10th February 2012 at 00:00

How not to do fractions.

It does not seem to matter whether the pupil is a fresh-faced Year 7 (P7) or a weary Year 11 (S4) who has been taught the topic for several years, when pupils are asked to add up two fractions, they confidently add the tops and the bottoms, writes Craig Barton.

What's the solution?

I think the only hope is to show them their answer simply cannot be right. I start by asking pupils which is bigger: one-third or one-quarter. After a brief discussion about pizza or cake, most are happy that a third is larger. I then ask if they can simplify the answer of two-eighths. After slicing up the pizza a few more times, we are happy that it is the same as one-quarter. Now I ask if they are happy with what is written on the board. After a bit of discussion, it soon becomes clear there is a problem: we had started with a third, added on something positive and ended up with an answer that we know is smaller than we started with.

This method does not teach pupils how to add two fractions, but it does show them how not to do it. Crucially, it shows them, in a way they can understand, that the method of adding tops and bottoms together cannot be correct. If they have discovered this for themselves, they are far more likely to remember it.

What else?

Fun Tarsia games may help to tackle this problem. Alternatively, try one of the many fractions tasks in the TES Topic special collection.

From lesson plans to activities and worksheets to assessment, CIMT offers a full fractions unit.

Log-in as an existing print or digital subscriber

Forgotten your subscriber ID?


To access this content and the full TES archive, subscribe now.

View subscriber offers


Get TES online and delivered to your door – for less than the price of a coffee

Save 33% off the cover price with this great subscription offer. Every copy delivered to your door by first-class post, plus full access to TES online and the TES app for just £1.90 per week.
Subscribers also enjoy a range of fantastic offers and benefits worth over £270:

  • Discounts off TES Institute courses
  • Access over 200,000 articles in the TES online archive
  • Free Tastecard membership worth £79.99
  • Discounts with Zipcar,, Virgin Wines and other partners
Order your low-cost subscription today