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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 1 - Fractions (including decimals and percentages)

New Curriculum

  • recognise, find and name a half as one of two equal parts of an object, shape or quantity
  • recognise, find and name a quarter as one of four equal parts of an object, shape or quantity

Non-Statutory Guidance

Pupils are taught half and quarter as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole.

Links and Resources

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.
Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10

Connections within Mathematics

Making connections to other topics within this year group

When teaching and learning is focused on fractions in Year 1, there are many links that can be made to other areas of the mathematics curriculum;

Number and place value:

  • Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least.

Addition and subtraction:

  • solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9.

Multiplication and division:

  • Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Measurement:

Compare, describe and solve practical problems for:

  • lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]
  • mass/weight [for example, heavy/light, heavier than, lighter than] capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]
  • time [for example, quicker, slower, earlier, later]

Making connections to this topic in adjacent year groups

Early Years Foundation Stage

Numbers: children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer.They solve problems, including doubling, halving and sharing.

Year 2

Pupils should be taught to:

  • recognise, find, name and write fractions ⅓, ¼, 2⁄4 and ¾ of a length, shape, set of objects or quantity
  • write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of 2⁄4and ½.

Non statutory guidance

Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet ¾ as the first example of a non-unit fraction.

Pupils should count in fractions up to 10, starting from any number and using the ½ and 2⁄4equivalence on the number line (for example, 1¼ , 12⁄4 (or 1½ ), 1 ¾, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one.

Cross-curricular and real life connections

Fractions, in particular halves and quarters, can be linked to many different ‘real-life’ contexts. Children naturally use the term ‘half’ or ‘halve’ in general conversation. Encourage them, and the adults working with them, to refine their use of the word, and try to use it accurately.

‘Introduction to Fractions’ from Nrich provides a series of 7 useful activities for connecting fractions to other activities, in the form of a trail.

Rationale for teaching fractions, with consideration of likely misconceptions

An overall guide to some of the complexities in teaching and learning fractions. Includes possible misconceptions as well as suggestions for activities.

Written for teachers of adult learners but nevertheless extremely useful for primary teachers too.

Aspects of a teacher’s mathematical knowledge in a lesson on fractions taken from: Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics . 29 (3), p1-6.

Journal article addresses teachers’ mathematical knowledge and looks into the factors which lie behind the fact that some pupils’ concepts of fractions are only partly developed.

This article looks into some different perspectives through which children see fractions. It looks into some of those perspectives, firstly by considering what happens in situations where learners are trying to create equal shares. From sharing using halves learners move to partitioning using other divisions, such as fifths or sixths.

Programme of Study statements Activities
A B
recognise, find and name a half as one of two equal parts of an object, shape or quantity
recognise, find and name a quarter as one of four equal parts of an object, shape or quantity  

Activity A - NRICH Making longer, making shorter

This activity includes doubling, halves and quarters in a very practical way using rods made from interlocking cubes. It gives children a practical context in which to explore simple multiplying and dividing, even if these particular terms are not used explicitly. It can provide a very useful context for introducing and using the vocabulary of halves and quarters.

Having multilink cubes for each child is essential.

Coloured blocks

Activity B – NRICH Happy Halving

This problem consolidates children's understanding of halving and will help them to develop their skills of visualisation.

It is important pupils are clear that, in this problem, the halves must be exactly the same size as each other. A precursor to this activity might be to show the group a square and ask them to split it in half in their "mind's eye". By discussing where they have imagined the "cutting line", the children will discover that there is more than one way to do this. From this point, you can talk about whether or not the two halves are the same size each time.

It may be useful for the pupils to have a sheet of the shapes. Alternatively, they could use a pegboard or geoboard to try out their ideas.

Dots activity

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

recognise, find and name a half as one of two equal parts of an object, shape or quantity

Here is a set of 12 pencils

Coloured pencils

How many is half the set?

Shade one quarter of each shape 

Shapes to shade

recognise, find and name a quarter as one of four equal parts of an object, shape or quantity

Four Children share 12 strawberies into equal parts.

How many strawberries will each child have?

Strawberries

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