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Mathematics in the EYFS: Data handling - Sort it out

Sorting items by different properties and comparing them is a skill that you can observe the children learning to use with increasing sophistication, as Sheila Ebbutt and Carole Skinner demonstrate.

Sorting, comparing and ordering are ways in which human beings organise information. Young children need to build up lots of experience of organising objects so they can develop abstract ideas of ways of categorising the attributes and functions of things in the everyday world. This helps them see connections and relationships between ideas.

As children experience different materials, experiment with their surroundings, sort out what they want to play with, and talk about these things, they notice similarities and differences. These similarities and differences form the basis of classification, and this is the basis of developing logical thinking.

When a child sorts through a collection of objects and finds all the buttons, they are forming a classification for 'buttons'. This is not as easy as it sounds - buttons may share no single characteristic other their function. Buttons come in various forms (with two holes or four, with a shank, as a toggle), shapes (square, round, oval, novelty shapes), materials (wooden, plastic, bone, metal), and they come in all shapes and sizes.

It is easier to sort objects that have the same name - as long as you can recognise the category of an object. Some buttons, for example, may not be recognisable as buttons if you've never seen them in use (such as a toggle).

You can also sort objects together that have a property in common, such as being wooden. This is harder, because some objects have only some wood on them, so the definition needs refining to 'things that have some wood in them'.

When we sort objects (such as 'buttons' or 'wooden things' or 'things I like'), we actually make two classifications: buttons, and things that are not buttons. It is as important to identify the property that rejected objects lack.

When children can sort objects by themselves, they may use very abstract classifications, such as 'these are the things I like'.

The more sophisticated the sorting, the more precise children need to be with their definitions. At what point does an object become smooth rather than rough? When does purple become blue and no longer purple? We also need children to be flexible with their thinking. We need them to be able to sort objects in different ways for different purposes. Things that are 'buttons' and 'not buttons' can be resorted into 'things with wood in them' and 'things with no wood'.

Data handling

Handling data, as well as being about classification, involves comparing sizes and quantities. Once you have classified objects, you can compare amounts: Are there more cars than other vehicles in this box? Children can set them out in two equal lines to find out. Which fruit do we like best - apples, pears or bananas? Children can draw a picture of themselves and line it up above the fruit they like best to see which one is the favourite fruit in the group.

Children learn to sort things by doing it themselves. There are many opportunities in the setting for the children to tidy things up, and to decide which things belong with which. You can involve them in organising where things are kept, and in recording with pictures where things belong. Children often decide to put things together in a surprising way. They might say, 'All these clothes in this drawer belong to the big teddy, and he likes wearing red', rather than putting all the sweaters together.

Treasure baskets, with a set of themed but disparate objects, are a good way of challenging children to classify in a more complex way. For example, children can explore a 'basket' of brushes, and sort out those that are similar in some way. They can sort the box of sparkly things into those they like best and those that are just all right, then find a different way of sorting them.

They can sort themselves out as a group, by finding out about preferences, and voting. To decide which song to sing or which book to read, the children can first make three suggestions. Each child can then put their photograph next to a picture relating to their preferred song or book. This way, they can see easily which has the most votes.

When comparing the quantities, children need to start with comparing the real objects. You will need to show them how to line up the cars one by one with the lorries to find out whether there are more cars than lorries. Drawing a picture of, or having a photo of, each vehicle is more abstract than using the real objects. A further, and much more difficult, abstraction is to represent each vehicle with a counter or a cube.

Work on sorting, classifying, comparing and ordering will help develop children's logical reasoning and problem-solving skills.

Helping children learn

- Encourage children to think of their own way of sorting objects.

- Provide a rich environment, with plenty of varied activities, and don't make things too easy for the children.

- Encourage children to be precise about why they have sorted objects in a particular way, and challenge them with another object that makes them think more clearly about their reasoning.

- Ask children to justify why they have not included certain objects in their sorting. What is common to all the objects they've left out?

- Expect children to be flexible in their thinking. Every now and then, re-classify the way objects are stored or tidied up in the setting.

- Talk with children about what they are doing. Adopt a 'softly-softly', wondering approach, rather than using too many direct questions: I wonder why you've put those things together ... Where will you put this van - with the cars or with the lorries, or somewhere else? We could see if any of these other things have got holes in too ... Let's see which is our favourite song today.

- If the children get stuck, provide prompts: Shall we put this over here? I wonder if that one goes there?

- At the end of the task, recap the problem-solving process with the child or the whole group: Let's tell how you decided where to tidy this away. First you ... then you ... And in the end you checked the other things in the boxes.

