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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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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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10 fun maths activities and games for the EYFS

With Famly since

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

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

1. Combine mathematical skills with fine-motor skills.

Number Hunt in Jelly by Hazeldene Family Centre

This fun maths activity:

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

What you need:

• Plastic Numbers

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

DIY Lego Pattern Cards by A Crafty Living

This fun maths game:

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

• Paper Cards
• Coloured Pencils
• LEGO Blocks

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

Missing Number Math Activity by Planning Playtime

This Early Years maths game:

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

• Craft Sticks (colour or plain)
• Clothes Pins

4. A simple game of swat the number.

Smack the Number Counting Game by Fun Learning for Kids

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

• One or two dice
• Fly swatter
• Sticky notes

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

Straw and Pom Poms Counting Game by Nurture Store

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

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

Get 50 free EYFS activities

6. A fun maths game to drive you dotty!

Number Dots and Easy Touch And Count Activity by Busy Toddler

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

7. A magnetic, mathematical, magical fishing game

Magnetic fishing number game by Messy Little Monster

This Early Years maths activity:

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

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

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

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

Egg Cracking Counting Activity by Modern Preschool

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

9. More fun in maths? Make it musical!

Top 10 Counting Songs by Super Simple Songs – Kids Songs

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

• A way to play music
• Your voice!

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

Valentine Math Activity – Broken Heart Numbers by Fun a Day

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

• Paper or card

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The big ideas

Official Danish Government Reopening Advice

Guidance from the Danish Health Ministry, translated in full to English.

UK Nursery Covid-19 Response Group Recommendations

The full recommendations from a working group of over 70 nursery chains in the UK.

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

Matt Arnerich

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

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• Eyfs Maths Activities Number Sense

EYFS maths activities – Early years and Y1 ideas

Play your way to a stronger number sense and get pupils off on the right foot with maths…

EYFS and Y1 are a time for building a love of numbers through counting, number rhymes and playing with the sound of number names . EYFS maths activities are therefore essential.

It’s where the foundations for maths are laid, and a great opportunity to show pupils just how enjoyable the subject can be!

There are various ways to make sure that pupils meet the expected progress while maintaining a sense of fun.

We simply need to make counting an adventure with some EYFS maths activities! Here are some ideas to get you started… 

Counting in movement

Make a circle with the class and count from zero to 10. Start by crouching down, then as the numbers get bigger, children grow upwards until they are standing and reaching up high. When they get to 10, they can jump! You could also incorporate this into daily exercise routines. 

Once they’ve mastered the concept, you can extend by counting from 10 to 20. Then start at 20 and count to 30, repeating in blocks of 10 until you reach 100.  

How about counting in 100s – start small again and count in hundreds to 1,000. Then in thousands to 10,000! You can also try counting in fives to 50, in twos to 20, and even counting backwards from 10, 20, or 100.  

Build up to starting at different/ random numbers to count on or back – an important skill. You can invite pupils to pick a number – maybe their front door number, the bus number they travel to school on, their big brother’s age, etc – and count on from there.  

Don’t worry if children can’t keep up all the time as they will enjoy the jumping and join in where they can, gaining practice and confidence as they go.  

Cross-curriculum EYFS maths activities

You can also incorporate counting practice into other subjects; you don’t have to explicitly teach a maths activities lesson to develop these skills.  

