maths problem solving for reception

Maths: Age 4–5 (Reception)

In Reception, your child will be introduced to numbers and counting, and will start to use basic mathematical language.  An interest in maths and problem solving will be encouraged through maths games and fun activities.

Much of your child’s learning will come from exploring and talking about maths in the world around them and there are simple things you can do at home to support their development.

How to help at home

You don’t need to be an expert to support your child with maths! Here are three simple but effective learning ideas that you can try with your child using everyday items at home.  

1. Building with bricks

Building things with bricks is a good way of developing maths skills through solving problems. For example:

How many red bricks are there? How many blue bricks are there? How many are there altogether?

Using blocks will also help your child practise using the language of maths. For example:

Hmm, I wonder which is the longest brick? Could you pass me the cube over there?

2. Talk about time

Talking about the time at which different things happen and looking at the clock together during the day is a great way to learn about time. This will help set the foundation for telling the time in later years.

For more advice, see our page on Learning to tell the time .

3. Count everything!

One of the first number skills your child will learn is counting. Practising counting will help them will all sorts of number problems that they will encounter as they get older.

Try to get into the habit of counting when you are out and about. For example:

How many buses have we seen? How many bugs are in the garden? How many lamp posts are on the street? How many squirrels have we seen?

For more games and activities to help your child with maths in the Early Years, take a look at our Fun learning ideas for four-year-olds .

4. Spot patterns

Look for repeating patterns   on curtains, wallpaper, or clothing. Ask your child:

Can you see a pattern? Tell me about it. What will come next?

Start patterns with blocks, beads, playing cards, and toys. Encourage your child to build on the pattern to make it longer. You could also look for patterns in time together (for example, seasons, months, or daily routines) and talk about what you notice, or listen for patterns in songs and clap the rhythm.

5. Practise forming numerals

Help your child to learn the numerals by exploring their shapes. You could have fun forming numbers in sand with a stick, or making numbers out of modelling clay. Write numbers for your child to copy, and hold your hand over their hand to help direct them.

Try holding their finger and forming the number in the air. Once they can trace out the shape of numerals, see if they can write numbers on their own.

Video playlist: Early maths skills

What your child will learn in Reception

In Reception, your child will learn to:

• Count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number.
• Use quantities and objects to add and subtract 2 single-digit numbers and count on or back to find the answer.
• Use everyday language to talk about size, weight, capacity, position, distance, time, and money to compare quantities and objects and to solve problems.
• Recognise, create, and describe patterns.
• Explore characteristics of everyday objects and shapes and use mathematical language to describe them.
• Age 3–4 (Early Years)
• Age 4–5 (Reception)
• Age 5–6 (Year 1)
• Age 6–7 (Year 2)
• Age 7–8 (Year 3)
• Age 8–9 (Year 4)
• Age 9–10 (Year 5)
• Age 10–11 (Year 6)
• Year 1 (age 5–6)
• Year 2 (age 6–7)
• Year 3 (age 7–8)
• Year 4 (age 8–9)
• Year 5 (age 9–10)
• Year 6 (age 10–11)
• Help with times tables
• Ratio & proportion
• Learning to tell the time
• Numicon parent guide
• MyMaths parent guide
• Maths activity books

Early Years Foundation Stage Activities

Recently published.

Scooters, Bikes and Trikes

When waiting for a ride on outdoor toys, children can consider which route they might take around the outside area and how long they will spend on their toy.

In this task, children make a collection out of some items and then discuss what they notice about their collection, focusing on the shapes and patterns that they can make.

Small World Play

This activity provides an engaging context for children to consider the space they will allocate for some 'small world' toys, and how many toys they will be able to fit into the space.

Sock Washing Line

In this task, children are encouraged to spot pairs of socks and to order the socks by size and length on the washing line.

Using Books: Maisy Goes Camping

In this task, the book 'Maisy Goes Camping' by Lucy Cousins introduces children to the idea of using the size and number of objects to work out how many will fit in a 'tent'.

Using Books: The Doorbell Rang

In this activity, the book 'The Doorbell Rang' by Pat Hutchins provides an engaging context in which children can explore sharing.

