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Ratio problem solving for 9-1 GCSE with answers

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

27 September 2017

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clareturnertutor

A good set of ratio questions that require problem-solving. Thank you for sharing.

Empty reply does not make any sense for the end user

Nice selection of questions, thank you.

This is an excellent worksheet for the most able students because it focuses on the harder questions that initially cause them problems that are reasonably easy to overcome.

Lovely selection of questions, thank you.

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Resourceaholic

Ideas and resources for teaching secondary school mathematics

• Blog Archive

20 December 2017

New gcse: ratio.

• Mel from JustMaths collated ratio Higher GCSE questions from sample and specimen papers here , and has written up her solutions here . 
• If you subscribe to MathsPad then you'll be pleased to hear that they have lovely resources for ratio including a set of questions for Higher GCSE  with loads of examples like the problems I've featured in this post.  
• Don Steward has plenty of ratio tasks  including his set of ' Harder Ratio Questions ' and a really helpful collection of GCSE ratio and proportion questions .
• On MathsBot you can generate ratio questions, revision grids and practice papers. Select 'ratio, proportion and rates of change' at the top.
• There are exam style questions in this collection from Lucy Kilgariff on TES.
• OCR has a 'Calculations with Ratio' Topic Check In  and AQA has a Ratio and Proportion Topic Test .
• David Morse of Maths4Everyone has shared a set of revision exercises and ratio exam style questions .

20 comments:

My ratio pages don't get much attention - not sure why since I think they're instructive and easy to use. They don't support the particular type of harder questions described in the post (but I'll look to add something along those lines), but they do help understanding the concept of a ratio and it's utility. Manipulation of ratio quantities: http://thewessens.net/ClassroomApps/Main/ratios.html?topic=number&path=Main&id=7 Introduction to the ratio concept: http://www.thewessens.net/blog/2015/03/19/ratios-the-super-fractions/ Bar model visualisation of ratios: http://thewessens.net/ClassroomApps/Models/BarModels/visualfractionratio.html?topic=models&path=Models&id=17 Multiplicative word problems: http://thewessens.net/ClassroomApps/Models/BarModels/multiplicationwordproblems.html?topic=models&path=Models&id=8 Ken

Fantastic! Thanks Ken.

Thanks so much for your blog on ratio question types. Although I've been a maths teacher/tutor for over 30 year, ratio has always been a bug bear for me. I could wing it with old style gcse because I learnt the types of solutions required, however I have been stressed on the new types. This blog has made me think through ratios and I am certainly a lot happier. Bryan

Excellent, I'm so pleased it helps.

On your fractions approach, a quick trick is to realise that a/c = a/b x b/c. Makes it quite quick to work out (That is, if the students are good with cancelling down when multiplying). However, what I find confuses students about writing ratios as fractions is that it confuses the part:part idea of a ratio with the part:whole idea of a fraction. Perhaps that's why it's somewhat counter-intuitive. Also, final point is that ratios (fractions) and vectors is another application of harder ratio questions that often pops up on the new GCSE. Thanks for the post, Farah

Thanks for the comment!

This is a fabulous resource on work that is missing from the new GCSE texts that I have seen. Lovely challeging questions to make students think.

Thanks! Glad it's helpful.

I've been using equivalent ratios for these type of questions. Find what doesn't change - the total number of sweets. Write ratios as equivalent ratios where the parts that doesn't change are the same. 3:7 has 10 parts, 3:5 has 8 parts LCM of 8 and 10 is 40 Ratios are 12:28 and 15:25 Number of sweets given is 3. Also works for following question Ratio of blue to red counters in a bag is 1:2, I add 12 blue counters and the ratio is 5:7. How many red counters are in the bag? What doesn't change? Red counters LCM of 2 and 7 is 14 Ratios are 7:14 and 10:14 3 parts are 12 counters, 1 part is 4 counters and 14 parts are 56 red counters. Also Jill is 4 times older than Jack. In 14 years time the ratio of Jack's age to Jill is 5:7. How old is Jill now? Ratios are 1:4 and 5:7. What doesn't change? The difference between their ages Find two equivalent ratios where difference between them is the same. 4 - 1 = 3 and 7 - 5 = 2 LCM of 2 and 3 is 6 Equivalent ratios are 2:8 and 15:21 13 parts = 26 years, 1 part is 2 years, Jill is 16.

This is the approach I use. I think it's logical.

Thank you! Yes, this is logical. Same approach as bar modelling (but without the visual).

Oops, my mistake, third example should be .....in 26 years time the ratio of their ages is 5:7 ..... I did try to represent these using bar modelling at first but struggled to find a model that was intuitive and actually helped with the question. I would be grateful if anyone has ideas on this.

Although some bar modelling experts would disagree, I don't think bar modelling is intuitive/helpful for harder ratio questions. Bar modelling is fantastic for easier ratio questions, but when the questions get more complicated it's often really hard to figure out how to draw the scenario - definitely not as easy as some people make out!

Thank you for the post. Brilliant as usual. I actually did the sweets question in my class once. I simply said that Alice fraction of sweets changed from 7/10 to 5/8 when she gave the 3 sweets away. If we just subtract those fractions, the fraction remaining, 7/10 - 5/8 = 3/40. This means that Alice originally had 40 sweets.

Hadnt considered tis method but I love it

Thanks Stephen. I guess it makes sense, as the fraction lost is equivalent to the 3 sweets divided by the total.

Love this! Thanks for sharing.

Hi Jo, thanks for the post which I came across via a tweet you put out a couple of days ago - which also tied in with a question and the same method I saw in my step-daughters book the very next day - freaky! It is a more compact method than I would normally use in my teaching and will be switching to it. I think the only tweak I might make is to write the algebra ratio above the numeric one so the starting fractions are (7x-3)/5 : (3x+3)/3 The reason being that some students might get a little scared seeing algebra as part of the denominator but less so when faced with a number.

Good idea - thank you!

Hi Jo, One method I use when teaching questions like the first one above (Alice gives 3 sweets to Olivia) is the following. To begin with Alice has 7/10 of the sweets and then after giving three to Olivia, her share has reduced to 5/8 of the sweets. So Alice's share has reduced by (7/10 - 5/8=) 3/40 which is equivalent to 3 sweets, therefore there must be 40 sweets in total. Students can then proceed in answering the relevant question. I must admit I only use this method with the top sets.

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Ratio problem solving

A KS4 maths worksheet resource to practise more difficult problems involving ratio. These questions require students to recognise that the first step is to consider how the initial ratio has altered to achieve the final ratio. Solutions could be achieved by setting up an algebraic equation to solve. 

Step-by-step answers are provided. 

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Ratio Diagnostic Questions

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• Each question has one correct answer and three carefully chosen incorrect answers that are designed to identify and highlight fundamental misconceptions
• The questions include topics such as simplifying ratios, writing ratios in the form 1:n, dividing a quantity into a ratio, combining ratios, and map scales.

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