Below is a collection from our Early Years Foundation Stage activities which are suitable for parents and children to explore at home together. We hope you enjoy being mathematical as a family! You may also like to read our article Developing Pattern Awareness with Young Children.
This collection is part of our Maths At Home Summer Challenges.
Beat the Clock
Age
3 to 5
Children use everyday language to talk about time, to compare quantities and to solve problems
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Children often count actions and see if they can do things more quickly.
Adults could time children's activity for a minute and suggest things to do.
The Activity
Set a timer for a minute (or half a minute) and count how many actions the child can do in that time, such as star jumps, hops, or writing their name.
Set a timer for a minute (or half a minute) and count how many actions the child can do in that time, such as star jumps, hops, or writing their name.
Encouraging mathematical thinking and reasoning:
Describing
Encourage children to discuss the numbers of actions they did within the time frame using comparison words (e.g. more, fewer). How many star jumps did you do? How many hops? Which did you do more of?
You did more jumps - does that mean you are getting faster or slower?
Encourage children to discuss the numbers of actions they did within the time frame using comparison words (e.g. more, fewer). How many star jumps did you do? How many hops? Which did you do more of?
You did more jumps - does that mean you are getting faster or slower?
Reasoning
What do you think you can do more of in a minute, star jumps or twirls? Why do you think that is?
Try again - can you do more this time?
What makes you think you are getting faster? Or slower?
How many times do you think you can do 'heads, shoulder, knees and toes'? How many claps or stamps do you think you can do in half a minute?
What do you think you can do more of in a minute, star jumps or twirls? Why do you think that is?
Try again - can you do more this time?
What makes you think you are getting faster? Or slower?
How many times do you think you can do 'heads, shoulder, knees and toes'? How many claps or stamps do you think you can do in half a minute?
Opening Out
Can you think of some other actions you can do in a minute? Writing your name? Singing happy birthday all the way through?
Can you put your coat and shoes on in a minute?
Stand up with your eyes shut: sit down when you think a minute is over. How close were you? Did you think a minute was a shorter or longer time than it really is?
Can you think of some other actions you can do in a minute? Writing your name? Singing happy birthday all the way through?
Can you put your coat and shoes on in a minute?
Stand up with your eyes shut: sit down when you think a minute is over. How close were you? Did you think a minute was a shorter or longer time than it really is?
Recording
Shall we write down how many jumps you do each time, so we can keep track. What do these show?
Shall we write down how many jumps you do each time, so we can keep track. What do these show?
The Mathematical Journey
Counting and cardinality:
- counting actions - using the number sequence, tagging each item and saying the total
- comparing quantitites and numbers, more / less / fewer / not as many
- ordering several numbers most / biggest number / smallest number
- estimating numbers
Matching numerals and amounts:
- writing and reading numerals
Measures:
- using language: quickly / fast / faster / slower; takes a long / short time
- predicting and explaining that the shorter time things take the more you can do in a minute (and vice versa): 'Clapping is really quick so you can do lots'
- generalising: 'if it takes a long time you get a small number'
Development and Variation
There are a huge variety of activities which children might suggest, some very brief, like clapping (or blinking!) and some taking longer, like twirling round (or winking!). Outdoor activities might include running/hopping the length of a path, or throwing and catching a ball. Indoor activities might include saying a rhyme or singing songs.
Longer activities, such as running round a circuit, can be timed to the nearest minute and the number discussed. Does a smaller number of minutes mean that you are getting slower or faster - and why? Timings for daily activities such as getting dressed or tidying away toys can be recorded and compared.
You should brush your teeth for two minutes (twice a day) - can you guess when two minutes is up?
There are a huge variety of activities which children might suggest, some very brief, like clapping (or blinking!) and some taking longer, like twirling round (or winking!). Outdoor activities might include running/hopping the length of a path, or throwing and catching a ball. Indoor activities might include saying a rhyme or singing songs.
Longer activities, such as running round a circuit, can be timed to the nearest minute and the number discussed. Does a smaller number of minutes mean that you are getting slower or faster - and why? Timings for daily activities such as getting dressed or tidying away toys can be recorded and compared.
You should brush your teeth for two minutes (twice a day) - can you guess when two minutes is up?
Resources
You can use the digital timer on a phone, or a wind-up kitchen timer which 'pings'. Egg-timers may be less effective as they do not make a noise when the time is up (and do not provide options and numbers to discuss).
A number track or ruler of some kind is useful to refer to, for children to see how to write the numbers.
You can make a 'tocker' with a coffee jar lid, a lump of playdough or blutak, and a piece of card stuck on to provide a pointed 'handle', on which you can draw a face and hat. Pull the point so it is flat on the table and then release it: the lid should 'tock' several times to and fro before coming to rest. Use this time period to see how many things you can do. Or make tockers with different lids or amounts of playdough and set them off at the same time to see how long they keep tocking.
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A number track or ruler of some kind is useful to refer to, for children to see how to write the numbers.
You can make a 'tocker' with a coffee jar lid, a lump of playdough or blutak, and a piece of card stuck on to provide a pointed 'handle', on which you can draw a face and hat. Pull the point so it is flat on the table and then release it: the lid should 'tock' several times to and fro before coming to rest. Use this time period to see how many things you can do. Or make tockers with different lids or amounts of playdough and set them off at the same time to see how long they keep tocking.
Download a PDF of this resource.
Acknowledgement: Penny Latham
Can you build this?
Age
3 to 5
Exploring characteristics of shapes
Using both everyday and mathematical language to describe shapes, talk about positions and solve problems
Using both everyday and mathematical language to describe shapes, talk about positions and solve problems
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Children enjoy construction activities - and a challenge!
Adults could make simple models for children to try and copy.
The Activity
The adult makes a simple construction with a few blocks or pieces of Lego, and challenges the child to copy it with the same pieces or from a selection. Use more different pieces to increase the challenge.
The adult makes a simple construction with a few blocks or pieces of Lego, and challenges the child to copy it with the same pieces or from a selection. Use more different pieces to increase the challenge.
