Maths Revision: Visualising Difficult Maths Problems

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We’ve all been there. You’ve stayed up until a (hopefully) reasonable hour the night before your maths exam: committing maths formulae to memory, sharpening your pencils, reminding yourself a bajillion and one times to show your working out.

You think you’re ready. You’re confident. You could write out the quadratic formula blindfolded. You could rationalise the socks off that surd. You could eat a parallelogram for breakfast!*

* Don’t eat a parallelogram for breakfast.

Then, halfway through your calculator paper, BAM! You’re hit with a wall of text!

“What is this?”

“Where are the numbers?”

 “Isn’t the English Literature paper next week?”

“Where’d I put my dictionary?”

“What’s a metaphor like?”

With the maths GCSEs having moved to a more problem-solving approach, chunky worded questions are more and more common. But, never fear. A few simple diagrams may just be your salvation…

Example:

5 animal shelters are being surveyed by a government organisation.
One of the shelters has both cats and dogs but no other animals. At this shelter, 16 dogs are surveyed.
The ratio of the number of cats to the number of dogs at the shelter is 1:2.
The other 4 shelters only have cats. Each of the 5 shelters have the same number of animals.
Work out the total number of animals that are surveyed.

Now. Let’s break this down and visualise the problem.

5 animal shelters are being surveyed by a government organisation.

It may sound silly and unnecessary but… draw 5 boxes to show the 5 shelters. It doesn’t have to be neat; all it needs to do is kick-start your thought process.

Visualising 1

One of the shelters has both cats and dogs but no other animals. At this shelter, 16 dogs are surveyed.

Add any extra information to your diagram as you go along.

Visualising 2

The ratio of the number of cats to the number of dogs at the shelter is 1:2.

We can show this information on the diagram by splitting the box into the ratio 1:2.

Visualising 3

At this stage, you can also calculate the number of cats at this shelter from the number of dogs. Notice that this is the first time in the problem that we’ve actually done any calculations but we already have a framework in place for completing the rest of the question.

Visualising 4

The other 4 shelters only have cats. Each of the 5 shelters have the same number of animals.

From the information in our diagram and the final part of the question, it is much easier to see what we need to do to answer it.

Visualising 5

Work out the total number of animals that are surveyed.

Last step. Nearly there!

Visualising 6

And there we have it. 120 cats and dogs!

Diagrams can be a massive help but don’t go overboard in your exam. If you spend the better part of your 90 minutes carefully drawing Billy and Mandy picking 753 apples and dividing them between baskets, you probably won’t get those method marks.

 

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