Splitting the total when a ratio is given is a fairly basic bit of number maths. I first encounter this at middle school level, typically for an 11+ or 13+ maths ISEB entrance exam, or at GCSE maths.
I made a video three years ago on how I explain how a total is split into a given ratio.
Once you have watched the video you will notice how I use whitespace to decode the question and make the problem clearer first.
The problem is a simple one, there are 140 students at a school and the ratio of girls to boys is 3:4. How many girls and how many boys are there at the school?
I first put down the information in a very compact and clean form. Writing the ratio down, and the letter G and B above the relevant part of the ratio. I also write out the total number of students below.
The key to ratio questions is finding 1 part and then amplifying the 1 part to 3 or 4 parts later. Once you have 1 part, it is easy to find as many other parts as you want. So I work out that:
3 parts + 4 parts = 7 parts.
7 parts = 140 students
1 part = 140/7 = 20 students
3 parts = 20 students x 3 = 60 students
4 parts = 20 students x 4 = 80 students
And that’s the question done! Please let me know if you have any comments on the video or this method below.
Below are a few tips for those students who struggle with particular questions in maths, find it frustrating, or freeze doing tests. The new 9-1 grading system has more challenging questions than we have seen previously, so these tips are more important than ever.
- If practising for an exam, do not attempt past papers under timed conditions straight away, instead bitesize the whole process and first do the paper without any time constraints. Time pressure causes the mind to rush and freeze up and you are working at very limited mind capacity to problem solve effectively. Once confident at solving questions with unlimited time, you can gradually introduce a time limit.
- In geometry questions, a 4 colour pen is invaluable. Are there any parallel lines involved? Then sketch the parallel lines in red. You will be surprised by how much new information is now revealed and you can “see” the problem much clearer with colour.
- Make sure you use a rough column (on the right hand side) or rough paper to write out what you are thinking, even if it simple multiplication. The more you free your mind (working memory, a bit like computer RAM) up from irrelevant information, the more “space” there is for your mind to solve the actual problem. Think of a shopping list, it is tempting to remember it all, but once you’ve put it on paper you can focus on other things. The other benefit of writing out is that it gives the examiner important clues to your thinking. I marked thousands of GCSE exam scripts for an exam board and we were trained to pick out even the smallest hint that you are thinking along the right track. Just one number scribbled might get you extra method marks!
- The use of white-space on paper is worthy of a chapter in itself. But in summary : Use lots of paper and space to write. When your writing gets squashed into a corner or at the side of the page, it clutters the mind as well. So use plenty of space when writing. Even if your mind feels cluttered, the use of nice open white space will clear things out in your head too.
- Cuisenaire rods are an invaluable resource for primary school children starting off in maths, or those with Dyscalculia. Anything physical that you can touch, see and move around is invaluable. Lego cubes are superb for working out plan and elevation drawings.
- Say it out while writing. This might seem a bit odd, but when you say out something as you write it, it really helps you process things much better. In fact this is the kingpin of my method when tutoring maths online to my students.
- Stuck at a problem for ages? Leave it, and come back to it and start again on a clean, fresh piece of paper. Your subconscious is very powerful and may have solved (or part solved) the problem while you were having your break.
- Ask for help: Ok, so you tried everything and nothing so far has helped. Don’t be afraid to ask for help, there are so many that can help you. Your teacher, any place where there are extra maths lessons, maybe a relative or even other students that you know. Try talking out the problem with friends and you may find that in trying to explain the question you’ve already solved it. And of course, you can always ask the help of a tutor too.
So there you have it. I use these methods when tutoring maths. Pretty much at all levels from primary, to Common Entrance 13+, to iGCSE maths exams, and during A Level maths tuition sessions online. My list is by no means complete and I am very curios to know how you get yourself unstuck, or if you are a teacher yourself please do write in the comments below and let me know what you think.