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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 mathematical investigation and exploration, 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 problem solving in mathematics can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand as 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, and where 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
Problem solving in mathematics 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 problem-solving skills and apply their mathematical knowledge.
You can effectively support children’s developing 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 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 – providing 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.
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 such as leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud, sand and 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, with sparkly marker pens and a shiny ‘Spell Book’ to stick these in and temporary mark-making opportunities such as chalk on slate.
The important thing with open-ended problem-solving experiences like this is to observe, wait and listen and 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, and the strategies they use to solve problems – what happens if they want eight pebbles and they run out? What do they do next?
When supporting children’s 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 – e.g. “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 – e.g. 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 problem-solving opportunities that extend this interest.
This activity offers opportunities for classifying, sorting, counting, adding, 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 (lining paper is great for this), using masking tape. 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 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 vehicles, make new ‘parking lots’ with masking tape, and create labels for the groups, if they choose.
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, with the children.
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 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, string.
● Rucksacks, water bottles, compass 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, and 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, and 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 explore measures (weight) as well as cooperating and finding 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: “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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10 Simple Activities to Teach Your Preschooler Problem Solving
By: Author Tanja Mcilroy
Posted on Last updated: 7 Nov 2022
Categories Cognitive Development
During the first years of a child’s life, an important set of cognitive skills known as problem-solving abilities are developed. These skills are used throughout childhood and into adulthood.
Find out what problem solving is, why it’s important and how you can develop these skills with 10 problem-solving games and activities.
What is Problem Solving in Early Childhood?
So, what exactly is problem solving? Quite simply, it refers to the process of finding a solution to a problem .
A person uses their own knowledge and experience, as well as the information at hand to try and reach a solution. Problem solving is therefore about the thought processes involved in finding a solution.
This could be as complex as an adult working out how to get out of a financial crisis or as simple as a child working out how two blocks fit together.
Problem Solving Skills for Kids
Problem-solving skills refer to the specific thinking skills a person uses when faced with a challenge. Some problems require the use of many skills, while others are simple and may only require one or two skills.
These are some examples of problem-solving skills for preschoolers , as listed by kent.ac.uk .
- Lateral thinking
- Analytical thinking
- Decision-making skills
- Logical reasoning
- Persistence
- Communication skills
- Negotiation skills
The Importance of Developing Problem-Solving Skills in Early Childhood
Problem solving is a skill that would be difficult to suddenly develop as an adult. While you can still improve a skill at any age, the majority of learning occurs during the early years.
Preschool is the best time for a child to learn to problem solve in a fun way. The benefits of learning early will last a lifetime and the beauty of learning anything at a young age is that it is effortless .
It is like learning to play an instrument or picking up a new language – it’s just much easier and more natural at an early age.
Of all the many things preschoolers need to learn , what makes problem solving so important?
There aren’t many situations in life, at work or at school that don’t require some level of problem resolution.
Child’s play itself is filled with opportunity upon opportunity to solve all kinds of tricky situations and come up with solutions to challenges.
Problem Solving in Preschool
During the foundational years, children are constantly solving problems as they play .
Here are just a few examples of problem solving in early childhood :
- Resolving a fight over the same toy
- Reaching a ball that’s stuck in the tree
- Forming a circle while holding hands
- Making a bridge to connect two block towers
- Tying or untying a shoe
- Making up rules for a new game
- Trying to get the consistency of a mud cake right so it stops falling over
The more creative play opportunities and challenges children are given, the more they get to exercise their problem-solving muscles.
During free play , there are non-stop experiences for this, and parents and teachers can also encourage specific problem-solving skills through guided activities .
Problem Solving for Older Children
During the grades, children experience problems in many forms, some of which may be related to their academic, social and emotional well-being at school. Problems may come in the form of dealing with life issues, such as:
- Problems with friendships
- Struggling to understand something during a lesson
- Learning to balance the demands of sport and homework
- Finding the best way to study for a test
- Asking a teacher for help when needed
Problems will also form a large part of academic life as teachers will be actively developing this skill through various activities, for example:
- Solving a riddle or understanding a work of literature
- Working on projects with a friend
- Finding solutions during science experiments
- Solving mathematical problems
- Solving hypothetical problems during lessons
- Answering questions and completing exam papers
Children who have had practice during preschool will be a lot more capable when facing these challenges.
Solving Problems in Mathematics
Mathematics needs to be mentioned separately as although it is part of schooling, it is such a huge part and it depends heavily on a child’s ability to solve problems.
The entire subject of mathematics is based on solving problems. Whether you are adding 2 and 3, working out how many eggs will fit into each basket, or solving an algebraic expression, there is a problem in every question.
Mathematics is just a series of problems that need to be solved.
What we refer to as problem solving in Maths is usually answering word problems .
The reason many children find these so difficult to answer is that the question is presented as a problem through a story, rather than just numbers with symbols telling you what operation to use (addition, division, etc.)
