How to help every child understand ratio

From TES.

Dividing a quantity unevenly is an abstract idea that most children struggle with.  As the problems become more complex, people struggle all the more to see what to do, for example:

  1. Jack and Jill share £28 in the ratio 5:2, how much does Jack receive?
  2. Jack and Jill share some money in the ratio 5:2.  Jack receives £15, how much does Jill receive?
  3. Jack and Jill share some money in the ratio 7:3.  Jack gives £20 of his money to Jill, so now they have the same amount each.  How much money do they have altogether?

Even a child who successfully gets their head around the process of ‘adding the numbers, divide by that amount, multiply by each number separately,’ for question 1, is then straight away often stumped by what to do when faced with question 2.  The abstract calculation is a nightmare for most.

There are two effective techniques for making ratio problems concrete that somehow seem to slip people for a long time, and those who know about them seem to come across by chance.  Here’s the first.

The Box Method

Draw out boxes to represent the ratio.

Box method for learning ratio


It quickly makes much more sense to a person now that they will need to share out the £28 from question 1into 7 boxes.

Box method for learning ratio


By this point it’s painfully obvious to anyone that Jack receives £20, and Jill receives £8.

This method copes equally well with question 2.


Click to continue reading on

About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.
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