# Bar modelling

Bar modelling is an approach that was developed in Singapore in the 1980s and has proven to be an effective problem solving strategy for pupils. They were developed to help students visualise problems by turning abstract words into pictorial models.

Bar models do not give solutions to a problem but rather aid with finding the solution. Bar models may also need to be adapted as new relationships or information becomes clear.

The best way to explain bar modelling is to go through a problem and see how it can be used.

This is a basic addition problem and it is where pupils would first experiment with bar models. The blue bar represents Daniel's books and the orange bar represents Leah's books. Both bars combined will represent the total number of books. The bars that pupils draw do not have be an exact length or size - it is an approximate representation of a quantity. It is really important however that the bars are in proportion to each other, so for example the orange bar should be slightly longer than the blue bar because it represents one more.

Comparison bar models can be used for subtraction, for example;

This is a basic subtraction problem and as you can see the top bar represents the 'whole' amount (Paul's pencils). This time Fran's pencils are represented underneath. This helps pupils visualise how much greater/smaller one quantity is. When completing problems like above pupils might not need to draw a representation for it as they may already know the answer. However they should practise bar modelling with questions that are not too challenging at first so they become used to and familiar with how they work.

Lets now look at a more complex problem and how bar modelling can help:

"Sarah is three times as old as Omar. Jack is twice as old as Omar. Susan is two years older than Jack.

Altogether their ages sum to 26 years. How old is Susan?"

Bar modelling question from Eoin Gill on Vimeo.