to be found. One goal is to build a tower with tyres, but the problem is how to lift and place the tyres.

Another goal is to fetch the tyres to add to the tower, but the problem is how to get the tyres to the tower. Another goal is to make the tower as tall as possible, but the problem is how to reach the top of the growing tower - and so on.

Seeking solutions to the problems involves analytical reasoning, conscious or unconscious. How do I move the tyre? Turn it into a wheel by putting it on its edge and rolling it.

Later, during circle time, the children talked about their play with the tyres. Although there was not a lot of talk during the activity, just brief and necessary instructions and comments, the children were able to put into words what they had been doing.

THE NATURE OF PROBLEM-SOLVING

Problem-solving is an integral part of everyday provision, an expectation rather than an added extra, and it relies on a 'have a go' ethos. Successful problem solvers have these kinds of strategies:

- setting themselves a goal - recognising there are obstacles in the way of the goal - getting a feel for the nature of the obstacles - having a sense of possible ways of overcoming the obstacles - planning ahead, and predicting what will happen - checking progress as they go - trying out different possibilities in a systematic way - trying different approaches to see which will work best - looking for even better solutions.

Children who feel confident and secure in their surroundings, and free to make choices, are better able to solve problems, both on their own and collaboratively.

Problems can be minor and arise incidentally, or they can be major projects. But the most important thing is for children to set themselves a challenge, or to engage with the challenge that is there, and then to know that they can choose their own ways of solving it. If children are told the problem and then told the method to use to solve it, they are not problem-solving.

To become confident, proficient problem solvers, it stands to reason that children must have access to a wide range of appropriate resources they can use independently.

The ethos of the setting must support their investigations and allow them to move resources between areas of provision. For example, the children working with the tyres knew with confidence that they could move the tyres around, they could fetch a chair, and they could empty into the tower a range of objects at their disposal, without adult intervention. One of the important things about problem-solving is that it involves choice and that children have opportunities to reason and make decisions.

WHY IS PROBLEM-SOLVING IMPORTANT?

Two highly influential thinkers have stressed the importance of problem-solving as a vehicle for learning: Piaget and Vygotsky.

Piaget thought that children under seven saw the world differently from older children and adults, and they need time to explore the world in their own way. These are some of Piaget's key ideas:

- Children need to be in charge of their own learning by choosing their own activities and taking their own time in that exploration.

- We should provide children with materials to explore, such as block play, role-play materials, small-world toys, and so on. We should involve children in planning the uses of these resources, such as setting up a shoe shop or organising a picnic.

- We need to observe children to find out what they are focusing on and what their interests are, and respond to them if they ask for it. Our role as an adult is as a facilitator in their play.

- We should be aware of the stages of learning that children go through so that we can offer appropriate materials and activities for each stage, and note when children become 'ready' for the next stage.

- We should value each child as an individual.

Vygotsky emphasised collaborative and guided problem-solving. He focused on the social aspect of children's learning, and how they develop their thinking skills through shared experiences. This meant that language is a vital tool for thinking and for sharing ideas. He also looked at the roles of older children and adults in influencing learning. These are some of Vygotsky's key ideas:

- Children learn best through active self-directed play.

- Children learn more effectively in collaboration with other children and with adults.

- Our role is to offer help and support in helping children learn how to do things they cannot quite do on their own. Language is very important here.

- We need to observe children to find out where they are on their own learning trajectory.

- We must focus on language, as this is vital in helping children make sense of the world.

- We must be sensitive in how we take part in children's learning. Sometimes we can take the lead and instruct, at other times we will have minimal engagement.

The EPPE (Effective Provision of Pre-School Education) project corroborated Vygotsky's ideas, by finding that quality conversations between adults and children, and children and other children, enhanced children's problem-solving and reasoning skills. The work of the nursery settings in Reggio Emilia also puts into practice Vygotsky's ideas, with children and adults working collaboratively on long and complex projects.

Children's thinking will only develop well if they can spend their time solving problems. As they solve problems, their confidence and self-esteem increases. However, their self-esteem will decline if they fail too often to solve a problem. The role of the adult is so important in providing appropriate help, support, knowledge and skills.

Problem-solving involves reflection and thought. The adult can help by modelling strategies and encouraging children to talk about their methods. Children can develop a range of methods by collaborating with adults and with other children, and by discussing the range of methods.

HELPING CHILDREN BECOME PROBLEM-SOLVERS

- Create an atmosphere where exploration and having a go are more important than getting the right answer or doing the expected thing to please an adult.

- Provide a rich and stimulating environment, with plenty and varied activities, and don't make things too easy for the children.

- Be an opportunist and look for problem-solving possibilities in everyday activities, such as parties, picnics, tidying-up, arriving and leaving, charity events, a new baby, children's own interests.

- Approach everyday activities as problem-solving opportunities. In adult-led guided learning sessions, make sure children have choices within the framework of the objectives of the session. For example, if children are focusing on counting, play an interesting game that involves choices.

- If children ask you to be involved in their problem-solving, prompt them with comments or questions that will help them to continue to grapple with the problem themselves, or supply further resources that will keep the problem with them. A comment or a look can be as effective as questioning. Certainly, asking questions should not be an inquisition, but a collaborative conversation.

What do you think would help you to reach up there?

Mmm ... I don't know ... What have you tried so far?

Why didn't that work? I wonder if there is another way of doing it.

I wonder if we need anything else here to help us.

How does it look now?

I'm not sure I can do it either! Let's have another go.

- In group sessions, encourage children to describe their play, and the problems they tackled and overcame. Invite them to share ideas and thinking to show what they have done.

- If children are becoming frustrated, or if you feel they are on the cusp of new learning, introduce them to a technique or strategy for taking them on to the next step of learning. You can suggest breaking the problem down into smaller steps, or draw their attention to key features or clues.

- On the other hand, also allow children to get into a muddle so they can see that they need to think things through and develop systematic strategies. Don't take the problem away from the children. Healthy confusion is a good starting point for trying to sort things out.

- Make sure that children have long, uninterrupted periods of time at their own self-directed play.

- Observe children regularly to gain insights into their learning. Analyse and interpret these observations to help understand how to support them in their further learning.

For children to engage in and learn from problem-solving, they need to solve problems that they understand, in familiar contexts, where the outcomes matter to them, either on their own or in collaboration with others. They need to have control over the problem-solving process, and the problems should involve knowledge and skills they are confident with. They should have the opportunity to talk about the process, and have adult help to scaffold smaller steps in the process where they need it.

Two boys are playing with the tyres in the outdoor area of the setting. Their play leads them to start piling one tyre on top of the other. There are lots of tyres lying around the grassy area, and gradually they collect them and add them to their growing cylindrical tower.

Two more children join them, but in a different activity. They each find a container - one a bucket and spade and the other a dustpan and brush - and they gather up leaves and twigs and stones and empty them into the growing tyre cylinder.

The children building the tower have difficulty manipulating the tyres, as they are big and unwieldy. They have to turn each one on its edge and try to roll the tyre along. Sometimes another child sees this going on and volunteers to help.

Lifting the tyres increasingly higher is also difficult and reqiures two children, at least. As the tower grows, one child runs off and fetches a chair, puts it up against the tower, and lifts each tyre up on top. Meanwhile, the fillers continue to collect material to put into the central cavity.

Now that the hole is deeper, they add larger items such as lumps of wood and bark from the digging area. There are eight or nine tyres, one on top of the other. The children work at this activity for an hour and a half with no adult intervention. There is an adult observing from time to time and making notes.

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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.

• Description
• Learning Outcomes
• Institution

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).