Tuesday, 7 May 2013

Collecting like terms a story of cards and beer

How to have success with Algebra

Collecting like terms
Have you taught collecting like terms, thought most pupils understood it, only to discover the next lesson your back at square one?  

Use this idea and you'll find far greater success. It is simple and easy to use.

I like most maths teachers used the fruit analogy. You know  what I mean, let 'a for apple and b for banana', then expected pupils to add a + 4b +2a + 2b. 

Virtually impossible to take that amount of fruit into the classroom as a visual aid. Reduce the stress in your life by using this idea. The visual aid you'll need? You can carry it around in your pocket.

A story of how cards and beer solved an algebra problem.

Whilst having a chat with my friend Dave he confided in me that his daughter Emily was very worried about Maths. Dave being an intelligent and perceptive fellow had come to the right man. 

Having taught Maths since 1975 I had seen many a youngster through the years struggle with what is thought to be  difficult subject and during this time I had even picked up some good ideas on how to overcome some fundamental problems.


Dave's problem

‘What’s the problem Dave?’


‘It’s this Algebra thing, you know when you put all those a b and c’s together.’ He replied with a worried look and furrowed brow. ‘It was something like 4x + 3y then you had to add it to
x + 5y.’


Collecting like terms is what we call it in the trade. All I need is a beer, a pack of cards, pen and paper and your undivided attention and I’ll show you how to teach Emily to collect like terms.’


Pack of cards

Dave intrigued provided me with a pack of cards, a beer, pen and paper and his undivided attention. I dealt him ten cards face down and asked him to sort them into their respective suits. He had 4 spades, 2 clubs, 1 diamond and 3 hearts.

The first set of terms

‘OK Dave write down what you’ve got but don’t bother with the full names of the suits, lets have a code for each, what do you suggest?’ 

Quick as a flash he came up with s, c, d and h, no fool this boy I thought. I suggested also using + instead of ‘and’ because I knew his spelling wasn’t up to much. He then wrote down



Algebra begins
4s + 2c + d + 3h


I then dealt him another 10 cards. The results were 3 spades, 2 clubs 2 diamonds and 3 hearts, I encouraged him to write the results underneath the original using our code or notation as we Mathematicians like to call it. His paper now looked like this

The second set of terms
4s + 2c + d + 3h


3s + 2c + 2d +3h


I drew a line underneath and said add them, his results were


Collecting like terms
7s + 4c + 3d + 6h


‘You’ve just done algebra, collecting like terms to be precise’ I explained. ‘So if you had 4h + 3s and added it to 7h what would you have?’ ‘11h + 3s’.


‘Now if I changed the h to x and s to y’?


‘11x + 3y. So just treat them as if they are suits in a pack of cards, how many of each do you have. Is that right?’ ‘Sure is'I replied. ‘Oh boy 11x + 3y, I can do algebra, you wait until I show Emily.  

Then 4x + 3y  added to x + 5y is 5x + 8y. Wow it’s easy, there is only one thing I don’t understand where does the beer come into it?' 
‘It’s for me, cheers!’

You might also like to read my post Solving equations with a frog


 A great collection of starters for a classroom is '101 Red Hot Starters.'

'Start your lessons with a bang! Letts Red Hot Starters contains a bank of snappy, interactive starter activities. Each starter consists of a simple, effective activity involving minimal preparation, answers and suggestions for differentiation.'




Follow me on twitter @croftsr1


  • More resources for your classroom click on resources