Encouraging mathematical thinking and reasoning:
Describing
That's great! But look very closely: how is your model different from mine?
Which block do you need to put to the right of / above / below / behind this red one?
Your blocks are all pointing the same way - can you see these ones are crossways?
That's great! But look very closely: how is your model different from mine?
Which block do you need to put to the right of / above / below / behind this red one?
Your blocks are all pointing the same way - can you see these ones are crossways?
Reasoning
How do you think you need to change yours to make it look the same as mine?
How do you need to turn that brick to make it look the same?
How do you think you need to change yours to make it look the same as mine?
How do you need to turn that brick to make it look the same?
Opening Out
Take a photo of a secretly made model and see if the child can copy that, using the same pieces.
What do you think is at the back, underneath the red brick?
I've made a little model which I've got hidden under the table - I'll see if I can tell you how to make it. First, take a blue brick, then put a yellow one on top...
Can you make a secret model with five bricks and describe it for me to make?
Take a photo of a secretly made model and see if the child can copy that, using the same pieces.
What do you think is at the back, underneath the red brick?
I've made a little model which I've got hidden under the table - I'll see if I can tell you how to make it. First, take a blue brick, then put a yellow one on top...
Can you make a secret model with five bricks and describe it for me to make?
Recording
Let's take a photo of your best one and see if you can make it again tomorrow.
Can you do a drawing of your model?
Let's take a photo of your best one and see if you can make it again tomorrow.
Can you do a drawing of your model?
The Mathematical Journey
Properties of shapes:
- selecting appropriate blocks to match others, correctly identifying properties such as flat, curved etc.
- using informal shape language - sharp, slopey, pointy, like a brick, arch, box, roof etc.
- using mathematical shape language - corner, side, edge, flat, curved, rectangular, cylinder etc.
Properties of shapes:
- selecting appropriate blocks to match others, correctly identifying properties such as flat, curved etc.
- using informal shape language - sharp, slopey, pointy, like a brick, arch, box, roof etc.
- using mathematical shape language - corner, side, edge, flat, curved, rectangular, cylinder etc.
- copying arrangements and relative positions of bricks
- rotating pieces to match
- using positional language - on top of, next to, underneath, in front of, behind, between, left, right etc.
- constructing a 3D model from a 2D picture; identifying hidden pieces which are not visible in the picture; drawing a model with key features
Measures:
- identifying longer and shorter pieces to match those in the model
Development and Variation
Make more complex models, with more pieces and varied shapes.
Use more challenging language like between, in front of, behind, overlapping, at right angles.
Show a model quickly and hide it again: can the child look closely then draw it from memory?
Make some pictures with 2D shapes, and draw outlines for children to fit shapes into. (See Learning Trajectories website for 2D 'picture maker' videos: https://www.learningtrajectories.org/)
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Make more complex models, with more pieces and varied shapes.
Use more challenging language like between, in front of, behind, overlapping, at right angles.
Show a model quickly and hide it again: can the child look closely then draw it from memory?
Make some pictures with 2D shapes, and draw outlines for children to fit shapes into. (See Learning Trajectories website for 2D 'picture maker' videos: https://www.learningtrajectories.org/)
Resources
Building blocks, interlocking bricks, Lego or other construction material, 2D shapes and picture outlines
See Erikson Early Mathematics Collaborative website for other ideas: https://earlymath.erikson.edu/foundational-concepts/spatial-relationships/
Building blocks, interlocking bricks, Lego or other construction material, 2D shapes and picture outlines
See Erikson Early Mathematics Collaborative website for other ideas: https://earlymath.erikson.edu/foundational-concepts/spatial-relationships/
Download a PDF of this resource.
Acknowledgement: Penny Latham
How long are you?
Age
3 to 5
Children use everyday language to talk about size, to compare quantities and objects and to solve problems
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Children often enjoy measuring themselves with different things.
Adults could provide a variety of things to use as measuring units and compare results.
The Activity
The child lies down and the adult 'measures' the child, by putting a marker by head and feet, then stretching a piece of tape as long as the child. They find out how many pens will match this, carefully placed end to end, making sure they are straight, with no gaps or overlaps. Repeat with other things of uniform length, some long, some short (such as rolled up sheets of newspaper, spoons, buttons, Lego or Duplo bricks) to make several 'trails' of equal length and compare the results.
The child lies down and the adult 'measures' the child, by putting a marker by head and feet, then stretching a piece of tape as long as the child. They find out how many pens will match this, carefully placed end to end, making sure they are straight, with no gaps or overlaps. Repeat with other things of uniform length, some long, some short (such as rolled up sheets of newspaper, spoons, buttons, Lego or Duplo bricks) to make several 'trails' of equal length and compare the results.
Encouraging mathematical thinking and reasoning:
Describing
What do you notice about using the pens and the paper rolls? How many pens does it take to match the tape?
You are 20 pens tall! How many paper rolls tall are you?
You are 3 and a bit rolls long/not quite 3 rolls long.
What do you notice about using the pens and the paper rolls? How many pens does it take to match the tape?
You are 20 pens tall! How many paper rolls tall are you?
You are 3 and a bit rolls long/not quite 3 rolls long.
Reasoning
I wonder what will happen if we measure with Lego bricks? Why do you think there will be more?
There are some gaps between the dinosaurs - do you think that matters? Does it matter if they are all not the same length?
I wonder what will happen if we measure with Lego bricks? Why do you think there will be more?
There are some gaps between the dinosaurs - do you think that matters? Does it matter if they are all not the same length?
Opening Out
Which did we use most of? Which needed the smallest number?
You are three and a bit rolls long - what do you think we could use to measure the extra bit - little Lego bricks?
How many pens tall do you think your grown-up will be?
What other things are about the same height as you? Which are shorter or taller?
How tall are you with the measuring tape - what numbers can you see? Are you more or less than a metre tall?
How many footsteps tall are you? (Make sure you walk heel to toe and in a straight line!)
Which did we use most of? Which needed the smallest number?
You are three and a bit rolls long - what do you think we could use to measure the extra bit - little Lego bricks?
How many pens tall do you think your grown-up will be?
