![]() ![]() We can also see the single percentage multiplier for the calculation – the strategy that is considered the ‘endgame’ for percentage change at GCSE. We have the quantities in the question (160 is 100%) and the quantity we need to find (120%). This is a snapshot of the key information from the ratio table above. Learners can also “build up” amounts by using addition or subtraction to combine previously-found quantities, such as adding 10% and 5% to find 15%.Īs learners become more experienced, it may be appropriate to push them further, by considering contracted ratio tables: When finding 20%, some may like to find 10% and double, some may divide by 5 to go straight to 20%, and some may have other strategies. The ratio table also allows and encourages learners to work flexibly. The main advantage of a ratio table over a bar or DNL is that scaling is no longer an issue – for example, both bar and DNL become difficult to work with for percentages less than 5%, as you’re trying to cram working into a small space. Finally, add 160 and 32 to get the answer 192.To find 20%, we can divide by 10 and multiply by 2.If we’re increasing by 20%, then we need to find 20% of 160 and add it on.Begin the table by writing the whole amount (160) as equal to 100%.The ratio table is an extension of these models, rather than a starting point in its own right: In the example above, we can see the multiplier 1.6 to get from the bottom line to the top – this represents 1%, so we can begin to have discussions with learners about unitary methods. For example, it is more natural to then begin to talk about the connection between the two number lines and what this represents. This retains the visual spacing aspect of the bar model, but requires learners to think more carefully about related quantities. However, it’s important that students are not taught how to use a ratio table as ‘a method’ or a magic bullet just before exams.Ī ratio table is part of a continuum of models for proportional reasoning, beginning with the bar model:Īt some point, it becomes appropriate to remove some structure – so learners move on to a double number line (DNL): ![]() What does a ratio table show?Ī ratio table helps to visualise multiplicative relationships. The solutions given below are in no way endorsed by Edexcel. The examples used in this blog are adaptations of previous Edexcel GCSE exam problems. ![]() There is also a ratio tables worksheet aimed at students, with a variety of exam-style questions which can be solved using ratio tables. Towards the end of this blog, you can find some practice ratio questions to try for yourself, along with a suggested pathway to solve using a ratio table. After they sat the non-calculator paper, I sat down and went through the exam, and found 7 out of 24 questions which lent themselves to solutions using ratio tables – you can read that blog via the links at the bottom.Īs I’ve spent the last few months immersed in analysis of the most recent series of GCSE maths exams, I thought it would be an interesting exercise to repeat, this time looking at the opportunities to solve problems using ratio tables on the Foundation papers. I immediately saw the advantages of ratio tables as a problem-solving strategy – at the time I had a group of grade C borderline students who were sitting the (old) Higher paper. I first encountered ratio tables while participating in an NCETM project on multiplicative reasoning in 2014, coinciding with lots of curriculum development work for GCSE 2015. Ratio tables are extremely powerful for giving learners a step-by-step representation on which to ‘hang’ their working out, or help to scaffold problems that they may not immediately see a route through.
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