Wrapping Parcels

In this activity, children have the opportunity to wrap some toys and to measure and discuss the size of the box or wrapping paper that they will need.

Early Years Articles

Developing Pattern Awareness with Young Children

This article explores the importance of pattern awareness with young children.

Young Children's Mathematical Recording

In this article, Janine Davenall reflects on children's personalised mathematical recordings as part of a small research project based in her Reception class.

Mathematical Problem Solving in the Early Years: Developing Opportunities, Strategies and Confidence

In this article for Early Years practitioners, Dr Sue Gifford outlines ways to develop children's problem-solving strategies and confidence in problem solving.

What to Expect, When? Parents' Guide 2015

This short article critiques the 'What to Expect, When' guidance, written for parents who want to find out more about their child's learning and development in the first five years.

The Value of Two

Ruth Trundley outlines her doctoral research and concludes that development of an understanding of cardinality is a crucial element of counting that can be overlooked.

Developing Number Through Tidying Up

This article describes how one nursery setting focused on tidying up time as a context in which to explicitly target the development of number and calculation skills.

Early Years Mathematics: How to Create a Nation of Mathematics Lovers?

In this article, Dr Sue Gifford outlines how we can create positive attitudes and higher achievement in mathematics, starting in the Early Years.

Mathematical Problem Solving in the Early Years

This article describes how the NRICH Early Years resources aim to further develop young children's natural problem-solving abilities in the context of mathematics.

A Good Foundation for Number Learning for Five Year Olds?

This article, written by Dr. Sue Gifford, evaluates the Early Learning Numbers Goal in England, in the light of research.

Early Years Activities Format Explained

Why we've written what we've written... DOWNLOAD HERE

Further Resources

In this task, children will learn different ways of representing the same number.

Owl's Packing List

In this activity, children can practise reading numbers and counting items in order to help Owl pack for his holiday.

Water, Water ...

This task provides a real-life context for children to compare capacities in order to choose the biggest container for their lemonade.

Number Book

Creating a 'Book of Four' provides an opportunity for children to collect groups of four objects and consider how the groups of objects are similar.

In this activity, children will use the language of weight when comparing objects on a balance scale.

Cooking with Children

By following some simple recipes in this task, children can practise the skills of measuring and counting ingredients.

Mud Kitchen

When playing in this mud kitchen, children will be using the language of size and capacity to choose utensils for different tasks.

Shapes in the Bag

In this task, children put their hands into a bag and describe what shape they think they can feel and why.

I Have a Box

In this activity, having access to a mystery box will spark children's imagination and encourage them to describe what they notice about the box.

Making Caterpillars

By making 'caterpillars' in this activity, children will have an opportunity to practise using language of length and width, as well as using non-standard measures to compare lengths.

Building Towers

In this task, children will explore 3D shapes when selecting which shapes to use in their tower.

By making 'paths' out of different materials and discussing these, children will develop their shape and space language in this activity.

Golden Beans

This task provides children with an opportunity to count 'golden beans' and find a number card to represent how many they have.

This dice activity encourages children to relate the number on the dice to the number of teddies they need to choose.

This activity involves sorting toys into categories by using comparing and classifying skills.

Making a Picture

This task provides an opportunity for children to work together to make a picture, discussing with each other which position they want to put each shape in.

Making Footprints

In this activity, children will develop an awareness of the faces of 3D shapes by using them to make 'footprints' in soft dough.

Incey Wincey

In this game, children roll the dice and count how many steps to move the spider up or down the drainpipe.

Maths Story Time

This story provides an engaging context for children to share out the treasure fairly among the characters.

Exploring 2D Shapes

In this task, children will make shapes out of loops of string and discuss what they notice about their shapes.

Comparing the wrapped presents in this activity will give children the chance to explore and discuss weight, including the idea that large objects aren't necessarily the heaviest.

Number Rhymes

In this activity, the rhyme 'Ten Green Bottles' is used to encourage children to count backwards to work out how many bottles are left.

In this task, children will practise using a variety of timers to work out how many items they can put into a jar before the time finishes.