What other things are about the same height as you? Which are shorter or taller?
How tall are you with the measuring tape - what numbers can you see? Are you more or less than a metre tall?
How many footsteps tall are you? (Make sure you walk heel to toe and in a straight line!)
Recording
Let's take a photo of the 'trails' we've made.
Let's write the numbers of papers and pens, and centimetres tall you are. How can we make the calculator show these numbers?
Let's take a photo of the 'trails' we've made.
Let's write the numbers of papers and pens, and centimetres tall you are. How can we make the calculator show these numbers?
The Mathematical Journey
Counting and cardinality:
- counting objects using the number sequence, tagging each item and saying the total
- comparing quantities and numbers, more / less / fewer / not as many
- ordering several numbers most / biggest number / smallest number
- estimating numbers
Matching numerals and amounts:
- writing and reading numerals
Measures:
- using language: tall, height, long, short, longer, length
- predicting and explaining that the shorter things are the more you will need and vice versa: 'The buttons are really small so we will need lots'
- generalising: 'If you get really long things you don't need as many'
Development and Variation
Predict and compare the number of things needed to measure an adult.
Cut a piece of string the length of the child - or use strips of newspaper joined together with sellotape - and try to find things the same length, commenting whether they are shorter or longer.
Tape pieces of newspaper together, draw round the child with a marker pen and cut out the silhouette, then mark the length in a straight line, so the child can see that their height is the distance between the top of their head and the bottom of their feet lying down or standing up.
Cut pieces of string (or paper strips) the same length as the child's reach (finger tip to finger tip with arms outstretched) and compare - are they the same? Compare this to head circumference. Find strips to match other body parts such as length of feet or waist.
How many of your own feet tall are you?
(With several children, focus on comparing the numbers and lengths of things used to measure, but not children's heights, as no-one likes being the shortest!)
Measure heights with a measuring tape and discuss the fact that there are 100 centimetres in a metre, and whether the child is more or less than a metre.
Predict and compare the number of things needed to measure an adult.
Cut a piece of string the length of the child - or use strips of newspaper joined together with sellotape - and try to find things the same length, commenting whether they are shorter or longer.
Tape pieces of newspaper together, draw round the child with a marker pen and cut out the silhouette, then mark the length in a straight line, so the child can see that their height is the distance between the top of their head and the bottom of their feet lying down or standing up.
Cut pieces of string (or paper strips) the same length as the child's reach (finger tip to finger tip with arms outstretched) and compare - are they the same? Compare this to head circumference. Find strips to match other body parts such as length of feet or waist.
How many of your own feet tall are you?
(With several children, focus on comparing the numbers and lengths of things used to measure, but not children's heights, as no-one likes being the shortest!)
Measure heights with a measuring tape and discuss the fact that there are 100 centimetres in a metre, and whether the child is more or less than a metre.
Resources
Rolled up sheets of newspapers (secured with a piece of sellotape), pens, Lego bricks, spoons, buttons, coins or anything of roughly uniform length.
Rolled up sheets of newspapers (secured with a piece of sellotape), pens, Lego bricks, spoons, buttons, coins or anything of roughly uniform length.
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Download a PDF of this resource.
Acknowledgement: Penny Latham
Making Footprints
Age
3 to 5
Exploring 3D shapes
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Children often enjoy making footprints in soft materials.
Adults could use this idea to encourage children to develop an awareness of the faces of 3D shapes.
The Activity
Provide children with soft dough and a selection of small wooden blocks of various shapes. Talk about experiences of making footprints in sand or snow. Encourage children to select a block and press it into the dough to make a 'footprint'. Show how to run a finger around the edge of the impression to feel the perimeter.
Provide children with soft dough and a selection of small wooden blocks of various shapes. Talk about experiences of making footprints in sand or snow. Encourage children to select a block and press it into the dough to make a 'footprint'. Show how to run a finger around the edge of the impression to feel the perimeter.
Encouraging mathematical thinking and reasoning:
Describing
Tell me about what you've made.
Can you see other blocks that might make the same footprint?
Look at the block and the footprint it has made side by side. What's the same and what's different?
Tell me about what you've made.
Can you see other blocks that might make the same footprint?
Look at the block and the footprint it has made side by side. What's the same and what's different?
Reasoning
What will happen if we stand the shape back in its footprint?
How do you think this shape made this footprint?
What will happen if we stand the shape back in its footprint?
How do you think this shape made this footprint?
Opening Out
What will happen if we turn the shape over and make a new footprint?
How many different footprints do you think you can you make with this shape?
Which shapes might have made this footprint?
What will happen if we turn the shape over and make a new footprint?
How many different footprints do you think you can you make with this shape?
Which shapes might have made this footprint?
Recording
Draw around a block. Look at the shape you have made.
Is it the same shape as the footprint?
Draw around a block. Look at the shape you have made.
Is it the same shape as the footprint?
The Mathematical Journey
Properties of shapes:
- using everyday language to describe the shape of each block and the impressions it makes, e.g. flat, sharp, slopey, pointy, like a brick, ball, box, roof, etc.
- using mathematical language to talk about the attributes of each block and the impressions it makes, e.g. curve, side, corner, flat, rectangular
- connecting the shape of a face of the block to the shape of the impression made by it
Same and different:
- developing language to describe similarities and differences e.g. bigger, smaller, longer, shorter, like a ..., same as ..., straighter, more curved, rounder, more pointy
Development and Variation
Children could:
Story, rhyme and song links
The Blue Balloon by Mick Inkpen
Changes by Anthony Browne
The Six Blind Men and the Elephant by Clare Boucher and Rachel Merriman
Jack and Jill (good for slopes and rolling)
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- Print with cut vegetables and paint.
- Solve old-fashioned picture cube puzzles.
- Investigate shadow play.
- Press natural materials such as pebbles, twigs, cones and flowers into soft earth.
- Make handprints in salt dough that can be baked to keep.
- Dip feet in baby talc to make prints on black paper.
- Balloon print - dip a partially-blown balloon into paint to print.
- Play with shape sorter toys in which blocks are fitted into shaped slots.
