19 May 2014


Surds - what a fabulous topic to teach! I love the abundance of resources available and I’ve listed some of my favourites below.

Two things I always do when teaching surds:
  • Pupils list the first twelve square numbers in their books for reference throughout the lesson. They need to readily recognise square numbers in order to simplify surds so the more they practise listing them, the better.
  • When manipulating expressions containing surds (eg expanding brackets) I make comparisons to what they already know about algebra. For example √2 and √3 can be thought of in the same way as x and y (ie not ‘like terms’) whereas 2√3 and 5√3 can be thought of in the same way as 2x and 5x (ie we can add them to get 7√3).

The NCETM suggests a couple of nice ‘hooks’ for getting started teaching surds:
  • Ask pupils to find a way of drawing a line with a length of exactly √5 units (the hypotenuse of a right angled triangle with sides 2cm and 1cm) 
  • Ask pupils to divide the length of an A4 piece of paper by its width. Repeat for A3 and A5. What do they notice? (The answer is always √2)
This blog post has some more ideas for introducing the concept of surds. And I like this on the history of surds.

Here’s some great teaching resources (there's hundreds more online). Most of these work equally well at GCSE and A level:

For a lovely set of surds problems, see my Problem Sets page.

Finally, if you're looking for something really creative, check out this Wheel of Theodorus Art Project.

Edit 29/12/14: Thanks to @runningtstitch for suggesting an alternative method for simplifying surds:


  1. What a fabulous summary of several lesson plans!

  2. I wrote more about surds here:


  3. Thanks for these. This year I've started teaching simplifying surds using a prime factor tree. It works perfectly and removes the need for a list of square factors.

  4. The factor tree method is one that I was shown by one of my students this year. This comes after teaching this topic for the past 5 years, and learning it back in school. Just goes to show how we're always learning...

    1. Agree! It's great to be shown new methods.