Comparing quantities and measuring are complex skills. Comparing lengths or weights or objects against each other or against a measure, such as a tape or a gram weight, is a complicated process. Sometimes we only need rough measurements and sometimes it is important to be more accurate. One of the skills children will learn is knowing when accuracy matters.
Measuring is something we do all the time, so there are lots of words we can use for comparison: big, small, wide, narrow, tall, short, for example. Young children need to play at measuring to have the opportunity to use as many words as possible.
While children are comparing the length, weight, volume or capacity of objects, they are also beginning to gain an understanding of the conservation of measures - that length, weight and so on, don't change arbitrarily, even though the appearance of an object might change. In other words, the child needs to eventually know that they still have as much dough - the weight is the same - whether it is in a lump or rolled flat. And they will know that their height stays the same whether they are in a big hall, where they feel small, or in the playhouse, where they feel big.
COMPARING QUANTITIES
How children learn
Children learn about comparing and using the language of measures as a result of exploring a wide range of materials and objects in lots of different situations. Initially they compare things according to less formal measures: 'These cups look the same', 'This book is nicer than that one'. This helps them to develop the idea that comparing things is something we do in life.
A child's interest in measures often arises through contrasts: big and little bears, fast and slow cars, high and low towers. At other times they will compare three or more things, such as putting Goldilocks' three bears in order of size.
Children usually gain an understanding of length by directly comparing two objects. The longest of two pencils or ribbons, for example, can be found by putting the two items next to each other, relying on a combination of trial-and-error and estimation to find out. A similar development of children's understanding of weight happens as they directly compare two objects. It is much later that they begin to make the distinction between weight and size or use a balance.
Children also develop an interest in measures by watching adults and copying: they like to use a tape measure and 'read off' the number; they may try to 'measure' water in a jug with a ruler. Although they don't fully understand these measuring instruments, playing with them links what they do with the adult world.
Helping children learn
- Talk about lengths, distances, weight and time without measuring them. Talk about what a long way it is to the park, how heavy a box is to carry, or what a short time it took to tidy up.
- Read stories about tall giants, long caterpillars, small mice and things that happened a long time ago or yesterday. Involve the children by encouraging them to act stories out.
- Compare two things directly, one against the other: find which bead string is the longest, stand the teddies next to each other and see which is the tallest. See which bowl holds the most by filling one with rice and tipping it to the other bowl.
- Discuss the importance of lining up the ends in order to work out which of two things is longer.
- Introduce measuring tools: centimetre tapes, rulers, simple balances and spring balances, jugs with measures and litre containers, sand-timers and stopwatches. Using real measuring equipment gives children the opportunity to practise being measurers.
Progression
- Uses hand movements to indicate size, and words such as big or little, to indicate size or weight without comparison.
- Experiments with fitting objects into containers or clothes on to dolls or teddies.
- Uses sight to estimate and judge size and fit more or less accurately.
- Begins to appreciate that some things can be large but not heavy, and tests weight by lifting objects.
- Selects from a range of words, such as 'thick' or 'thin', to describe an object.
- Is likely to distinguish between the vocabulary or weight and the vocabulary of size - for example, talks about 'tall' when building; talks about 'heavy' when using the balance.
- Begins to use comparative words, such as 'taller', 'shorter', 'heavier'.
CHILD-INITIATED PLAY
Weighing in
Set up a weighing area and resource with a range of weighing equipment, such as large bucket-balances, kitchen scales, stand-on scales and any other weighing machines that will give the children an opportunity to weigh large and small items. Introduce a block and tackle system for really heavy objects.
Develop the play by adding pricing: weighing heavy objects costs 2p, lighter objects 1p. Let children build a 'Speak your weight' teddy weighing machine and take it in turns to be its voice.
Ball sorting
Resource the outdoor area with two buckets, one labelled 'large' and the other 'small', and a collection of large and small balls. The children can throw or sort the balls into the correct bucket. Extend the play by introducing a medium-sized bucket and asking the children to explain why they are putting a particular ball into a particular bucket.
Lots of lentils
Put out a tray with tiny containers, such as doll's house cups, film canisters, mustard spoons and bottle lids, along with a tub of lentils. Children can fill and empty containers with the lentils. Extend the play by adding pricing: lentils cost 1p per mustard spoonful. Find out how much each tiny cupful is worth.