Why not try… 

• Use coloured spots to jump from one to another, tracing different paths while counting. 
• Throw bean bags into a bucket, counting at the same time from a given starting point. You could design this as a team game, an individual task or just taking turns as a whole class as part of a guided PE lesson. 
• Count with the children as you set up hoops around the hall, then ask them to count as they throw a given number of bean bags or other objects in each hoop.  
• Use a tennis ball or similar to throw and catch with a partner, bounce on the floor, bounce against a wall – how many catches or bounces can children do without dropping the ball? 
• Count actions such as star jumps, bunny hops, frog hops, rolls, turns, etc.  
• Use clapping patterns to count. Start with everyone clapping individually as you count, then clap and tap knees. Can anyone think of another simple pattern to clap? E.g. tap your head, clap, tap your head, clap, repeat. 
• Working in pairs, facing each other, use a simple clap-slap rhythm to start. Clap hands – right meets right – clap hands – left meets left – clap two hands together – then repeat. To extend, make up new rhythms and patterns. These are EYFS maths activities that children love to make up in the playground. 
• Play ‘pass an instrument’. While in a circle, a child counts four beats on a tambourine before passing it on, keeping the rhythm going. This is a great way to introduce counting ready for multiplication tables, using different amounts of beats. You can count in twos, three, fours, fives, etc. Repeat with different instruments – can you pass around two instruments together, then more? Work towards each child having an instrument to count with. Practise language skills by asking them to hold the instruments high or low, or to turn around, or swap with their neighbour and keep counting!   
• When baking, count the number of different ingredients you need for your recipe.  
• Count using eggs in boxes – if there are six eggs in each box in sets of twos, you can count in twos and sixes. 
• How many spoonfuls do you need of each ingredient to make a cake? How many stirs does each child have as they take turns to mix it? Count the cake cases; how many do you need to fill a tray? Arrange in sets of two, four or six to practise multiples. 
• Count the cooking time when using a microwave, counting the seconds in each minute as you wait for the timer to finish.  

Nursery rhymes and songs

• Nursery rhymes are great for developing a feel for rhythm, recognising rhymes and practising articulation with words. They are also great vehicles for counting – forwards and backwards! Begin with simple rhymes such as Baa, baa black sheep (demonstrating the number three); Round and round the garden (also showing three), and This little pig went to market (demonstrating five). Simple rhymes like this can help build up an understanding of small numbers and counting using fingers. 
• There are also lots of accumulative rhymes that start with a larger number and count backwards. Even though they seem tedious (they are quite long) children love them! Try Five little ducks went swimming one day , Ten green bottles , Ten fat sausages , There were ten in the bed , One man went to mow, etc. These EYFS maths activities can help pupils develop a good understanding of counting backwards that will really help them when they are ready for more formal calculations.  

Sorting and tidying

It goes without saying that counting can be integral to all activities that involve sorting, tidying and collecting.

Encourage your class to count while sorting and tidying up at the end of the day, using cars, Lego, home corner objects, books, etc.

You can count while collecting items outdoors, too, such as pebbles, conkers, and leaves. The list is endless.  

The value of counting

Counting confidently is a valuable skill that should not be underestimated.

Being able to count forwards and backwards will give a good grounding for all number work.

Remember, every time you are counting with your class, you are strengthening their early mathematical development. 

How many more ways can you find to count with your children? 

EYFS and Y1 maths guidance

Mathematics

• Developing a strong grounding in number is essential so that all children develop the necessary building blocks to excel mathematically.  
• 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.  

Early learning goals (ELG): numerical patterns

Children at the expected level of development will: 

• Verbally count beyond 20, recognising the pattern of the counting system.  
• Explore and represent patterns with numbers up to 10, including evens and odds.  

Y1 non-statutory guidance

Children should be able to: 

• Count within 100, forwards and backwards, starting with any number.  
• Count forwards and backwards in multiples of 2, 5 and 10, up to 10 multiples, beginning with any multiple, and count forwards and backwards through the odd numbers.  

Madeleine Fox is an educational writer and former SEN teacher. Download our pack of  Year 1 maths worksheets .

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• EYFS Statutory Framework

Problem Solving, Reasoning And Numeracy

By Guest, August 31, 2009 in EYFS Statutory Framework

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I'd be really interested to know anyone's experience of successful activities that have helped to engage children in aspects of problem solving, reasoning and numeracy. In particular, I'm looking for ideas of hands-on activities related to numbers, shapes, measuring and sums (the latter involving various types of calculation – addition, subtraction, multiplication, division, estimation etc). Activities that involve some type of physical or creative element would be ideal! Keen to bring some fun into mathematical learning, and to encourage children to explore for themselves.

Any ideas gratefully received. Thanks for your help!

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Welcome KDicker and congratulations on your first of hopefully many posts.

I'm unsure of the age you work in but I am in F2 and we used the outdoor area for many PSRN activities.

