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Learning and Development
Maths problem-solving activities for Early Years settings
- Written By: Judith Dancer
- Subject: Maths
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?
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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- Maths: Open-ended Investigations
- Mathematical Problem-solving
Reception Maths: Open-ended Investigations Mathematical Problem-solving
Problem-solving tasks develop mathematical skills and problem-solving tactics. These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside.
Session 1 Shape
Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.
Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.
Shape Hunt By looking for and finding shapes, children gain an awareness of similarities of shapes in the environment. They match shapes by recognising similarities and orientation, show curiosity and observation by talking about shapes and begin to use mathematical names for shapes.
More Shapes By looking for and finding shapes formed by windows, children gain an awareness of shapes, practise matching them, and begin to use mathematical names for them. Use language such as ‘square’ to describe the shape of solids and flat shapes.
- More Shapes
Sorting While playing with and arranging twigs, stones, leaves, etc., children can be encouraged to take an interest in shape and space. They can talk about similarity and difference, while sorting objects. Developing mathematical ideas and methods can be used to solve practical problems.
Session 2 Position and Direction
Trails Remember… just about anything you do indoors in maths can be done outside. Some children ‘come alive’ once out of the classroom and may just surprise you with the observations they make or the learning behaviours they show.
Scooters, Bikes, Trikes Riding a scooter, bike or trike prompts counting, consideration of same and different, and position and spatial properties.
- Scooters, Bikes, Trikes
- The Mathematical Journey
Obstacle course Children use everyday language to talk about position, distance and time when running, or walking, an obstacle course. They compare quantities and objects and solve problems.
- Obstacle Course
Milk the Maths: Wellies Encourage children to use everyday language to talk about position whatever they are doing! Putting wellies away is a colourful opportunity.
- Milk the Maths
Session 3 Number and Shape
Holes When digging holes children can use number names in order in familiar contexts. They can use everyday language to talk about size, capacity, position, distance and time. Holes offer fun opportunities to compare quantities and objects and to solve problems.
The Mud Kitchen Ask children questions about shape, space and measure while exploring mud. Consider similarities and differences.
- Mud Kitchen
Planting and Gardening While working in a school garden, children can practise using numbers to identify how many objects there are in a set. They say and use number names in order in familiar contexts, and count everyday objects.
- Planting and Gardening
Hoist Playing with a bucket on a hoist, children can use numbers to identify how many objects there are in a set. They can use everyday language to talk about size, capacity, position, distance and time and compare quantities and objects and to solve problems.
Session 4 Number and the Language of Addition/Subtraction
Leaves When playing with leaves, children have opportunities to see that numbers identify how many objects there are in a set and to say and use number names in order in familiar contexts. They can begin to use the vocabulary involved in adding and subtracting. They can relate addition to combining two and subtraction to ‘taking away’.
Tin Can Alley Play with cans to explore number names in familiar contexts and to.count up to 10 everyday objects. Children can begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.
- Tin Can Alley
Sand to Sandpit Children can fill a sandpit (or move sand from one place to another) and count up to 10 everyday objects and begin to use the vocabulary involved in adding and subtracting.
- Sand to Sandpit
Logs Put logs onto a trolley and say and use number names in order in familiar contexts. Count and use vocabulary involved in adding and subtracting. Show curiosity and observation by talking about shapes. Begin to use mathematical names for shapes.
More Logs Playing with logs offers countless opportunities to practise counting! Children can also begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.
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Early Years Foundation Stage Activities
Explanation of Our EYFS Format
Here you can find out more about how we structure our EYFS activities.
Early Years Activities - Number
Early Years Activities - Measures
Early Years Activities - Shape and Space
Early Years Activities - Pattern
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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.. 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.
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.
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.
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.
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.
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.
 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 .
 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 .
 Piaget, J. (1983). Piaget's Theory. In P. Mussen (ed). Handbook of Child Psychology. 4th edition. Vol. 1. New York: Wiley.
 Unicef. (2018). Learning Through Play. Available: https://www.unicef.org/sites/default/files/2018-12/UNICEF-Lego-Foundation-Learning-through-Play.pd .
 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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