- Use cutters to make gingerbread or pastry shapes.
Story, rhyme and song links
The Blue Balloon by Mick Inkpen
Changes by Anthony Browne
The Six Blind Men and the Elephant by Clare Boucher and Rachel Merriman
Jack and Jill (good for slopes and rolling)
Resources
Optional: Encourage children to explore making 'footprints' using everyday objects such as hands and feet, spoons of different sizes, dice, lolly sticks, leaves, shells, small world play equipment or pieces of other construction kits.
- Soft dough
- Selection of wooden blocks of various shapes
- Rolling pin to 're-flatten' the dough
- Camera or video camera for recording results
Optional: Encourage children to explore making 'footprints' using everyday objects such as hands and feet, spoons of different sizes, dice, lolly sticks, leaves, shells, small world play equipment or pieces of other construction kits.
Download a PDF of this resource.
Long Creatures
Age
3 to 5
Using everyday language to talk about size
Exploring characteristics of objects and using mathematical language to describe them
Exploring characteristics of objects and using mathematical language to describe them
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Children often enjoy making things out of thin card, pretending they've made worms, snakes, caterpillars, lizards etc.
Adults could provide craft materials for children to decorate, or other materials like linking cubes to make long narrow shapes.
The Activity
Provide thin card, that is long and narrow, for children to fold in different ways to make creatures that vary in length. Linking cubes, pipe cleaners etc. could also be used.
Provide thin card, that is long and narrow, for children to fold in different ways to make creatures that vary in length. Linking cubes, pipe cleaners etc. could also be used.
Encouraging mathematical thinking and reasoning:
Describing
Tell me about the long creature that you've made.
How does yours compare to the others that your friends have made?
Tell me about the long creature that you've made.
How does yours compare to the others that your friends have made?
Reasoning
Tell me about making it longer/shorter.
If you were to put yours with other ones what could you say about them?
Tell me about making it longer/shorter.
If you were to put yours with other ones what could you say about them?
Opening Out
Can you find a way of making it longer/shorter than any of the others?
Have a look at everyone's creatures. Could you group them in some way?
Can you find a way of making it longer/shorter than any of the others?
Have a look at everyone's creatures. Could you group them in some way?
Recording
Do you want to make a label for your creature and give it a name?
How could you show how long your creature is?
Do you want to make a label for your creature and give it a name?
How could you show how long your creature is?
The Mathematical Journey
Properties of shapes:
- discovering the best shapes to use by analysing their properties
Position and spatial properties:
- investigating how all the creatures that they make can be extended
- comparing the positions of creatures
Same and different:
- comparing the shapes and sizes of all the creatures that they make, in particular describing relative lengths i.e. comparing their creature's length before and after extension and/or comparing the length of their creature with another child's
- developing language to compare and contrast the shape/size of their creatures with others' e.g. longer, shorter, thicker, thinner...
Development and Variation
Similar mathematical discussions could arise from play with modelling clay, play-dough or plasticine, for example.
Children might also enjoy using ribbon/wool/string to go around different objects and realising the need for it to be longer.
Similarly, children could be given presents and wrapping paper. This may provoke discussions about the size of the piece of paper in relation to the size of the present (see the activity Wrapping Parcels).
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Children might also enjoy using ribbon/wool/string to go around different objects and realising the need for it to be longer.
Similarly, children could be given presents and wrapping paper. This may provoke discussions about the size of the piece of paper in relation to the size of the present (see the activity Wrapping Parcels).
Resources
You will already have lots of materials in your setting which would lend themselves to this activity. You might provide:
You will already have lots of materials in your setting which would lend themselves to this activity. You might provide:
- materials which have the potential for creating long creatures, and perhaps are able to be decorated
- fabrics or other items that can be stretched or made shorter
Download a PDF of this resource.
Packing
Age
3 to 5
Sorting and describing, using mathematical properties such as size, shape, weight, capacity and pattern
Counting and comparing numbers
Counting and comparing numbers
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Children often enjoy putting 'like' things together, when putting things away and gathering them together.
Adults could have lots of boxes (or trays), perhaps 'shoe-box' style, available for children to use as well as large groups of small items like zoo/farm animals, train set carriages or any similarly shaped items.
The Activity
You could provoke the children by saying something like, "These have all got muddled up" as you present them with an assortment of small items.
You could provoke the children by saying something like, "These have all got muddled up" as you present them with an assortment of small items.
Encouraging mathematical thinking and reasoning:
Describing
Tell me about your box and the ... you are putting away.
How many will fit? Will they all fit?
Tell me about your box and the ... you are putting away.
How many will fit? Will they all fit?
Reasoning
Looking at all the boxes we've got here, who has the most ... in their box?
How do you know?
Could we fit more/fewer in ...'s box?
Looking at all the boxes we've got here, who has the most ... in their box?
How do you know?
Could we fit more/fewer in ...'s box?
Opening Out
Which boxes/trays would be best for keeping which things in?
Are some things better to be kept in something other than a box or tray? If so, what?
Which boxes/trays would be best for keeping which things in?
Are some things better to be kept in something other than a box or tray? If so, what?
Recording
Do you want to make a new label for the box showing how many are inside?
Do you want to make a new label for the box showing how many are inside?
The Mathematical Journey
Properties of shapes:
- choosing particular trays/boxes for particular objects having analysed the properties of the shapes involved
Same and different:
- grouping according to a rule, e.g. "These are good for our artwork when we need to stick bits onto card"
Counting and cardinality:
- noticing that amounts increase as more are gathered together
- counting and cardinality - progressing from knowing some number words to saying one number for each object, then knowing the number of the whole group
- relative number size - comparing numbers
- part-whole numbers - noticing numbers within numbers, for subgroups within collections
Development and Variation
Many settings use songs associated with different parts of the day. Using such songs can help children focus on packing things away.
Similar aspects of learning and development are highlighted in the activity Collecting found in the NRICH EYFS collection. Tidying is also linked to this activity but has more of a numerical focus.
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Many settings use songs associated with different parts of the day. Using such songs can help children focus on packing things away.
