Ratio and Bar models - 3 key questions

My intern has recently been discovering bar modelling as she looks for ways to introduce percentages and ratio. It led me to reflect on one of my first uses of the bar model a good few years ago - in helping pupils see the differences between three types of ratio sharing questions.

Those with longer memories will remember that most ratio exam questions would usually be of the type where you had to share an amount over the whole ratio; and that many pupils came a cropper when they switched questions and gave the value of one part of the ratio. So many pupils had become fixated on the process of "add the parts of the ratio together, divide then multiply" which of course only worked for sharing over the whole ratio. Better pupils then started to solve both types of problems, but mainly by learning when to add and when not to. A few years ago a question previously unseen in recent memory crept in which gave the value of how much bigger one part was than another. Many pupils failed to solve this type of problem because they hadn't been prepped for it before; they didn't really understand how ratio worked they had just been taught to solve certain types of problem. This is what led me to the bar model for the first time, as a way of illustrating the difference in these different approaches to ratio. Allow me to illustrate with 3 questions

Set up: Alfie, Bort (Simpsons reference!) and Claire share some money in the ratio 2:3:5

I start with the line to set up all 3 questions and then bring in the bar model.

Pupils tend to be quite happy that this shows the ratio 2:3:5

From there I introduce question 1:

1) If they share £150 in total how much does each person get?

This leads us to the idea that the whole rectangle being worth £150 and so dividing the £150 into 10 parts. The bar model and solution ends up looking like this...

Now to introduce question 2:

2) If Bort get £150, how much do the other two people get?

This leads us to the idea that only the orange section is worth £150, and so this time we divide the £150 into 3 parts. The bar model and solution ends up looking like this...

Finally to introduce question 3:

3) If Claire gets £150 more than Bort, how much does each get?

Comparing the orange to the pink section we see that the pink section has two more parts, so these two parts have to make £150. That means we are now dividing the £150 into 2 parts. The bar model and solution ends up looking like this...

Pupils commented on how much clearer their understanding of how to solve ratio problems was and in the follow up questions were able to apply themselves much more to different types of ratio problems.These days I only ever introduce sharing with a ratio like this, and mix the questions as early as possible, Given that the bar model can then be used to link to fractions, decimals, percentages (points to those who can translate all of these problems into percentage problems) I think it is well worth exploring this approach with your pupils.