The ‘Big Ideas’ in Teaching and Learning Fractions and the New National Curriculum
Big Idea II Fractions as Numbers
What does the research say?
There is a large body of evidence to indicate the usefulness of using numberlines to develop conceptual understanding of whole number and decimals (Siegler et al, 2010) but little in a similar vein for rational numbers (Nunes et al, 2009). As has been mentioned above there is evidence that pupils are commonly introduced to fractions in the context of part/ whole relations but are not exposed as widely to fractions in other forms. Although part/ whole and quotient situations are important, so too is an understanding that fractions are numbers with magnitude in their own right and that they hold positions on a numberline. Both Nunes (2009) et al and Seigler et al (2010) propose that it is safe to assume that the credibility of the numberline for developing whole number sense should be equally credible with rational numbers. Siegler et al also suggest that the numberline is a useful way of teaching ‘fraction density’ i.e. understanding that there are infinite fractions between any two points on a numberline.
A fraction’s order of magnitude is however more difficult to interpret than whole numbers because its magnitude is determined by the relationship between the numerator and denominator. This requires a complex knowledge of fractions to order and compare them (Nunes et al, 2009).
Where does this ‘big idea’ occur in the new programme of study for mathematics?
- Pupils should count in fractions up to 10, starting from any number and using the 12 and 24 equivalence on the number line (Non Statutory Guidance)
- count up and down in tenths
- count up and down in hundredths
Misconception 1: The number 12 lies half-way between any two labelled integers on a numberline
Count from 0 beyond one in different factional steps pointing along an unmarked counting stick. Label 0 and another integer (within the possible range) on the counting stick. Discuss where 12 could be and why.
Misconception 2: Fractions have to be smaller than 1 whole.
When counting in fractional steps, provide visual representations to represent the count. Then introduce the symbolic representation.
How do you currently encourage counting in fractional steps in your teaching?
Can be used to support pupils’ developing conceptual understanding of this ‘big idea’ (fractions as numbers)?
When counting in fractional steps, provide visual representations for each step in the count.
Play this slide to accompany counting in fifths.
When pupils are confident introduce the symbolic representation to accompany the count.
Play this slide to accompany a count.
Use fraction bars to accompany a count. With each count, a further fractional piece is shaded. Remember to count past one and over other whole numbers. Play this slide to accompany a count.
Watch the Developing fluency - counting in fractional steps video clip from our Supporting the new National Curriculum suite of materials to see how to use the counting stick to develop fluency in counting forwards and backwards in fractional steps beyond one whole.