One way that children learn about addition is through practical experience. In everyday life, we add when we combine two sets of objects, such as opening a packet of six cakes and a packet of four cakes and putting them on a plate. Sometimes we then count to find the total; in general, we find the total mentally. Experience shows children that six cakes and four cakes always make ten cakes.
In subtraction too, children learn by practical experience. They learn that removing a particular number of things from a group always leaves the same number of things. And again, this helps them learn about numbers in the abstract. A set of six cars with two removed always leaves four so, eventually, they learn that 6 minus 2 is 4.
Addition and subtraction
How children learn
Children learn about addition and subtraction through meeting simple number problems as part of their daily life and by being encouraged to talk through how to find the solution.
Children's experiences of playing games that involve winning or losing a number of objects as they progress around the board or move along a track give them opportunities to be involved in doing lots of adding and taking away in a fairly short period of time. Playing in a group or family situation lets them see how adults or older children do addition and subtraction.
Many children begin to understand a notion of addition as they learn clapping songs, and finger rhymes that they have to act out first with the right hand and then the left and then both hands together.
Helping children learn
- To help children learn about addition, provide plenty of practical experience - games as well as real addition situations - involving objects, people, pictures and sounds. Introduce all the relevant language to help children talk about what is happening.
- To help children learn about subtraction, provide practical experience involving sets of objects, people and pictures where some objects are hidden or removed. And, again, model the relevant language for children to acquire for themselves.
- How many do you think there will be altogether?
- I wonder how many there are left.
- Have you got fewer pencils than I have?
- There were three dinosaurs in the box and two have escaped. How many are still in the box?
- I think five fingers and five fingers together makes ...
- If there were eight frogs sitting on a log and one jumped off, how could you work out how many were left sitting on the log?
- Have you got more or fewer pennies than you started with?
- Ask children to roll two different coloured dice together and to collect that many counters. Then discuss which colour counters there are more of.
- Ask children to dig up buried treasure from the sand tray with a friend and work out how many things there are altogether.
- Encourage children to make a ten-bead necklace and decide how many of each bead they need.
Assessing progress in addition and subtraction
- Joins in number rhymes and songs about increasing and decreasing numbers of fish, birds, sausages
- Responds to the instruction to take more counters, bricks, or buttons, or to remove some
- Uses counting to find the new number of items in a small group after some have been added or removed
- Uses counting to find the total number of items in two separate groups
- Uses counting to find the number left when some have been removed from a larger group
- Predicts results before they know the actual answer to an addition or subtraction situation: 'I think it will be seven'
- Can answer questions such as: 'There are five bugs in the box and two have escaped; how many are left?'
- Can mentally add 1 or 2 or subtract 1 or 2, to or from a number up to 10 or 20
- Knows all the number bonds up to 5 or more: 3 and 2 makes 5
- Knows that when a group of three or four beans is split up, the total is still the same.
Child-initiated play
Yours and mine Provide a selection of small, interesting baskets, bags or trays and interesting collections of items to fit inside them. Invite the children to choose a container and some items to put in it. Encourage them to talk about and compare their container with that of a friend. Develop the activity by playing 'Give again' with two or three children. The children take turns to give one or two things from their collection to the person sitting next to them. They count how many they have left or have gained each time.
Trams Use two shoeboxes decorated to resemble a two-carriage tram and make a queue of small-world characters waiting for the tram. The children decide how many should go in each carriage. Develop the play by adding more characters and another two-carriage tram.
Take some away Provide a set of small, lidded containers and fill half of them with different objects. Leave the other half empty so that the children can remove some objects from one container and put them in an empty container.
Adult-led activities
Chips for everyone Give everyone two paper plates. Take it in turns to take one scoop of chips (counting sticks) from the pan and put some chips on each plate. Help children decide if the two plates have the same number of chips on them or not: 'I think there are more chips on this plate. What do you think?'
Magic purses game Each child has a purse and there is a bank of pennies on the table. Everyone puts four pennies in their purse. A magician puppet says how many pennies to take out of the purses and then guesses how many are left in each purse. The children empty their purses and check. 'How many do you think are left? How many did we take away?'
Provision
Music area Provide instruments that make distinct sounds (drums, tambourines, chimes), chalks and boards. Together use two different instruments to make up simple five-beat tunes, such as two beats on the drum and three beats on the tambourine.
Find a way to record the music and display it for others to try. 'Can you remember how that music went? Can we work out how to play this on the board?'
Outdoor area Provide a collection of cardboard boxes, a soft ball tied with string attached to a washing line, easel and paper for scoring. Build a wall with cardboard boxes and swing the ball at the wall twice. Each time, count how many boxes were knocked down.
Record the total on a score board. 'How did you find out how many boxes there were to start with? Do you know a way to work out that total?'
IMPORTANT WORDS AND PHRASES
add, take away, leave, make, sum, total, altogether, enough, not enough, double, more, less, count on, How many more to make ...?, How many are left?
ASSESSING CHILDREN'S DEVELOPMENT
If a child
- comments that they and a friend 'both have the same' when each child has two pieces of apple
then they may be on this step
- compare two small groups of objects, saying when they have the same number
- show curiosity
If a child
- responds to the instruction to take one or two more bricks, or to give one or two coins to a friend
- counts up to three or four objects, even when these are not all together, such as two cherries on a plate and another cherry on the table
- can help you count four bears, and say there are still four bears, even when you move them around
then they may be on this step
- show an interest in number problems
- separate a group of three or four objects in different ways, beginning to recognise that the total is still the same
- adapt their behaviour to different events
If a child
- counts the paint brushes in the jar, in order to find the total number when some more have been added
- counts the paint pots on the table in order to find the number left when some have been removed
then they may be on this step
- find the total number of items in two groups by counting all of them
- use own methods to solve a problem
- show confidence
If a child
- With five counters, can tell you how many they would have if you gave them three more
- With six counters, can tell you how many they would have left if you took two of them away
- Can find out how many bears there are in two houses by counting both sets
then they may be on this step
- relate addition to combining two groups
- relate subtraction to taking away
- use developing mathematical ideas and methods to solve practical problems
- maintain attention and concentrate
If a child
- Finds out how many there are altogether by combining two lots of objects and counting them
- Takes away by removing six objects from a set and counting what remains
- Solves imaginary problems set in a familiar context
- Seems to just know some number bonds
then they may be on this step
- use a range of strategies for addition and subtraction, including some mental recall of number bonds
- 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 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.