Long Creatures

In this task, making a variety of long creatures out of card will provide an opportunity for children to discuss and compare lengths.

Shopping - Pirate Poundland

In the pirate pound shop, children can practise their counting skills by choosing ten items to spend their ten pounds on.

When tidying away toys in this activity, children will use their counting skills to check that all the toys are in the box.

This activity encourages children to practise their sharing and counting skills by putting small objects into some baskets.

Tubes and Tunnels

When investigating these tubes, children will have the opportunity to practise using everyday language to talk about length, size and position.

Position with Wellies

This task uses the familiar situation of a shelf of objects to encourage children to use positional language and follow directions to find their wellies.

Early Years Books

Publishing information about books we have referenced (and others that have been recommended to us by you).

The Box Game

In this game, children will use their addition and subtraction skills to keep track of the number of toys hidden inside a box when toys are added in or taken out.

Double Trouble

This story about some troublesome dogs encourages children to find and model doubles of different numbers.

This task provides children with the opportunity to investigate halving different shapes and check that they have made two halves.

Pattern Making

In this activity, there are lots of different patterns for children to make, describe and extend.

Estimation Station

This activity involves filling a jar with small objects to encourage estimation and counting skills.

The Spring Scale

Using the spring scale in this activity provides an engaging context in which children can explore and discuss the weight of different objects.

How can you help us develop these resources?

Send us some real examples of the activities in action, send us your feedback, the layout:, the activity:.

• Register for our mailing list

• Teach Early Years
• Teach Primary
• Teach Secondary
• Technology & Innovation
• Advertise With Us

• Free Reports
• Have You Seen
• Learning & Development
• A Unique Child
• Enabling Environments
• Positive Relationships
• Nursery Management

Home > Learning & Development

Learning and Development

Maths problem-solving activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

Share this:

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 .

You may also be interested in...

• Great ways to support communication, language and literacy
• How to provide outstanding learning in the outdoors
• Award winners announced

Subscribe to Our Newsletter

I agree to the Terms & Conditions and Privacy & Cookies Policy.

How TickiT products fire children’s imagination to inspire learning

Teach road safety with Brake’s free Beep Beep! Day resources

Metacognition: Being and becoming a learner

Get advice on addressing racial inequity with HFL Education’s online conference

View all Top Products

Katie and the Giant Problem

Recommended for you...

Learning with Nursery Rhymes

How Montessori’s Human Tendencies Affect How Young Children Learn

Observations – using a strengths-based approach

Editors picks

Early Years Topic: The Vets

Early Reception Maths Worksheets (age 4-5)

The ability to calculate mentally lies at the heart of success with number and the importance of a good start cannot be over emphasised. Some children will only be four when they start in Reception, others will only have two terms before moving on to Year 1. Some will have been to nurseries or play groups and some will not so there will already be a wide difference in the knowledge and understanding that children bring to the classroom.

In Reception counting will be mainly oral and practical. Children will be encouraged to say the number names in familiar contexts such as number rhymes, songs and stories.

They will learn to recite the number names in order and continue to count from one and later from a given number (e.g. count on from 4). Fingers can, of course, be a great help at this stage.

Practical apparatus is essential; counting a number of objects, first up to five and then progressing to 10, using one to one correspondence with each object. Whether its peas in pods, coins on a table or sweets in a jar, there are an amazing number of opportunities both at home and in the classroom.

Part of this is for children to realise when counting that the number of objects is not affected by their size or position; six sweets are still six sweets whether they are spread out or close together.

Children will also learn to count back from a given number. There are lots of fun rhymes and songs to help with this, such as, ‘Five little ducks went swimming one day’ and ‘ten green bottles’.

Over time children will begin to recognise a small number of objects without having to count them all.

Whilst most work will be practical there are also opportunities to use worksheets and we are delighted to announce that all our Early Reception worksheets have been updated, with clearer displays, fonts etc. in the categories:

• Counting and Matching
• Early Counting
• Writing Numbers as Digits
• Writing Numbers as Words
• Counting On and Back
• Number Lines
• Ordering Numbers

Each category has many resources within so why not jump in and explore the site?