Similar aspects of learning and development are highlighted in the activity Collecting found in the NRICH EYFS collection. Tidying is also linked to this activity but has more of a numerical focus.
Resources
Any objects and resources that need to be 'put away'.
A range of containers, for example, trays, boxes, baskets etc.
Any objects and resources that need to be 'put away'.
A range of containers, for example, trays, boxes, baskets etc.
Download a PDF of this resource.
Tubes and Tunnels
Age
3 to 5
Using everyday language to talk about size, length, position and distance
Understanding the characteristics of 3D shapes
Understanding the characteristics of 3D shapes
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Children often enjoy playing with tubes, rolling them, putting things in them and rolling things down them.
Adults could provide an assortment of all kinds of tubes, for example from the insides of wrapping paper, new tubes for hamsters/guinea pigs, straws, large ones from carpets etc.
The Activity
This is very much a child-initiated activity with the children freely playing with the tubes, perhaps making a telescope, perhaps blowing through them, perhaps rolling things down them, perhaps laying them on their side and forming a stack, etc.
This is very much a child-initiated activity with the children freely playing with the tubes, perhaps making a telescope, perhaps blowing through them, perhaps rolling things down them, perhaps laying them on their side and forming a stack, etc.
Encouraging mathematical thinking and reasoning:
Describing
Tell me about the tubes you are using.
What are you using the tubes for?
Tell me about the tubes you are using.
What are you using the tubes for?
Reasoning
How could you use another tube?
I like what you have done. How would you do it again?
How could you use another tube?
I like what you have done. How would you do it again?
Opening Out
Can you explain to ... what you have done?
What could you do with your tube next?
Can you explain to ... what you have done?
What could you do with your tube next?
Recording
[At the conclusion]
How can you show what you've done/made/discovered?
[At the conclusion]
How can you show what you've done/made/discovered?
The Mathematical Journey
Size and measures:
- using language to compare the sizes of the tubes, for example, wider, narrower, longer, shorter, fatter, thinner etc.
- developing language to describe the sizes of things going through the tubes
Properties of shape:
- understanding and appreciating the properties of the tubes (of any cross-section) which make then good for ...
- knowing what rolls well
Position and spatial properties:
- learning where to place the tubes to achieve what you want
- talking about where the tubes are in relation to things around them and other tubes
Development and Variation
There may be tubes that will slide inside each other, producing a telescope effect, which can lead to other discussions about length.
You could use gutters to channel water, sand or small pebbles.
Further activities that help children experience the properties of other shapes may be appropriate to lead on to from this one, such as Building Towers and Making Caterpillars.
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There may be tubes that will slide inside each other, producing a telescope effect, which can lead to other discussions about length.
You could use gutters to channel water, sand or small pebbles.
Further activities that help children experience the properties of other shapes may be appropriate to lead on to from this one, such as Building Towers and Making Caterpillars.
Resources
An assortment of cardboard tubes e.g. carpet tubes, kitchen roll tubes, music rain sticks ...
Play tunnel (the collapsible kind).
Various food containers with different cross-sections.
An assortment of cardboard tubes e.g. carpet tubes, kitchen roll tubes, music rain sticks ...
Play tunnel (the collapsible kind).
Various food containers with different cross-sections.
Download a PDF of this resource.
Dice
Age
3 to 5
Counting, matching numerals and amounts
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Children often enjoy rolling dice, particularly large ones.
Adults could provoke children's thinking by suggesting an appropriate challenge, for example, “Roll the dice, take that number of teddies out of the box and put them around the picnic table.”
The Activity
Join with a group of children who are already rolling the dice and show how they can use the dice in order to choose the number of teddies/dolls etc. to join them for the picnic/tea party (perhaps in the role play area).
Join with a group of children who are already rolling the dice and show how they can use the dice in order to choose the number of teddies/dolls etc. to join them for the picnic/tea party (perhaps in the role play area).
Encouraging mathematical thinking and reasoning:
Describing
Tell me what the dice says.
Tell me about the teddy you've got to choose.
Tell me what the dice says.
Tell me about the teddy you've got to choose.
Reasoning
Have we got room for any more teddies?
Have we got enough teddies?
Have we got room for any more teddies?
Have we got enough teddies?
Opening Out
Could we play this game with something else?
Is that more than/less than/the same as your last roll?
Could we play this game with something else?
Is that more than/less than/the same as your last roll?
Recording
How can you show how many teddies there are round the table?
What would you like to take a photograph of?
How can you show how many teddies there are round the table?
What would you like to take a photograph of?
The Mathematical Journey
Counting:
- saying one number for each object
- remembering the pattern of the number sequence
- understanding cardinality i.e. that the last number gives the total
Matching numerals and amounts:
- reading numerals/interpreting dots with the purpose of seeing how many there should be
- comparing the value of numerals
Development and Variation
A precursory activity might be to use just a coloured dice and ask children to find items which match the colour thrown.
As a follow-up activity, invite three groups of children to focus on three different collections. For example: cars, building blocks and farm animals. One child rolls the dice and each group selects that number from their collection. You could then provoke discussion between the three groups.
Ask children what they would do with two dice, one with dots and one with colours, which are rolled at the same time.
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A precursory activity might be to use just a coloured dice and ask children to find items which match the colour thrown.
As a follow-up activity, invite three groups of children to focus on three different collections. For example: cars, building blocks and farm animals. One child rolls the dice and each group selects that number from their collection. You could then provoke discussion between the three groups.
Ask children what they would do with two dice, one with dots and one with colours, which are rolled at the same time.
Resources
Large dice (with dots/numerals/colours).
If possible, large dice with replaceable faces, for use with children who are only confident with numbers 1-3, for example.
Easy access to the usual collections found in your setting e.g. teddies/building bricks/cars etc.
Large dice (with dots/numerals/colours).
If possible, large dice with replaceable faces, for use with children who are only confident with numbers 1-3, for example.
Easy access to the usual collections found in your setting e.g. teddies/building bricks/cars etc.
Download a PDF of this resource.
