Category: Proportional Reasoning

Looking at the Ratio Grid Questions from the EDEXCEL June 2020 Paper Mathematics Paper 2 (Foundation)

The exam paper referred to in this post can be found here. For each question which is compatible with Ratio Grids, I work through a similar example, then you can try the actual exam question. The answers to the exam paper can be found here. This is a calculator exam.

You will need to be able to complete a ratio grid to follow this page – so watch this 2 minute video!

Similar to Question 4 – write a fraction as a percentage

Similar to Question 13 – A machine filling containers with items – how many left over?

Similar to Question 14: Drawing a Pie Chart

Similar to Question 16. How many marks needed to pass an exam?

Similar to question 17: Making Orange Juice

Similar to question 17b: Simplify a ratio (Calculator method)

Similar to question 19: Sharing money without knowing the total

Similar to question 20: Shopping with a ratio

Similar to question 23: Different sized boxes

Similar to question 28: Exterior angles in a polygon

Percentages Using Ratio Grids

If you are not already confident using RATIO GRIDS then watch this video first!

What is 35% of £14?

What is 15% of £85?

My savings target is £5500. I have saved £2640. What percentage have I saved?

Jo scored 65% in a test. She scored 26 marks. What was the test marked out of?

A tree was 15m tall in January. Now it is 18m tall. What is the percentage increase in height?

Another tree has grown 15% since January. It is now 46m high. What was its height in January?

Now try some problems yourself:

notes-sheet-6-percentagesDownload

Currency Conversion using Ratio Grids

Check out the Introduction to Ratio Grids if you are not already an expert!

When you are asked to do a currency conversion, you will usually be given an exchange rate first, as in this question:

“George changes some pounds into Euros. The exchange rate is £1=€1.18. If he changes £350 into Euros, how many Euros will he receive?”

Draw a simple Ratio Grid and give headings of £ and €. Put the numbers 1 and 1.18 in the correct columns. Then, the final number from the question, £350, goes in the £ column under the 1. Putting the numbers into their correct places is easy if you have headings! Put a ring around the empty space – that is where your answer will go.

In this grid, the 2 multiplying numbers are the “1.18” and the “350”, and you will divide by 1. So the sum will be 1.18×350÷1.

The answer is 413, and it is clearly in the Euros column, so give your answer as €413.

It’s easy if you get the headings right!

If you want lots of practice, Mr Corbett has a great set of currency conversion questions.

For lots of simple questions click here and the answers are here

Exam-style questions are here** and the answers are here. (Mr Corbett doesn’t use Ratio Grids so his methods won’t look the same, but the answers are all the same, obviously!)

** Some of these questions are really challening – they may require 2 ratio grids, so think carefully! If an exchange rate changes, you will need a new grid for the new rate.

Solving Ratio Problems

If you don’t yet know how to work out the 4th number in a ratio grid, watch this video first!

The videos on this page use the worksheet “Ratio Problems” which you can download:

ratio-problemsDownload
Simplify a Ratio using a calculator
Split Money using a ratio
Wordy Ratio problem about socks
Wordy ratio problem given one of the values and not the total
Ratio problem sharing sweets

Answers

Notes sheet 4 ratio answersDownload

Introduction to Ratio Grids

Ratio Grids can be used whenever you have a problem that starts with 3 numbers, and you have to times and divide. They are a clear way of laying out your working, and knowing which order to do the calculation.

You will need a calculator to do the practice questions, but first, here are 2 videos. The first shows you how to solve a small ratio grid, the second deals with the larger ones:

Larger Ratio Grids
ratio grids questions v2Download

Click here for asnwers

Your comments are very welcome – please use the box below.

Now you can use Ratio Grids to solve a Maths Problems, here are some types of problem you can try:

Recommending mathsbot.com

I am grateful to Mr. Holding who teaches locally for this link. So simple! Lots of GCSE questions presented one at a time. A couple of examples are reproduced below.

http://mathsbot.com/gcseQuestionshttp://mathsbot.com/gcseQuestions

The Proof Questions on this site are invaluable – the best collection I have seen.

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Ratio Grids Topic Overview

I invented “Ratio Grids” to help students who struggle with Proportional Reasoning. The philosophy includes:

  • All proportional reasoning sums are essentially the same – times 2 numbers and divide by a third. If one of the numbers is one, then it’s just a multiply or a divide.
  • Students who get used to working a problem “forwards” often struggle to work backwards, but mathematically there is no difference!
  • Skills gained working with ratios can be applied to shopping, percentages, similar shapes, stratified sampling, speed, density, and other “per” problems, Direct and Inverse proportion, currency conversions, unit conversions and the Sine Rule, without learning shed loads of new stuff.
  • Students often get in a muddle because they do sums and lose hold of the units of numbers so although they get a correct answer they don’t realise what it means! Ratio hold the units of numbers as well as the numbers themselves.
  • Students sometimes try to mix different units inappropriately in their working. With ratio grids this is much less likely.
  • Start at the beginning with the Introduction to Ratio Grids

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