Popular Resources

Have a look at some of our popular resources in this category.

Draw lines to match the number of monsters and apples.

Counting up to 3 and circling the correct number.

The very earliest work with number is incredibly important and here we have a set of worksheets which helps with recognising the numbers from 1 to 5. You will need a set of crayons so that the apples can be coloured correctly.

Matching sets to numbers: ladybirds

Counting and colouring from 1 to 3.

Draw lines to match the number of chickens and eggs.

A look at numbers from 0 to 10.

Understanding 'more than' and 'less than' are key concepts in the early years. Here is a set of worksheets which concentrates on which group of animals there are less of.

Subscribe to our newsletter

The latest news, articles, and resources, sent to your inbox weekly.

© Copyright 2011 - 2023 Route One Network Ltd. - URBrainy.com 4.0

Get step-by-step solutions to your math problems

Try Math Solver

Get step-by-step explanations

Graph your math problems

Practice, practice, practice

Get math help in your language

Cookie Consent

We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ad personalisation and measurement.

Clicking "Accept" will allow us and our partners to use cookies, learn more in our cookie policy or to change your cookie preferences, click "Manage".

To find out more about cookies and the types of cookies we are setting please visit our cookie policy .

If you'd prefer that certain types of cookie are not saved on your browser when visiting our website, use the toggles below to adjust those preferences and click "Save choices".

Strictly Necessary

These cookies are necessary for the website to function and without them you would not be able to reliably use the website. For example, logging into your account or completing forms.

Analytics Cookies

A series of cookies that collect anonymised data on how users interact with our website. This anonymous data helps us improve the website with a focus on its users, for example, ensuring the most popular content is easier to access.

View associated providers +

Marketing Cookies

These cookies track your online activity to help advertisers deliver more relevant and personalised advertising or to limit how many times you see an ad. These cookies can share that information with other organisations or advertisers.

Problems of the day

March Problems of the Day 2020 – KS2/KS3 Full Set

Here's the full set of KS2/KS3 problems from this year, along with answers.

March Problems of the Day 2020 – KS1 Full Set

Here's the full set of KS1 problems from this year, along with answers.

March Problems of the Day 2019 – GCSE Full Set

A set of GCSE problems covering content for foundation, foundation/higher crossover and higher. We hope they are useful in the run up to the exams. Good luck! #MathsEveryoneCan

March Problems of the Day 2019 – KS2 Full Set

Here is the full set of questions for KS2 Problems of the Day from March 2019.

March Problems of the Day 2019 – KS1 Full Set

Here is the full set of KS1 Problems of the Day that were released throughout March 2019.

March Problems of the Day 2018 – KS2 Full Set

For the month of March, each day we publish some reasoning and problem solving questions for use with your classes in the run-up to SATs. Practice is crucial to maths success, and our questions are designed to support your daily routines. These problems can be used across Y5 and Y6 throughout the year.

March Problems of the Day 2018 – KS1 Full Set

For the month of March, each day we publish some reasoning and problem solving questions for use with your classes in the run up to SATs. Practice is crucial to maths success, and our questions are designed to support your daily routines. These problems can be used across Y1 and Y2 throughout the year.

Early Learning Goals

Want to know more about how ELGs are covered across this area of learning and others?

Reception , Maths , Units:

Early mathematical experiences, pattern and early number, numbers within 6, addition and subtraction within 6.

Measurement

Shape and sorting

Calendar and time, numbers within 10, addition and subtraction within 10, numbers within 15, grouping and sharing, numbers within 20, doubling and halving, shape and pattern, addition and subtraction within 20, depth of numbers within 20, numbers beyond 20.

• Math Forum/Help
• Problem Solver
• College Math

Math Practice

Problems for 1st grade, problems for 2nd grade, problems for 3rd grade, problems for 4th grade, problems for 5th grade, problems for 6th grade, problems for 7th grade, problems for 8th grade, problems for 9-12 grade:, quadratic equations.