Mud Kitchen
Age
3 to 5
Using everyday language to talk about size, weight, capacity, position and distance
Explore characteristics of everyday (kitchen) objects and using everyday language to describe them
Explore characteristics of everyday (kitchen) objects and using everyday language to describe them
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Children often enjoy digging in soil (mud), filling containers and emptying them, engaging in imaginative play and talking freely.
Adults could provide an assortment of all kinds of objects from a kitchen - pots, pans, a water supply, large and small kitchen utensils etc.
The Activity
Create a child-initiated mud kitchen play area where a small number of children at a time can explore, imagine and create.
Create a child-initiated mud kitchen play area where a small number of children at a time can explore, imagine and create.
Encouraging mathematical thinking and reasoning:
Describing
Tell me about this ...
What's over there?
Tell me about this ...
What's over there?
Reasoning
Why do you need that other pan/pot/ladle/spoon...?
Is there anything else you can think of that could be here? Why would it be useful?
Why do you need that other pan/pot/ladle/spoon...?
Is there anything else you can think of that could be here? Why would it be useful?
Opening Out
What would you like to do with this?
Here are some new ... (items not seen before).
Is that pan/pot/ladle/spoon big enough? (Can you find one that is?)
What would you like to do with this?
Here are some new ... (items not seen before).
Is that pan/pot/ladle/spoon big enough? (Can you find one that is?)
Recording
Would it help you remember this if you took a photo?
Would it help you remember this if you took a photo?
The Mathematical Journey
Counting:
- saying one number for each object (e.g. when voluntarily counting the number of pots/dishes filled with mud!)
- remembering the pattern of the number sequence
- understanding cardinality i.e. that the last number gives the total
- beginning to use counting to solve practical problems e.g. sharing out pots amongst the group
Same and different:
- describing the utensils and what they are doing using the language of comparison e.g. bigger, smaller, taller, longer, shorter, wider, narrower...
Shape, space and measure:
- using everyday words and mathematical words to describe utensils or what they have made e.g. “I want a round jar!”
- using everyday words to describe position e.g. “The pot's behind all the spoons!”
- using everyday words to describe capacity and ordering items according to capacity
Development and Variation
Very similar mathematics could result from water play and sand play, both of which encourage exploration of shape, size and capacity.
Children's thinking could be extended to include ideas about weight by introducing a balance or see-saw into the environment.
Giving children opportunities to explore any new area that you have created will result in them 'doing mathematics', whether they are using ideas associated with number, shape, position or measures, or a combination of the above!
Very similar mathematics could result from water play and sand play, both of which encourage exploration of shape, size and capacity.
Children's thinking could be extended to include ideas about weight by introducing a balance or see-saw into the environment.
Giving children opportunities to explore any new area that you have created will result in them 'doing mathematics', whether they are using ideas associated with number, shape, position or measures, or a combination of the above!
Resources
Obviously, an outdoor area with soil is necessary!
Other useful items include:
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Obviously, an outdoor area with soil is necessary!
Other useful items include:
- Kitchen utensils (pots, pans, spoons, spatulas etc.)
- Large cable drum (to use as a table)
- Play cooker
- Small blackboard
- Water
- De-commissioned microwave oven
- A range of sizes of plastic tubs
Download a PDF of this resource.
Pattern Making
Age
3 to 5
Making and describing patterns
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Children often enjoy spotting patterns and making patterns with lots of different things, including themselves.
Adults could provide a 'pattern of the day' with objects for children to copy, extend and create their own. They could make deliberate mistakes for children to spot. Parents and carers could join in.
The Activity
Children copy and continue an AB repeating pattern with blocks, then do it in other colours and with other materials such as small toys, leaves and twigs or by printing and sticking shapes on long pieces of paper. They can progress to more complex ABB or ABC repeating patterns and to make growing patterns.
Children copy and continue an AB repeating pattern with blocks, then do it in other colours and with other materials such as small toys, leaves and twigs or by printing and sticking shapes on long pieces of paper. They can progress to more complex ABB or ABC repeating patterns and to make growing patterns.
Encouraging mathematical thinking and reasoning:
Describing
What do you notice about the pattern?
Can you say the colours - red, blue, ...?
Tell me about your pattern.
What do you notice about the pattern?
Can you say the colours - red, blue, ...?
Tell me about your pattern.
Reasoning
What is the same and what is different about this one and your copy?
I wonder which one goes next? I think the next one is blue - oh, don't you agree?
Can you explain how the pattern should go?
What is wrong with this pattern?
Is that something you know or did you guess?
What is the same and what is different about this one and your copy?
I wonder which one goes next? I think the next one is blue - oh, don't you agree?
Can you explain how the pattern should go?
What is wrong with this pattern?
Is that something you know or did you guess?
Opening Out
Can you make your own pattern along this strip?
What is the pattern called?
What is the rule for your pattern?
How is your pattern like this pattern? How is it different?
Can you continue this staircase pattern? What do you notice?
Can you make your own pattern along this strip?
What is the pattern called?
What is the rule for your pattern?
How is your pattern like this pattern? How is it different?
Can you continue this staircase pattern? What do you notice?
Recording
Can you record your pattern with stamps?
Can you make a staircase pattern with stickers?
Can you record your pattern with stamps?
Can you make a staircase pattern with stickers?
The Mathematical Journey
Patterns:
- copying the pattern by matching cubes one at a time
- copying by complete units e.g. picking up a red and a blue cube together
- continuing the pattern in ones or in complete units
- correcting an error e.g. spotting a missing cube or reversed colours
- identifying the rule of the pattern - "It should go red, blue, blue"
- noticing a growing pattern - "It's like a staircase"
Counting and cardinality:
- counting the number of items in the unit of repeat, or the towers in a staircase pattern
Adding and subtracting:
- generalising about a staircase pattern - "It's one more each time!"
Position and spatial properties:
- using the vocabulary of position - "The red comes next", "It's blue between the red and the yellow"
- reversing units to make reflecting patterns e.g. ABC CBA
Development and Variation
Provide more complex repeating patterns: ABC, ABB, ABCD.
Vary the materials and media, indoors and out.