This means a child is forced to think carefully, understand the problem and determine the best way to solve it.
These problems can involve various units (e.g. mass, capacity or currency) as well as fractions, decimals, equations and angles, to name a few. Problems tend to become more and more complex over the years.
My experience in the classroom has shown that many, many children struggle with solving word problems, from the early grades right into the senior years.
They struggle to analyze the question, understand it, determine what information they’ve been given, and what exactly they are required to solve.
The good news is that exposing a child to regular problem-solving activities and games in preschool can greatly help him to solve word problems later on in school.
If you need one good reason to do these kinds of activities, let it be for a smoother experience in mathematics – a subject so many children unnecessarily fear.
Problem Solving in the Workplace
Adults in the workplace seldom thrive without problem-solving skills. They are required to regularly solve problems .
As adults, employees are expected to independently deal with the frequent challenges, setbacks and problems that are a big part of every working environment.
Those who can face and solve their own problems will go further and cope better than those who seek constant help from others or cannot show initiative.
Some career websites even refer to problem solving as a universal job skill. They also mention that many employees are not good at it.
Again, although it may seem far removed, learning this skill at a young age will help a child cope right into adulthood and in the working world.
How to Teach Children Problem-Solving Skills
If early childhood is the best time to grow these skills in your young children, then how does one go about teaching them to toddlers, preschoolers and kindergarteners?
Problem solving can be taught in such a way that you expose your child to various opportunities where they will be faced with challenges.
You would not necessarily sit your 3-year-old down and tell or “teach” him all about fixing problems. Instead, you want to create opportunities for your child to grow this skill .
Using the brain to think and find solutions is a bit like working a muscle over time. Eventually, your muscle gets stronger and can handle more “ weight. ” Your child will learn to problem solve in two ways:
- Incidentally – through free play
- Through guided opportunities provided by a parent or teacher
If you make a point of encouraging thinking through games and activities, your child will develop stronger skills than if you let it all happen incidentally.
Problem-Solving Strategies and Steps
If we take a look at the steps involved in solving a problem, we can see that there are many layers involved and different types of skills. Here are the problem-solving steps according to the University of Ken.
Step 1: Identify the problem
Step 2: Define the problem
Step 3: Examine the options
Step 4: Act on a plan
Step 5: Look at the consequences
Therefore, activities at a preschool level need not present complicated high-level problems.
- A simple activity such as identifying differences in a picture can work on the first skill needed – identifying a problem.
- Playing with construction toys can develop a child’s ability to try various solutions and examine the options when faced with a problem such as trying to find the best way to build something.
- Playing Tic-Tac-Toe would make a child predict the consequences of placing their mark in a particular square.
The most basic of activities can work on all these skills and make children competent solution finders.
How to Teach Problem Solving with Questions
The language you use around your child and your questioning technique will also greatly affect their understanding of a problem or challenge as merely something waiting for a solution to be found .
While your child is playing or when she comes to you with a problem, ask open-ended questions that will guide her in finding a potential answer independently. Use the steps listed above to formulate your questions.
Here are some examples of questions:
- What do you think made the tower of blocks fall down?
- If we build it again, how can we change the structure so that it won’t fall down next time?
- Is there a better way we can do it? If you think of a different way, we can both try it and see which works better.
- Did that work? The tower fell again so let’s try another solution.
Resist the temptation to fix every one of your child’s problems, including conflict with friends or siblings. These are important opportunities for children to learn how to resolve things by negotiating, thinking and reasoning.
With time, your child will get used to seeing a problem, understanding it, weighing up the options, taking action and evaluating the consequences.
Problems will be seen as challenges to be faced logically and not “problems.”
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10 Problem-Solving Activities for Preschoolers
Here are 10 simple, easy games and problem solving activities for kids at home or at school. Many of them are the kinds of activities children should have daily exposure to.
Puzzles are one of the best thinking activities out there. Each puzzle is basically one big set of muddled-up things to be sorted out and put back together again. Find out why puzzles are important for development .
Children should have regular exposure to puzzles. They are great for developing thinking skills.
2. Memory games
Memory games will develop your child’s memory and attention to detail.
Get your own memory game cards by downloading the FREE set of printables at the end of the post.
Use pairs of matching pictures and turn them all face down, shuffled, on a table. Take turns choosing any two cards and turning them face up on the table. If you turn over a matching pair you keep the cards and if the pair doesn’t match, turn the cards back over until it is your turn to try again.
Encourage your child to concentrate and pay attention to where the pictures are and try to find a matching pair on each turn.
3. Building with Construction Toys
Construction toys such as engineering blocks , a proper set of wooden blocks or Legos should be a daily staple in your home.
Everything your child builds is a challenge because it requires thinking about what to build and how to put the pieces together to get a design that works and is functional.
Leave your child to construct freely and occasionally set a challenge and ask him to build a specific structure, with conditions. For example:
- Make two towers with a bridge joining them together
- Build a creature that stands on its own and has 3 arms.