The children chose to play skittles and used addition, subtraction and estimation.

Hoops and bean bags were also successfullly used once more with addition. The children gave and marked each hoop with a number and then attempted to throw a specific amount of bean bags into the hoops. If they went in the hoop they were awarded the points. This worked particularly well for large number additions too.

Struggling now off the top of my head its way past my bedtime! I will give it some more thought, but I'm sure many other brilliant ideas will be here before then!

Many thanks for your ideas, so promptly! It's really useful to know what works well. Skittles and throwing into targets sounds fun.

I'm looking at pre-school in particular. And keen to bring in aspects of problem solving wherever possible – to get the children thinking for themselves.

Thanks for your help.

http://www.childcareland.com/teach.html

has some really good ideas that you can quickly adapt

we numbered our bikes and then made car parking spaces with chalk on the ground and encouraged the children to find the parking bay that corresponded with their bike number.

snack times ideas are good for simple problem solving, i sometimes dont put enough bowls out, so they have to work out how many more they need, or if too many out, how many more than we need.

addition and subtraction we do during singing with songs like- 5 green speckled frogs, men in a flying saucer etc...

Number recognition and counting

• Use a pegged number line for counting, matching, missing number and jumbled up number games.

• Make a moveable number line using yoghurt pots. Label the pots with numbers. Children choose correct number of objects to put inside each pot and place in order.

• Make a vertical number line, using the children's handprints.

• Make a tactile number line using materials such as sandpaper, fur, cord, velvet etc. for a multi-sensory approach.

• Label attractive boxes with different numbers. Children place correct number of natural objects in each box e.g. shells, fir cones, conkers, feathers

• Place a few wooden/plastic numbers in a feely bag. Can children pull out a given number by feel only?

• Place wooden/plastic numbers in separate envelopes. Slowly pull them out one by one to reveal a small part of the number. How soon before the children can guess what the number is?

• Hang number cards on a mug tree. Can children hang the correct number of objects on each mug peg? Use scrunchies, rubber bands, bracelets, curtain rings

• Hang numbered pockets on the wall. Children place correct number of items in each pocket.

• Thread correct number of cotton reels/beads on to numbered laces.

• Hold a small number of marbles in your hand and slowly drop one by one into a covered container. Children listen carefully and tell you how many you dropped in.

• Show a number of objects on the floor. Cover them up. Can the children remember how many?

• Go for a number walk with a number card. See how many times the children can see that number e.g. on a bus, shop, menu, house, car

• Go for a number walk and take photos of numbers in the environment. Make a display of the photos.

• Collect examples of numbers on packaging, magazines, labels etc. from the environment and set up a display.

• Stick a number on each side of a box/tin. Children clip the correct number of pegs to each side of the container.

• Hide pieces from a number jigsaw around the room. Children have to go and find the pieces, bring them back to a central point and help put the jigsaw together.

• Label bikes and create numbered 'parking bays'. See if the children can park their bikes in the correct bays.

• Play musical instruments behind a screen a certain number of times. Can children tell you how many bangs on the drum, shakes of the maracas etc?

• Play an instrument a certain number of times. Can the children play their instrument the same number of times?

• Sing and act out number rhymes and songs.

Sand, water and malleable materials

• Find foam numbers in water or sand

• Make numbers out of playdough

• Draw numbers with fingers in shaving foam/paint/gloop

• Catch given numbers of floating objects in nets.

• Fill and empty a variety of containers (tall, short, thin, wide, large, small etc.) with water, sand or materials such as lentils and rice.

Creative Area

• Make models with different sized, shaped, coloured and textured boxes and materials.

• Print with different shaped objects.

• Collage large numbers and shapes.

Cooking and snack time

• Make number shaped biscuits

• Stick certain number of currants/chocolate drops etc. on cakes/biscuits

• Make a recipe book using pictures and numbers of cupfuls/spoonfuls needed for each recipe.

• Make menus with prices, for the role-play cafe.

• Cut up fruit into segments and portions. Talk about halves, quarters and shapes.

• Encourage children to pour drinks for themselves.

