18 August 2014

Introducing Algebra

Building a solid conceptual understanding of algebra is absolutely fundamental. As with fractions, it's essential that we get it right because it underpins so much of what follows. But, as with fractions, pupils can really struggle here.

Sometimes good teaching resources inspire us when we're looking for ways to structure and deliver our teaching. This post contains some recommendations that may give you food for thought when you’re planning your lessons.

Before teaching any topic for the first time it's really important to think about potential misconceptions. The best thing a student teacher or NQT can do is ask an experienced teacher. This algebra misconception summary is also helpful. 

The first time I taught algebra, I used this true/false activity to reveal any outstanding misconceptions in the last lesson of the sequence. As a newbie teacher, I was astounded by the mistakes pupils made, like putting both of these cards in the 'true' column:
This activity provided a good opportunity to have individual discussions with pupils and help them make sense of it all. So it’s useful both as a learning experience and for formative assessment.

I'm not stalking him, promise
I've featured resources from Don Steward in almost every blog post I've written. I make no apologies for this. His website is amazing. Here's a few highlights from his algebra collection:
  • Lengthy expressions is a nice way to get pupils used to forming expressions containing letters and numbers.
  • Expression pyramids are an engaging way to practise simplifying and this activity is a perfect extension.
  • In Steps, pupils have to determine what step has been taken to get from one expression to the next (see below).
  • Six expressions is a rich activity for pupils who've been taught how to expand single brackets.
  • Three sets of excellent activities help students explore concepts relating to simplifying and equivalence: 'equivalence', 'same and transformed' and 'equivalent things'.
Steps - Median Don Steward

There's lots more on Median Don Steward - look under the labels algebra, simplifying, expressions and substitution.

Fawn Nguyen’s Noah’s Ark
This is a lovely activity which gets pupils used to the idea of representing values with letters (or pictures in this case).
Noah's Ark by Fawn Nguyen

Visual representations
'I'm thinking of a number' questions are a good way to get started with solving equations. MathsPad had a nice card sort that makes the link between words and algebra. MathsPad also features a worksheet that uses visual representations to build an understanding of how to solve equations. The same approach is taken to rearranging formulae - this lesson plan features their range of associated resources.
More ideas
  • These slides from newmrsc (@_z_0_e) on TES are really good for a first look at algebra.
  • For substitution, I like this code breaker from Teachit Maths (and this second code breaker, which involves harder expressions). Substitution scenarios is nice too.
  • Great Maths Teaching Ideas has, well, some great maths teaching ideas... There's lots of algebra stuff on the website, like this ask ask trade activity for expanding single brackets. 
  • Lindsay Porter (@L1nd54y) suggests using manipulatives when teaching expanding brackets and forming equations. For example, put two chocolate coins and 20 pence in a bag. If we have five of these bags, what do we have? Anything involving chocolate gets my vote. 

I really recommend buying the ebook How to Start on Teach First: Maths by Kris Boulton, Bruno Reddy and Bodil Isaksen. The associated 'How to teach...' documents (accessed via Dropbox) are incredibly helpful. For example 'How to Teach Collecting Like Terms' has very clear explanations of misconceptions and teaching strategies for introducing algebra.

There's loads more resource recommendations, covering every aspect of Key Stage 3 and GCSE algebra, in my algebra resource library. Do comment below or tweet me if you have any more resources or ideas to add.

Image: crotchetycomics.blogspot.com


  1. You think algebra is something to be "introduced"?

    1. Hello Anonymous. It's just a title. Could you expand on your comment please?

  2. The longer I teach, the more props I use, especially for algebra!

    Even when 'reviewing' with older pupils I will still use concrete items, to good effect IMHO. I use yoghurt pots with x on them to emphasis that the letter is just a label on a container, holding a value that we cannot yet see; same label, same value. I use balance scales a lot for equations, specifically to reduce prevalence of x + 4 = 10, becoming x = 10 + 4; if I take four out of one side of the scales, can I put it in the other side to make them balance?

    I also increasingly put in the implied multiplication, especially elsewhere within the curriculum, so for example I tend to write C = π x d and, probably more importantly A = π x r², which helps reduce occurrence of the output being (π x r)².

    1. Thanks for your comment, very helpful. I like your yoghurt pot idea! It's great to hear different approaches.

  3. A nice collection of resources and ideas. Perhaps make it clearer that you would use the true/false activity in the first algebra lesson (I just had to re-read to see if the content matched the title!).

    I sometimes wonder if I should just substitute 'algebra' with 'playing', as we're just playing around with numbers and letters (and 'algebra' can sometimes send students to sleep even before they've given an activity a chance). I too am using more visuals and relating algebra to something more tangible.

    Thanks for the post Jo!

    1. Thanks Tim. I think some pupils are scared or bored by the term algebra but some are excited by it. It's nice to introduce something totally new in Year 7, makes a nice change for them!

  4. Readers who are interested in approaches to teaching algebra at primary school might be interested in this blog: http://year4atist.blogspot.fr/search/label/algebra

  5. Very informative and beautifully put up!