ADULT-LED ACTIVITIES
Stretching high
Tape a roll of paper to the wall. Ask everyone to put a fingertip in some paint and then stretch as far up the wall as they can and press on the paper to make a fingerprint (the idea is to make a line of fingerprints across the paper). Write each child's name next to their print. Extend the activity by discussing whose fingerprint is the highest up.
How far up the wall can you stretch?
How will we know who can stretch the furthest?
Footsteps
Cut out footprint shapes from newspapers or magazines. Ask the children to make a footprint line between two different places, such as the book corner and the sand tray, and the book corner and the door. Extend the activity by deciding which line was the longest.
I wonder whether it's further from here to the front door or the back door?
How do we know that door is further away?
PROVISION
Water area
- Provide a large jug of water and collection of small containers, glitter, pebbles, thick plastic freezer bags.
- Add glitter to the water to make a magic potion and find out how many containers you can fill with a jugful of potion. How many would you need to fill the jug half full?
- Pour a container of potion into a freezer bag. Ask the children holding it in their hand how many containers of potion a giant could hold.
Can you hold it all in your hands?
How will you know when it is half-full?
Construction area
- Provide large plastic building bricks, wooden blocks, a digital camera.
- Build the tallest tower that you can, decide whether or not it is taller than anyone in the room and discuss how to reach the top of the tower.
- Go for a 'tall walk'. Take photographs of tall buildings and cranes to display in the construction area.
Which one do you think is the tallest?
Does anyone know how to use measuring tapes?
Important words and phrases
Long, short, tall, high, low, wide, narrow, deep, shallow, thick, thin
Weight, weigh, heavy, light, balance
Full, empty, half-full
More, less, shorter, longer
About the same, just over, just under, too much, too little
Today, tomorrow, yesterday
ASSESSING CHILDREN'S DEVELOPMENT
IF A CHILD
Brings you, when asked, the 'big one' or 'small one' of two toys
Has an undeveloped sense of size, trying to fit, say, a small dress on to a large teddy
Can say whether it is fair or not when one child has more juice
then they may be on this step
Use language such as 'big' and 'little'
Have a positive approach to new experiences
IF A CHILD
Puts the big plates in one pile and the small plates in another pile
Makes statements using 'than', such as 'This is curlier than that'
Predicts (accurately or not) that the sand in the jug will fit in the bucket
Comments that the bucket of water is very heavy
then they may be on this step
Match objects by similarities
Adapt their behaviour to different events, social situations and changes in routine
IF A CHILD
Puts two laces side by side with their ends together when asked to find which is longer or shorter
Uses comparing words - for example, 'The cloak is too short'
Distinguishes between weight and size - says that the little tin of beans is heavier than the big cereal packet
Sequences story pictures, using words such as 'first' and 'last'
Programs the floor turtle to move so many units forward
then they may be on this step
Order two items by length or height
Cut material, paper or ribbon to size
Order two or three items by length
Order two items by weight or capacity
Instruct a programmable toy
IF A CHILD
Deals with imaginary comparisons - for example, 'When the baby gets bigger, the clothes will be too small'
Makes fine comparisons between things that are not very different - 'This mug's got more juice in it than that one'
Talks about time or speed, such as 'I want to finish before dinner' or 'I was quicker than he was'
then they may be on this step
Use language such as 'greater', 'smaller', 'heavier' or 'lighter' to compare quantities
Respond to significant experiences, showing a range of feelings
IF A CHILD
Puts three things in order - for example, orders three bears by height, then finds where a fourth item fits into the order
Counts to compare when measuring - for example, counts marbles in two boxes, then announces which is bigger
Watches you squash flat one of two identical dough balls, and says that they can make them the same again
Says it is still fair when they watch you give them and a friend the same amount of drink and then pour theirs into a different shaped mug
then they may be on this step
Know that counting can help them compare size, capacity or weight
Understand the length of something does not change if you bend it
Sustain involvement and persevere, particularly when trying to solve a problem or reach a satisfactory conclusion.
ABOUT THIS SERIES
This series aims to:
- build on practitioners' knowledge of how children acquire numeracy skills
- offer ideas on how to help children develop these skills.
Each part focuses on an aspect of numeracy included within the 'problem-solving, reasoning and numeracy' area of learning in the EYFS.
Authors Sheila Ebbutt and Carole Skinner are managing director and product development manager, respectively, of BEAM, which is dedicated to promoting excellence in mathematics education.
