Mathematics in the EYFS: Calculating - More or less

The earliest stages in knowing about addition and subtraction are focused on the simplest situations: those where you are adding one more or taking away so there is one less. These experiences can be related to the introduction of a 1-10 number track.

As children become more knowledgeable and more efficient at saying the number sequence, they begin to be able to identify the number before and the number after most numbers up to 10. At the same time they also become more expert at counting real objects, so they understand that the last number they say in the count describes the number of objects they have.

Combining both these bits of knowledge and understanding helps a child to know that if you add (or take away) an object, the total count is the next number (or the previous number) in the sequence. Number tracks, number lines and washing lines with number cards pegged on them, all help to present a model of numbers in a sequence. Going forward on the track, children will see that the next number is always one more and by going backwards along the track, that the next number will always be one less.

ONE MORE AND ONE LESS

How children learn

Young children can understand finding one more and one less if the idea is introduced in a way that is relevant and makes sense to them. They often start to develop their knowledge of calculation through meeting addition and subtraction situations in stories and everyday life.

It is through their play experiences of counting out quantities that they gain an understanding of what one more and one less might be. If children are involved in counting on and counting back games and activities, they will also use the language of 'more', 'less' and 'fewer' as they play, especially if you introduce a dice or spinner showing 'count back one' or 'count forward one'.

Using a track where some spaces are marked 'take one more' or 'give one more', where the children keep a running total as they play, will also support their growing understanding of the language of calculation.

Helping children learn

- Use the words 'more', 'less' and 'fewer' as you discuss what children are doing: Would you like more cherries or more grapes? You might need less paint on your brush. Why don't you put fewer bricks in the basket?

- Play games where children add or remove one object from a collection, such as taking another bead or putting back a brick. Sometimes count the changed set to establish that there is one more or one less than there was before.

- Provide activities using number tracks and washing line numbers where children deal with one more and one less in an abstract way (in that they are using numbers rather than objects). Draw attention to the next number of the track being one more than the number before.

- Make use of opportunities that occur during the day. Putting away games and equipment provides situations where you can deliberately make sure that there is one beanbag fewer than there should be or one too many pencils in the tin.

Measuring progress in counting

- Responds to the request to take more or give more of something but without noticing the quantity

- Responds appropriately to request to take one more of something

- Can count the two toys in a boat, and say that if one more got in, there would be three

- Can count the two toys in a boat, and say that if one got out there would be one left

- Can look at a number track and say the number one more or less than three or five

- Can use fingers to solve problems such as: Suppose you had five pennies and you dropped one down a hole. How many pennies would you have left?

- Says the number one more or one less than, say, 4 or 9, when asked.

CHILD-INITIATED PLAY

And another one Put together an interactive table display of lines of elephants, ducks, pattern blocks, bead strings, number cards and small cars, and encourage children to 'add one on', then reverse the procedure to 'take one away'.

Special offer Ask the children to help set up a pound shop with a 'buy one, get one free' offer. Put together pairs of objects for it. Use pound coins to pay for them. Then try a shelf of three for the price of two.

The one-more snake Resource the outdoor area with a collection of long scarves and encourage the children to play snakes by arranging themselves in a long line, each child holding one end of a scarf. As the snake winds round the area, children in the snake call 'one more'. Children join by picking up a scarf and joining on to the end of the line.

ADULT-LED ACTIVITIES

Give and take Each child has a collection of six small animals. They take it in turns to give one of their animals to the person sitting next to them. 'You've got one more animal now. How many does that make?'

I've got it Give everyone four plastic elephants and ask the children to close their eyes. You then say 'and one more is' and add an elephant to one of the sets of four. Ask the children to open their eyes and decide who got one more elephant. Let the children take turns to be the giver.

PROVISION

PE area Provide hoops, soft foam balls, beanbags, felt balls and buckets. Suspend hoops from a washing line and practise throwing three soft balls through the hoops and then one more ball. Discuss choosing three other soft throwing objects that are the same, and one more that is different. Do you all have the same number of things? How many would you have if you gave one to your friend?

Science area Provide balances, conkers, fir cones, stones, soft toys. Make Teddy balance the fir cones or the stones. Discuss what happens when you add more or take some off.

ASSESSING CHILDREN'S DEVELOPMENT

If a child

- talks about the need for 'more' of something: 'I need more juice'

- takes more of something (cake, sand, etc) when asked to do so

then they may be on this step

- begin to make comparisons between quantities

- know that a group of things changes in quantity when something is added or taken away have a positive approach to new experiences

If a child

- talks about 'one more' in the context of an activity where pencils or beads or biscuits are being given out

- responds to the request to take one more counter, acorn or domino or to put one back

- counts out two or three objects when asked to do so, then adds one more when asked, and can count the total

then they may be on this step

- show an interest in number problems

- compare two groups of objects, saying when they have the same number

- demonstrate flexibility

If a child

- adds 1 to (or subtracts it from) a number in the context of a rhyme or game

- points to the correct number on a number track when asked to show which is one more (or one less) than, say, 5 or 2

then they may be on this step

- say the number that is one more than a given number

- sometimes show confidence and offer solutions to problems

- display high levels of involvement in activities

If a child

- closes their eyes and tells you the number one more than or one less than, say 7

- looks at a number track and asks their friend if they can say the number one more or less than 7 or 9

then they may be on this step

- find one more or one less than a number from one to ten

- continue to be interested, excited and motivated to learn

If a child

- closes their eyes and tells you the number two more than or two less than, say 12

- solves imaginary problems set in familiar contexts, involving adding or subtracting 1, such as, if the prince got eaten too, how many people would be left on the ship?

then they may be on this step

- use a range of strategies for addition and subtraction

- sustain involvement and persevere, particularly when trying to solve a problem or reach a satisfactory conclusion

IMPORTANT WORDS AND PHRASES

as many as, more, most, less, least, fewer, fewest one more, one less make, altogether, How many? How many will there be when one more ...? before, after

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 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.