Views of a function Domain of a function Domain and range Range of a function Inverses of functions Shifting and reflecting functions Positive and negative parts of functions

Line graph intuition Slope of a line Slope intercept form Recognizing slope

Trygonometry

Probabilities, complex numbers.

Maths Reception Autumn Patterns

Hamilton's Reception Maths planning targets the key characteristics of effective early learning :

• Through Exploring and Playing , children independently engage with their peers and their environment.
• Active Learning group activities promote the motivation needed to be involved and to keep trying.
• Guided Creating and Thinking Critically supports development of problem-solving & reasoning skills.

Maths Out Loud : whole-class counting, repetitive chants, rhymes, songs and a linked story to enjoy together.

Exploring repetitive patterns (suggested as 5 days)

Exploring and Playing

• Activity Cards

Active Learning

Creating and Thinking Critically

Maths Out Loud

Show the 1-100 grid. We’re going to count all the way to 100 today! Point to each number as you do so, emphasise the numbers ending in 0 and 5, so that the children pick up on the pattern.

Do you notice any patterns in the 1-100 grid ? e.g. the columns of numbers ending in the same digits.

This is an activity which needs regular repetition so that more and more children will join in saying the higher numbers.

Chants/Rhymes/Songs

Join in with the patterns with the song Banana, banana, meatball by Blazer Noodle on www.YouTube.com.

There was an old lady who swallowed a fly has a super rhythm and repetitive nature.

Pattern fish by Trudy Harris.

You Will Need

Prepared cut-out snakes; paint; brushes; water; table covering; or playground chalks and access to the outside; Lego or Duplo bricks and baseboards; multilink cubes; linking elephants or other pattern-making equipment, e.g. peg boards, Numicon; shapes, or natural materials such as leaves; plain wallpaper/wall lining paper; large crayons or paint and sponges for printing; art shirts.

Interconnecting cubes in different colours; 2 drums, 2 wood blocks, 2 triangles and beaters; flat shapes: triangles, squares and rectangles (optional).

Paint and shaped sponges or gummed shapes; strips of card to make headbands; different coloured and shaped beads; strings/laces; fruit, e.g. bananas, strawberries, apples, pineapple, grapes; skewers; kitchen roll; interconnecting cubes in different colours.

Counting in 2s; odd/even numbers (suggested as 5 days)

Count to 20 WITHOUT the support of a number track or 1-100 grid. Children hold up a finger for each number to 10, then one finger for 11, 2 for 12 and so on, and wave 1 or 2 hands for 5, 10, 15, 20, shouting these numbers.

Be sure to pronounce the teens numbers very clearly, so children don’t confuse them with the 10s numbers, e.g. confuse fifteen with fifty.

This is an activity which needs regular repetition so that more and more children learn the teens numbers in order by heart.

One, two, buckle my shoe . Children could join in with this animated version of One, two, buckle my shoe from www.bbc.co.uk.

Eggs and Legs: Counting by Twos by Michael Dahl.

Toy animals; an ‘ark’; a soft ball; 10 socks; 2 lunch boxes; up to 10 real or play food items; numbered boxes.

Number cards 1 to 20 (see resources), 20 pegs and washing line; five replica 2p coins, washing line, 10 pegs; five 2p coins and a tin; 10 socks (preferably identical).

Even 2 to 10 cards; collections of up to 10 objects, e.g. pairs of shoes, pairs of cubes, pairs of eyes on soft toys, pairs of socks, etc.; cookie recipe (see resources); ingredients and cooking equipment; 20 chocolate buttons; plates; cubes; 1–10 number track (see resources); red and blue pencils.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Extra Support worksheets come with guidance for a teacher or TA working with small groups. They can make a significant difference to children working below ARE. Extra support is linked to individual objectives-based units, but you can also explore a set for a whole year.

Procedural fluency is fundamental to numeracy, and Hamilton's practice worksheets are carefully differentiated for children working toward Age Related Expectations (ARE), at ARE and at greater depth. Practice is linked to individual objectives-based units, but you can also explore sets of worksheets for the whole year.

This site uses cookies to give you the most relevant information. Learn more

Log in or sign up to get access to this resource

Become a friend.