Then watch your child wracking his brain until he finds a way to make his structure work.
4. Activity Books
These activity books are really fun and develop a child’s ability to identify problems and search for information.
5. Following Patterns
This simple activity can be played with a set of coloured blocks , shapes or counters.
Simply make a pattern with the blocks and ask your child to continue it. Vary the pattern by changing the colours, shapes or sizes.
This activity will train your child to analyse the given information, make sense of it, recognise the pattern and re-create it.
6. Story Time Questions
Get into the habit of asking questions during your daily story time that develop higher-order thinking skills . Instead of just reading and your child passively listening, ask questions throughout, concentrating on solving problems.
Here are some examples:
- Why do you think the bear did that?
- Do you think his friend will be happy? Why?
- What would you do if you were the monkey?
- How do you think Peter can make things better with his friend?
- If the crocodile had decided not to eat the rabbit, how could the story have ended?
7. Board Games
Board games are an excellent way to develop problem-solving skills.
Start off with simple games like Ludo and Snakes and Ladders to teach the skill of following rules and moving in a logical sequence.
Card games like Go Fish are also great for teaching young children to think ahead and solve problems.
8. Tic-Tac-Toe
This is a perfect game to teach decision-making skills , thinking before acting and weighing up the possible consequences.
Use a Tic Tac Toe Board or d raw a simple table like the one above on paper or a chalkboard. Take turns to add a nought or a cross to the table and see who can make a row of three first.
Your child will probably catch on in no time and start thinking carefully before placing their symbol. This game can also be played with coloured counters or different objects.
9. Classifying and Grouping Activities
This activity can be done with a tin of buttons or beads or even by unpacking the dishwasher. The idea is to teach the skill of classifying and categorizing information by learning with physical objects. Here are some other ideas for categorizing:
- Separate the washing – mom’s clothes, dad’s clothes, etc; or socks, tops, shorts, etc.
- Empty out the cutlery drawer for cleaning, mix all the utensils up and then sort into knives, tablespoons, teaspoons, etc.
- Classify and sort out the toys in your child’s bedroom together – all books, construction toys, soft toys, etc.
Here are more button activities for kids .
10. Building a Maze
This activity is lots of fun and suitable for any age. It is also going to be way more fun than doing a maze in an activity book, especially for younger children.
Draw a big maze on the paving with sidewalk chalk . Make passages, including one or two that end in a dead-end. Teach your child to find her way out .
As your child gets better at figuring out a route and finding the way out, make the maze more complex and add more dead-end passages.
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Friday 3rd of June 2022
hi maam , This Is Uma from India,Can i get this in pdf format or a book. Thank You
Tanja Mcilroy
Monday 6th of June 2022
Hi Uma, thanks for your message. These articles are not available in PDF, but you are welcome to copy and paste them from the website, as long as you add the reference: https://empoweredparents.co/problem-solving-activities-preschoolers/ Thanks for reading!
Wednesday 20th of May 2020
Very very useful content. Good work. Thank you.
Friday 22nd of May 2020
Thanks Ann.
Tuesday 19th of May 2020
Would like to download the free activity pack please.
Hi Kelly, Please download the activity pack on this page: www.empoweredparents.co
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Problem Solving
A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.
Problem Solving in Primary Maths - the Session
Quality Assured Category: Mathematics Publisher: Teachers TV
In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.
In a second video two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.
Cards for Cubes: Problem Solving Activities for Young Children
Quality Assured Category: Mathematics Publisher: Claire Publications
This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.
Problem solving with EYFS, Key Stage One and Key Stage Two children
Quality Assured Category: Computing Publisher: Department for Education
These three resources, from the National Strategies, focus on solving problems.
Logic problems and puzzles identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.
Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .
Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.
Primary mathematics classroom resources
Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics
This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.
Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...
8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.
Number Picnic: The problems make ideal starter activities
Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.
Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.
GAIM Activities: Practical Problems
Quality Assured Category: Mathematics Publisher: Nelson Thornes
Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.
Examples include:
*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.
*Beach Guest House - Booking guests into appropriate rooms in a hotel.
*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.
*Design a Table - Involving diagrams, measurements, scale.
Go Further with Investigations
Quality Assured Category: Mathematics Publisher: Collins Educational
A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.
Starting Investigations
The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.
The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.
NRICH Primary Activities
Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!
Mathematical reasoning: activities for developing thinking skills
Quality Assured Category: Mathematics Publisher: SMILE
Problem Solving 2
Reasoning about numbers, with challenges and simplifications.
Quality Assured Category: Mathematics Publisher: Department for Education
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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:
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.
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
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.”
Foundations — Your Reception Solution
This Early Years mastery programme encourages learning through play and sets children on a path to a deep understanding of maths.
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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Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical
Foundation Stage Problem-Solving Activities: Reasoning and Numeracy EYFS. Mathematics is one of the seven areas of learning defined by the Early Years
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