Curriculum 2014 – Teaching fractions at KS1
28 August 2013
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From 2014, children will learn about basic fractions from age five. Use paper-folding to teach these important concepts.
Fractions from age five
With the arrival of the 2014 primary maths curriculum, children will be introduced to basic fractions such as ½ and ¼ at the age of five – a subject currently left until pupils are aged seven to 11.
But is this such a change? Many schools already do that – but if you don’t teach fractions at this level, it’s worth familiarising yourself with the work of your colleagues higher up the school.
Children meet the concepts of ‘half’ and ‘quarter’ frequently in many different situations outside the classroom in their daily lives so engaging them in a discussion about halves and quarters will give you a sense of their level of understanding. For example, in the context of time children will hear ‘half-past’, ‘quarter-past’ and ‘quarter-to’. In the kitchen you will see measuring scales and kettles that have divisions of half pints as well as showing the amount of water as a decimal of a litre. In the supermarket children will see half-price offers.
Do you know all about fractions?But what about you? What’s your knowledge and understanding like? A simple starting point is to ask what a fraction is. Try defining what a fraction is and you’ll realise this is not as easy as it sounds. If you haven’t taught them for a while it’s worth reminding yourself that there are five basic types:
- A fraction as part of a ‘whole’ or a ‘unit’
- A fraction as a number
- A fraction as the result of division of whole numbers
- A fraction as ratio
- A fraction as an operator
There are various models for representing fractions and these can be categorised as discrete models (for example, individual objects such as sweets, marbles, counters, pencils) and continuous models (based on relative area or relative length). The new curriculum refers to both.
Children’s development of the concept of fractions will come over many years. The most important concept is that of the unit or whole, as all fractions are relative to a unit. Unit fractions are some of the earliest fractions that children will encounter in their everyday lives at school and outside of the classroom.
What we need to do is to support children so that they really understand halves and quarters at an early age – then they can develop their understanding of all the other fractions in KS2. There is a tendency to teach fractions through cakes, pizzas and colouring in or circling pictures. These are fine in themselves and play an important role, but not alone.
Fractions in paper-folding
Hands-on problem solving is key and paper-folding is a great starting point for getting children immersed in fractions.
Give children a strip of paper 20cm long and ask them to fold it into two equal pieces. Remember, rectangles and thin strips are suitable for all fractions at this stage but circles and triangles are less versatile for fractions like thirds.Ask these discussion questions:
- How many parts are there?
- How many folds are there?
- What do we call each part?
- Show me one half of the paper strip. Show me a different half. Write ½ in each half of the strip.
- How many halves are there in a whole?
- How many parts will there be?
- How many folds will there be?
- What do we call each part?
- Show me one quarter of the paper strip. Show me a different quarter. Label each quarter by writing ¼ each time.
- Show me two quarters. What is another name for two quarters?
- Which is larger: one half or one quarter? How do you know?
Children can then be asked to use their paper folding to show three quarters, four quarters, one half and one whole. In groups of three, challenge children to make a poster to teach others how to use paper folding to create different sorts of fractions.
Ensure that children understand that the bottom number of a fraction (the denominator) tells them how many pieces the whole is divided into. Emphasise that when a shape (or number) is divided into fractions such as quarters, each piece has to be the same size. Show children an example of a shape divided into four pieces but the pieces are not in quarters because they are not the same size. Ask which is bigger, a half or a quarter? By how much? Children can then show how much bigger and discuss how they found out.
‘Choose your chocolate’ challenge
Show children a bar of chocolate and say that there are two children in another class who are arguing about how much to have. Draw two speech bubbles on the board and write the following:
- ‘I’d like ½ of the chocolate bar because that’s bigger than ¼’
- ‘¼ is the biggest because it has got the biggest bottom number’
Ask children to discuss the statements in pairs. Would they choose a half or a quarter? How could they prove that ½ is bigger than ¼ using paper? Get them to demonstrate that just because the bottom number is big doesn’t mean it is the biggest fraction. Then move onto to talk about which is bigger, a half or three quarters? By how much? Which is smaller?
This will naturally lead into talking about the equivalence of fractions by asking which is bigger, a half or two quarters? And why stop there? There is no reason why you can’t keep on folding into eighths and beyond if children display a good understanding.
Other useful fraction tools
There are lots of ways of teaching halves and quarters. You could distribute a range of concrete materials such as fraction bars, Cuisenaire rods, string/paper clips and folded paper strips, pattern blocks, geoboards, and paper shapes of regular polygons. Get children to choose a material and then get them to show you what a half or a quarter looks like. Share ideas and the various representations including any misconceptions. Depending on what children choose they could draw or trace around fraction bars/rods, draw an empty line segment and indicate halfway, stick a folded strip into their maths folder or take a photo of their 2D representation.
Teaching all the various aspects of fractions can be challenging and children will need as much hands-on experience as possible. Paper-folding is a brilliant way to help children get off to a flying start and provides a solid foundation from which to explore further especially for moving onto objects that cannot be easily folded, cut or coloured into equal parts. Paper-folding sounds simple but when you first ask a class of five-year-olds to fold a piece of paper ‘in half’, you are sure to get some interesting results!
- Find out and start from what children know.
- Talk about how fractions are used in everyday life.
- Use lots of practical apparatus and visual examples.
- Make connections with other topics.
- Give lots of thinking time when asking questions.
- Delay formal fraction vocabulary until children are ready.
- Make activities enjoyable and fun with plenty of partner and group work.