Access to this resource requires a KS1 licence. Donate £33 to get individual access to your key stage.

Subscribe your School

Access to all key stages for up to 30 teachers.

Already have an account?

Log in to get access.

Reception Mathematics

Examples from our community, 10000+ results for 'reception maths'.

Need help? Open

• What our subscribers say...
• How to videos
• Create new account
• Reset your password

Reception maths: what your child learns

In Reception numeracy is taught as part of ‘Problem solving, Reasoning and Numeracy’, as the children get to grips with the ideas of numbers and calculations. Children will be working with numbers every day, in a range of different ways.

They will be using familiar objects to help them learn about how numbers are used in everyday life, and they will also be linking numbers to topic work; for example, if they are learning about dinosaurs they could be making dinosaur pictures out of shapes. They will be encouraged to be curious and explore numbers.

They will be playing number games, singing counting songs, making models and using the role-play area, as well as being introduced to the ideas of addition and subtraction. At home, try to talk about numbers – it’s important for children to see just how much maths is used in everyday life.

Reception maths – your child will be:

Numbers as labels and for counting

• Counting up to ten and beyond, using cardinal numbers
• Recognising the numbers 1 to 9
• Counting aloud in ones, twos, fives, tens
• Estimating a number of objects and checking by counting
• Matching and comparing the number of objects in two groups
• Counting out a number of objects from a larger group
• Positioning items according to their place in a group using ordinal numbers (first, second, third, etc.)

Start the Reception Learning Programme!

• Weekly maths & English worksheets direct
• Follows the National Curriculum
• Keeps your child's learning on track

Calculating

• Using a number line to count on and back
• Finding one more or one less than a number from 1 to ten
• Sharing objects into equal groups and counting how many are in each group
• Understanding that ‘addition’ means combining and ‘subtraction’ means taking away
• Finding the total number of items in two groups by counting them all
• Comparing numbers and recognising which is ‘more’ or ‘less’

Shape, space and measures

• Comparing quantities and using words such as ‘greater’, ‘smaller’, ‘heavier’ or ‘lighter’
• Recognising and creating their own simple patterns
• Naming and describing the shape and size of solid (3D) and flat (2D) shapes
• Using everyday words to describe the position of objects
• Sorting familiar objects and describing their differences and similarities
• Making patterns and building models
• Putting two or three items in order, according to their length or weight
• Matching shapes and patterns
• Building on a basic understanding of time: putting familiar events in sequence; measuring time, using a sand-timer

Try this at home

• Practise counting – you can do this anywhere: count toys, books, how many buses you see when you go out
• Play hide and seek – again, good practice for counting
• Save your cereal boxes and cardboard tubes for making models. Your child will think they’re making a castle; you’ll know they’re learning about shapes!
• Do a jigsaw together – a fun way to develop spatial awareness and matching skills
• Play card games – even a simple game of snap helps to develop number recognition
• Have a teddy bears’ picnic: count out toys, place settings, and share out the cakes
• Put up a height chart and mark each member of the family's height
• At bathtime, play with different-sized containers

Help consolidate your child's learning with some Reception maths worksheets and activities , and try some easy ways to engage your child with maths every day at home.

Check your Reception child's progress in maths with our free Reception maths Progress checks , three mini-tests for the autumn, spring and summer terms.

Explore the Reception English & Maths Learning Journey programmes.

More like this

• Practice Problems
• Assignment Problems
• Show all Solutions/Steps/ etc.
• Hide all Solutions/Steps/ etc.
• Graphing Functions
• Solving Equations and Inequalities
• Common Graphs
• Calculus II
• Calculus III
• Differential Equations
• Algebra & Trig Review
• Common Math Errors
• Complex Number Primer
• How To Study Math
• Cheat Sheets & Tables
• MathJax Help and Configuration
• Notes Downloads
• Complete Book
• Practice Problems Downloads
• Complete Book - Problems Only
• Complete Book - Solutions
• Assignment Problems Downloads
• Other Items
• Get URL's for Download Items
• Print Page in Current Form (Default)
• Show all Solutions/Steps and Print Page
• Hide all Solutions/Steps and Print Page

Section 3.4 : The Definition of a Function

For problems 1 – 3 determine if the given relation is a function.