Make action or sound patterns and record them with invented symbols.
Make growing patterns, e.g. going up in ones.
Make reflecting patterns with peg boards, mirrors and constructions.
Story, rhyme and song links
The Shopping Basket by John Burningham
There Was an Old Lady Who Swallowed a Fly
Goldilocks
The Gingerbread Man
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Vary the materials and media, indoors and out.
Make action or sound patterns and record them with invented symbols.
Make growing patterns, e.g. going up in ones.
Make reflecting patterns with peg boards, mirrors and constructions.
Story, rhyme and song links
The Shopping Basket by John Burningham
There Was an Old Lady Who Swallowed a Fly
Goldilocks
The Gingerbread Man
Resources
Coloured cubes, beads, small toys, leaves and twigs; printing and sticking shapes.
Pegboards, mirrors, construction materials.
Long strips of paper for making patterns.
See the Erikson Early Math Collective website for more activities about patterns.
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Coloured cubes, beads, small toys, leaves and twigs; printing and sticking shapes.
Pegboards, mirrors, construction materials.
Long strips of paper for making patterns.
See the Erikson Early Math Collective website for more activities about patterns.
Download a PDF of this resource.
Acknowledgements: Helen Thouless and the pattern group, Wandsworth
Cooking with Children
Age
3 to 5
Using everyday language to talk about size, weight, capacity and volume
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Children often enjoy joining in with cooking activities.
Adults could provide recipes and equipment, and a safe environment for the children to cook.
The Activity
Children love to cook! It encourages their independence and increases awareness of healthy eating choices. Cooking can also be rich with mathematical language and thinking. The children can follow a simple recipe to bake and cook, from gingerbread men to bread.
Children love to cook! It encourages their independence and increases awareness of healthy eating choices. Cooking can also be rich with mathematical language and thinking. The children can follow a simple recipe to bake and cook, from gingerbread men to bread.
Encouraging mathematical thinking and reasoning:
Describing
Tell me how we are going to make...
How much flour will we need?
Tell me how we made...
Tell me how we are going to make...
How much flour will we need?
Tell me how we made...
Reasoning
What if the mixture is too wet/dry? What do we need to add more of/less of?
Have we added the right amount of...? How do you know?
What if the mixture is too wet/dry? What do we need to add more of/less of?
Have we added the right amount of...? How do you know?
Opening Out
Provide further opportunities for children to follow recipes. For example, they could make play dough.
Provide further opportunities for children to follow recipes. For example, they could make play dough.
Recording
Would it help you remember what is here if you took a photo?
Could we draw/write something so someone else could have a go at making ...?
Would it help you remember what is here if you took a photo?
Could we draw/write something so someone else could have a go at making ...?
The Mathematical Journey
Counting skills:
- saying one number for each object (e.g. when counting out ingredients and spoonfuls)
- remembering the pattern of the number sequence
- understanding cardinality i.e. that the last number gives the total
Shape, space and measure:
Following a simple recipe to:
- use everyday and mathematical language to describe size, weight and quantity (e.g. half, quarter, a little, a lot, heavy, light, kg etc.)
- use scales to weigh out ingredients
Development and Variation
It is good to involve the children in the whole process, if possible. You could start with writing shopping lists, maybe include a trip to the shops to buy ingredients and then allow the children to cook as independently as possible. Encourage the children to read the recipe themselves, counting ingredients and how many spoonfuls or cups they will need.
It is important that the children use their critical thinking skills when following the recipe. Sometimes they might add a small spoonful which won't be enough. With support, they will need to think about how to fix this problem.
A recipe using spoonfuls requires children to use their counting skills, but you could use weighing scales or cups to encourage different levels of mathematical thinking.
It is good to involve the children in the whole process, if possible. You could start with writing shopping lists, maybe include a trip to the shops to buy ingredients and then allow the children to cook as independently as possible. Encourage the children to read the recipe themselves, counting ingredients and how many spoonfuls or cups they will need.
It is important that the children use their critical thinking skills when following the recipe. Sometimes they might add a small spoonful which won't be enough. With support, they will need to think about how to fix this problem.
A recipe using spoonfuls requires children to use their counting skills, but you could use weighing scales or cups to encourage different levels of mathematical thinking.
Resources
A collection of simple recipes that use visual cues and written number. Try to include a range of different recipes that require increasing skill and mathematical thinking.
A bowl and mixing spoon for every child - this is important as it will increase independence and mathematical thinking for every child.
Attractively presented and easily accessible ingredients for children to use in their recipe.
A camera might be useful for taking pictures.
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A bowl and mixing spoon for every child - this is important as it will increase independence and mathematical thinking for every child.
Attractively presented and easily accessible ingredients for children to use in their recipe.
A camera might be useful for taking pictures.
Download a PDF of this resource.
With thanks to Anna Tanton and children at Ludwick Nursery School who were the inspiration for this activity.
Number Book
Age
3 to 5
Counting reliably with numbers from 1 to 20
Sorting and describing
Sorting and describing
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Children often enjoy collecting objects and counting them, and many love having a sticker book.
Adults could suggest creating a 'number book' when they see a child picking up one or two related objects.
The Activity
Children are asked to collect four (or whatever number is appropriate) of a range of objects both indoors and outdoors, for example, they may choose four leaves, four stones, four play figures... They are invited to create their own book, 'My Book of 4', by sticking the objects into a plain-paged book, where appropriate, or by sticking in photos of the objects.
Children are asked to collect four (or whatever number is appropriate) of a range of objects both indoors and outdoors, for example, they may choose four leaves, four stones, four play figures... They are invited to create their own book, 'My Book of 4', by sticking the objects into a plain-paged book, where appropriate, or by sticking in photos of the objects.
Encouraging mathematical thinking and reasoning:
Describing
Tell me what you are looking for.
Tell me about these things you've collected.
Tell me about your book.
Tell me what you are looking for.
Tell me about these things you've collected.
Tell me about your book.
Reasoning
Do you need any more? How do you know?
Have you got enough? How do you know?
Have you got too many? How do you know?
Do you need any more? How do you know?
Have you got enough? How do you know?