• Share out biscuits/fruit together with the children.

• Count out fruit, biscuits, drinks

• Knock over numbered skittles

• Throw large dice and clap, jump, hop catch ball etc. correct number of times

• Throw correct number of beanbags into numbered containers

• Jump along numbered carpet tiles in order from 1-5/10

• Use large chalked shapes on the ground. Throw a shape dice, children run to correct shape. A harder version would be to add colours so children have to run to the red square, the green circle etc.

• Throw correct number of quoits over numbered cones.

Measuring and time

• Draw round hands and/or feet and cut out. Use for measuring activities and games.

• Give children a length of string, fabric or a ruler. How many things can they find that are longer/shorter?

• Place some pegs in a line on a pegboard. Can children add or take away pegs to make the line longer/shorter?

• Give children different sized containers. See how many conkers, cones, shells etc. they can fit inside them.

• Use role-play to encourage the children to find things to fit e.g. the right sized hat, belt, bag, container etc.

• Make a time line with photos of what the children do in the day e.g. register, snack, outdoor play ... encourage them to refer to it during the session.

• Use a sand timer at tidying up times in order to help children learn about the concept of time.

• Collect flat and 3D shaped items from the environment and make a display e.g. tins, food packets, money

• Stick a large favourite picture on to a piece of card. Cut into two or more shapes according to the ability of the child and see if they can put the picture together again.

• Carefully cut/break for example a toothpaste box, a flowerpot (watch edges) into pieces. Can the child put the item back together again?

• Play with flat shapes on the floor and find which are the same and which fit together.

• Cut sponges into different shapes and use to print shape pictures.

• Place shapes into a bag. Ask children to pull out a circle, a square, a curvy shape, a straight shape etc. by feel only.

• Go on a shape walk. Take a shape with you and look for that shape in the environment.

• Use shapes freely to make own pictures and patterns.

• Make shape biscuits.

• Make shapes with playdough.

• Mark out large shapes on the floor. Children run round to music and go and stand inside a given shape when the music stops.

• Children march/dance round to music. When the music stops, they make a shape with their body.

Questions to ask to help develop mathematical understanding and problem solving

• How much/many?

• How do you know how much/many?

• Are there enough?

• What can you tell me about...?

• How do you think you could...?

• Is there another way you could...?

• What's different/what's the same?

• Why did you choose this?

• What can you say about...?

• What might happen if...?

• Which of these go together?

• What comes next?

• What comes before?

• How did you guess?

• Why do you think...?

• Suppose...what do you think might happen then?

• What do we do now?

• Can you find one the same?

• Do you think this will fit/be enough?

• Which/who has more/less?

Can you make it smaller/bigger/longer/shorter...?

• What/who is first/second/last...?

• What could we use to help us?

• Why doesn't this work?

• What have you done so far?

• What else could we do to...?

• How did you work that out?

Thanks so much for all these great ideas. Lots of inspiration here! It is much appreciated. We will get going with our numbers exploration!

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EYFS Application Tasks

Task 1 Video

Task 1: Consider how challenge can be built within children's counting experiences in EYFS, with an emphasis on developing an understanding of quantity.

Task 2: read this article , which explains the importance of children's finger discrimination skills, and this article which explains the different concepts that fingers can develop. Here are some Finger Discrimination tasks by Youcubed .

Task 3 Video

Task 3: The Progression in Pattern document maps out how children's understanding of pattern can be deepened. Consider children's experiences of creating patterns in the EYFS provision.

Task 4: Consider how the subitizing cards, subitizing games and part-whole cards from the Early Number Sense resources can be used to develop children's fluency with small quantities. Also, think about how the Number Foundations Assessment can be used to assess children's early number or identify specific teaching points.

Task 5: This NCETM video shows children being taught to use finger gestures with accuracy. This NCETM video gives a range of ideas for playing with numbers inside and outside in EYFS.

Task 6: Consider the development of visual working memory, as described in this document.

Task 7: Watch the video below about laying the foundations for problem-solving by re-proposing play and engaging children in sustained shared thinking and reflect on the implementation of the principles in your setting.

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).