• \(\left\{ {\left( {2,4} \right),\left( {3, - 7} \right),\left( {6,10} \right)} \right\}\) Solution
• \(\left\{ {\left( { - 1,8} \right),\left( {4, - 7} \right),\left( { - 1,6} \right),\left( {0,0} \right)} \right\}\) Solution
• \(\left\{ {\left( {2,1} \right),\left( {9,10} \right),\left( { - 4,10} \right),\left( { - 8,1} \right)} \right\}\) Solution

For problems 4 – 6 determine if the given equation is a function.

• \(\displaystyle y = 14 - \frac{1}{3}x\) Solution
• \(y = \sqrt {3{x^2} + 1} \) Solution
• \({y^4} - {x^2} = 16\) Solution
• \(f\left( 0 \right)\)
• \(f\left( 2 \right)\)
• \(f\left( { - 4} \right)\)
• \(f\left( {3t} \right)\)
• \(f\left( {x + 2} \right)\)
• \(g\left( { - 6} \right)\)
• \(g\left( { - 2} \right)\)
• \(g\left( 0 \right)\)
• \(g\left( {t - 1} \right)\)
• \(g\left( {4w + 3} \right)\)
• \(h\left( 0 \right)\)
• \(h\left( { - 2} \right)\)
• \(h\left( 2 \right)\)
• \(h\left( {\sqrt x } \right)\)
• \(h\left( {3 - t} \right)\)
• \(h\left( 7 \right)\)
• \(f\left( 6 \right)\)
• \(f\left( 9 \right)\)
• \(f\left( {12} \right)\)

For problems 12 & 13 compute the difference quotient for the given function. The difference quotient for the function \(f\left( x \right)\) is defined to be,

• \(f\left( x \right) = 4 - 9x\) Solution
• \(f\left( x \right) = 2{x^2} - x\) Solution

For problems 14 – 18 determine the domain of the function.

• \(A\left( x \right) = 6x + 14\) Solution
• \(\displaystyle f\left( x \right) = \frac{1}{{{x^2} - 25}}\) Solution
• \(\displaystyle g\left( t \right) = \frac{{8t - 24}}{{{t^2} - 7t - 18}}\) Solution
• \(g\left( w \right) = \sqrt {9w + 7} \) Solution
• \(\displaystyle f\left( x \right) = \frac{1}{{\sqrt {{x^2} - 8x + 15} }}\) Solution

HIGH SCHOOL

• ACT Tutoring
• SAT Tutoring
• PSAT Tutoring
• ASPIRE Tutoring
• SHSAT Tutoring
• STAAR Tutoring

GRADUATE SCHOOL

• MCAT Tutoring
• GRE Tutoring
• LSAT Tutoring
• GMAT Tutoring
• AIMS Tutoring
• HSPT Tutoring
• ISEE Tutoring
• ISAT Tutoring
• SSAT Tutoring

Search 50+ Tests

Loading Page

math tutoring

• Elementary Math
• Pre-Calculus
• Trigonometry

science tutoring

Foreign languages.

• Mandarin Chinese

elementary tutoring

• Computer Science

Search 350+ Subjects

• Video Overview
• Tutor Selection Process
• Online Tutoring
• Mobile Tutoring
• Instant Tutoring
• How We Operate
• Our Guarantee
• Impact of Tutoring
• Reviews & Testimonials
• Media Coverage
• About Varsity Tutors

SAT II Math I : Solving Functions from Word Problems

Study concepts, example questions & explanations for sat ii math i, all sat ii math i resources, example questions, example question #1 : solving functions from word problems.

At Joe's pizzeria a pizza costs $5 with the first topping, and then an additional 75 cents for each additional topping.

Notice that the question describes a linear equation because there is a constant rate of change (the cost per topping). This means we can use slope intercept form to describe the scenario. 

Recall that slope intercept form is

Putting all these steps together we get:

Report an issue with this question

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below:

Contact Information

Complaint details.

Find the Best Tutors