Have you got too many? How do you know?
Opening Out
Provide further opportunities for children to do similar activities in different environments, e.g. on forest visits, in the playground, in the school garden, in the PE store...
Provide further opportunities for children to do similar activities in different environments, e.g. on forest visits, in the playground, in the school garden, in the PE store...
Recording
Will you keep that/them for your book?
How shall we put them in your book?
Could we draw/take a picture of these things for your book?
Will you keep that/them for your book?
How shall we put them in your book?
Could we draw/take a picture of these things for your book?
The Mathematical Journey
Counting skills:
- saying one number for each object
- remembering the pattern of the number sequence
- understanding cardinality i.e. that the last number gives the total
Same and different:
- grouping e.g. these are all leaves, these are all square-shaped buttons
Development and Variation
You could encourage children to group together to count their objects in total and perhaps to create a new book as a result.
You could suggest that the whole group/class creates a counting book of numbers in order from 1. Pairs of children could be given a particular number and asked to find that number of objects of their choice. You could then assemble the book as a whole group/class. It would be lovely for the book to follow the group up the school, where possible.
The following NRICH Early Years activities might offer similar mathematics: Tidying, Incey Wincey, Dice and Washing Line.
You could encourage children to group together to count their objects in total and perhaps to create a new book as a result.
You could suggest that the whole group/class creates a counting book of numbers in order from 1. Pairs of children could be given a particular number and asked to find that number of objects of their choice. You could then assemble the book as a whole group/class. It would be lovely for the book to follow the group up the school, where possible.
The following NRICH Early Years activities might offer similar mathematics: Tidying, Incey Wincey, Dice and Washing Line.
Resources
Simple plain-paged scrap books.
Glue/paste.
A variety of collections of objects in your setting, some of which may be present all the time, some of which may be introduced for shorter periods.
An outdoor space.
A camera will be useful to take photographs of the items that can't be stuck into the books.
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Simple plain-paged scrap books.
Glue/paste.
A variety of collections of objects in your setting, some of which may be present all the time, some of which may be introduced for shorter periods.
An outdoor space.
A camera will be useful to take photographs of the items that can't be stuck into the books.
Download a PDF of this resource.
Small World Play
Age
3 to 5
Using everyday language to talk about position and size, to compare quantities and objects and to solve problems
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Children often enjoy playing in an imaginary small world environment, for example, the zoo, jungle, farm, town map, with animals, cars, people...
Adults could provide small world play figures and an area with separate compartments or boxes, fences, sand, etc.
The Activity
Present the animals or characters and materials to make an environment for them. Below we use the farm as an example. Invite the children to make up a story about where the animals go. Then they might be rearranged or decide to go elsewhere.
Present the animals or characters and materials to make an environment for them. Below we use the farm as an example. Invite the children to make up a story about where the animals go. Then they might be rearranged or decide to go elsewhere.
Encouraging mathematical thinking and reasoning:
Describing
Tell us about where you have put the animals. What's happening - where are they going now?
What a lot of cows you've got! How many animals do you think the farmer has altogether?
Which animals do you think you have most/least of? How do you know?
Tell us about where you have put the animals. What's happening - where are they going now?
What a lot of cows you've got! How many animals do you think the farmer has altogether?
Which animals do you think you have most/least of? How do you know?
Reasoning
Why have you decided to put the cows here? Why is the pig-pen smaller than the sheep-pen?
What size field do you think the horses should have? Why do you think that?
Roughly how many pigs do you think will fit in that field you are building/have built?
How could the cows get to the milking parlour without going through the horses' field?
Why have you decided to put the cows here? Why is the pig-pen smaller than the sheep-pen?
What size field do you think the horses should have? Why do you think that?
Roughly how many pigs do you think will fit in that field you are building/have built?
How could the cows get to the milking parlour without going through the horses' field?
Opening Out
Rina wants to have a farm as well, how could she share some of your animals? Do you think the field for the cows could be any better - if so, how?
What if another five horses arrive? Will there be space in your farm for them? How will the farmer know if any of the animals are lost?
Rina wants to have a farm as well, how could she share some of your animals? Do you think the field for the cows could be any better - if so, how?
What if another five horses arrive? Will there be space in your farm for them? How will the farmer know if any of the animals are lost?
Recording
Let's make a picture of your farm. Can we show where the farmer should put all the animals?
Shall we have an animal stock-take?
Can you make a list or a tally of all the different animals on your farm today, so we can check that they are all there tomorrow?
Let's make a picture of your farm. Can we show where the farmer should put all the animals?
Shall we have an animal stock-take?
Can you make a list or a tally of all the different animals on your farm today, so we can check that they are all there tomorrow?
The Mathematical Journey
Shape and space:
- positional language e.g. next to, opposite, between, behind, underneath, inside, outside...
Measures:
- developing language to compare and contrast e.g. bigger, taller, much bigger, a little smaller...
- explaining that you can fit more sheep in a field because they are smaller
Number:
- counting and cardinality - progressing from knowing some number words, to saying one number for each object, then knowing the number of the whole group
- comparing numbers and estimating
Development and Variation
A visit to a farm or zoo can stimulate children's small world play. Observing the different enclosures and space that each type of animal requires provides an opportunity for children to discuss ideas about size and area.
Dinosaur caves, the zoo, the jungle, the sea-side, or a town map can enable similar mathematical talk.
Children's own collections of objects can provide similar opportunities - see the NRICH activity Collecting.
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Dinosaur caves, the zoo, the jungle, the sea-side, or a town map can enable similar mathematical talk.
Children's own collections of objects can provide similar opportunities - see the NRICH activity Collecting.
Resources
A range of materials for the children to make fences, compartments and environments e.g. recyclable boxes, material scraps, lolly sticks, sand etc.
Paper, card, pens and scissors for making labels, maps and plans.
A range of materials for the children to make fences, compartments and environments e.g. recyclable boxes, material scraps, lolly sticks, sand etc.
Paper, card, pens and scissors for making labels, maps and plans.
Download a PDF of this resource.
Acknowledgement: Helen J Williams