Progression

- Sorts a few objects that are like each other without being able to explain why they are like each other;

- Finds pairs of objects that are like each other, or makes a chain of linked objects;

- Sorts some objects and explains why, but leaves some out;

- Begins to re-sort objects, and then reverts to a previous way of sorting;

- Begins to make comparisons between quantities;

- Chooses a set of objects which are the same in some way and explains why those objects belong together;

- Compares two groups of objects by lining them up, saying when they have the same number;

- Sorts a set of objects and explains why, and explains why other objects are left out;

- Sorts a set of objects in different ways;

- Uses the mathematics they already know, but in a new context, such as lining up the teddies to vote, to see whether the big teddies or the little teddies will play in the garden today.

Child-initiated play

Stack the shelves

Children dress up in overalls and caps to organise the shelves in an area of the setting. Provide sticky labels and pens and pencils for children to record where things go.

Make a treasure basket

Set up a treasure basket packing area. Have a pile of baskets, and boxes of quantities of very different items. Challenge the children to make up a basket with a common theme, and to make a picture label for the basket showing why all the things are like each other. Or leave the basket for other children to guess the theme.

Adult-led activities

What's the same?

Show the children a basket of random objects. Explain that you are going to think secretly about how some of the things in the basket are the same. Take out one object at a time and either say 'Yes!' and put it in one place, or 'No!' and put it in another place. The children have to guess why the objects in the 'Yes!' pile go together.

Extend the activity to let children think of a way of sorting the objects - for example, you think these are all the furry ones? How can we check that?

Ask: Where do you think I'm going to put this one? On the 'yes' pile or the 'no' pile?

Jelly pots

Make jellies, with different-flavoured jellies in small plastic or paper pots. When they are set, work with the children to line them up to see which colour the children made the most of.

Ask: Do you think we made more yellow or more red jelly? How can we line up the jellies so that we can compare them? How do you know there are more yellow jellies?

Scavenger hunt

Give each child a small box and suggest that the children see how many different things they can find to put in their box, before it is full. After a box has been filled up, place the contents on a small tray so that the children can compare the contents of each box.

Ask: How can we line up the objects to compare them? Which box had the most things in? Can you think why all these things on this tray are the same in some way?

Provision

Science area

Provide a water tray and a basket of things to float and sink: paper, plastic bottle, shell, stone, cork, bubble wrap, ping pong ball, golf ball, plastic cup, pencil, polystyrene squiggles, feather, fir cone, paper bag, wooden peg, plastic peg, metal clip.

The children can sort the objects to find out those that float and those that sink.

Ask: I wonder if we can make that cup sink? Is there anything that neither floats nor sinks?

Music area

Provide items with potential for noise-making, such as paper, dry leaves, sandpaper, tin foil, yoghurt pots and tins with lids containing stones, beans, rice and so on, metal chains, wooden baby rattles, small blocks of wood, empty pots and tins, plastic ring necklaces, dried gourds, wooden spoons, tape recorder.

Experiment to find out the different sounds the objects make. Find out which sounds are like each other, and make up names for them. Children record sounds they have made and describe them.

Ask: I wonder what things will make a crackly sound? Can we find anything else that will clink when we shake it? How many things rustle when you move them? What sort of sound do all these things make?

About this series

This series aims to:

- build on practitioners' knowledge of how children acquire numeracy skillsL

- offer ideas on how to help children develop these skills.

Each part will focus 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.

Important words and phrases:

count, sort, group, set, match, same, different, the same as, compare, more, less, vote, table, graph, pattern, rearrange, separate, collect, another way, a different way, the same way

ASSESSING CHILDREN'S DEVELOPMENT
If a child:
Comments that the counter and the coin are both round
Collects all the 'big' leaves on the grass
Tries to organise the washing line numbers when they are in a muddle
then they may be on this step
Categorise objects according to their properties
Begin to categorise objects by properties such as shape or size

If a child:
Tackles a simple task, such as separating the spoons from the forks
When asked 'Which fruit do we like best - apples or bananas', offers the
right one
When matching play people to cars, talks about there not being enough
cars for people
then they may be on this step
Show an awareness of similarities in shapes in the environment
Begin to compare quantities

If a child
Collects up the correct pieces of jigsaw from a jumble
Picks up two objects and identifies them as wooden
Identifies favourite of three fruits correctly from a graph
Sticks three photos of children next to trike area and says that's all
the children there's room for
then they may be on this step
Match some shapes by recognising similarities and orientation
Order two or three items by length or height

If a child
Pulls out all the furry objects from a feely bag, and says that these
are all the furry ones and there are no furry ones left
Sorts the birthday cards into different boxes by their ages, and writes
the age on each box for the shop
Sorts the vehicles into three lines by colour, then draws a picture of
these lines
then they may be on this step
Sort familiar objects to identify their similarities and differences
Count how many objects share a certain property, presenting results
using pictures, drawings or numerals

If a child
Sorts shells by one criterion, then sorts them again by another
criterion
Works in a group to decide whose name is the longest by lining up letter
cards
Organises voting for the group's favourite story
then they may be on this step
Sort objects, making choices and justifying decisions
Use developing mathematical ideas to solve practical problems
Work as part of a group or class.