Maths Subject Knowledge: Proportion, Ratio and Scaling

Learn how to solve proportional reasoning problems and apply them to real-world contexts and STEM subjects.

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Maths Subject Knowledge: Proportion, Ratio and Scaling
The CPD Certification Service

This course has been certified by the CPD Certification Service as conforming to continuing professional development principles. Find out more.

Subject knowledge for teachers and educators without a maths background

Proportional reasoning and the use of ratios is required across different areas of the mathematics curriculum. It is essential to many areas of science and technology and is used in a range of situations in both life and work.

In this course we will explore different mathematical strategies to enable you to solve proportional reasoning problems. By participating in this course you will discover multiplicative reasoning strategies, links between ratio and proportion and the ability to scale things up and to scale things down.


  • Week 1

    Proportional reasoning

    • Introduction to proportional reasoning

      In this first activity, you'll understand that proportional reasoning is about multiplication. We introduce the idea of proportionally scaling up and down.

    • Using different methods

      You've been introduced to the basics of proportional reasoning, now let's apply these approaches to a common problem of scaling up and down recipes.

    • Applications: value for money

      To finish the first week, we look at an everyday situation: when shopping, how do you know you are getting value for money from multipacks?

  • Week 2


    • Introduction to ratio

      This week we look at ratio and using proportional reasoning to solve ratio problems.

    • Using different methods: ratios

      We'll now use the techniques we've looked at so far, and the three ways of solving problems, to take some new examples.

    • Sharing amounts using ratio

      We build upon our examples so far to consider ratios with three parts and ratio problems that involve sharing an amount using a ratio.

    • Further ratio problems

      For the final two examples this week, we use bar modelling to solve a problem of sharing and a problem that requires making ratios compatible.

  • Week 3

    Applications of proportional reasoning

    • Conversion of units

      This week we are looking at applications of proportional reasoning in daily life, science and engineering.

    • Proportionality represented with graphs

      Graphs can be a useful approach to solving proportional reasoning problems. Over the next few steps you'll look at how to use graphs and represent proportionality with graphs.

    • Compound measures

      Our third group of examples are known as compound measures. We look at common problems in physics such as speed, density and pressure.

    • Checking proportionality

      We look at a question of proportionality and return to the starting problem for the week to help assess whether a problem can be solved using proportional reasoning or not.

  • Week 4

    Taking proportional reasoning further

    • Proportional reasoning of area

      This week we look at proportional reasoning applied to area and volume. We start be looking at area and a simple, but effective way of converting linear scale factors to area scale factors.

    • Proportional reasoning with 3D objects

      Now we look at volume scale factors when using proportional reasoning with 3D objects and proportionality of surface area.

    • Test your understanding

      We revisit the watery problem from the start of the week, before providing you the opportunity to test your new understanding of proportional reasoning.

    • Reviewing your professional development

      Review your professional development and plan your next steps to sustain and develop the way you plan for learning.

Who is this accredited by?

The CPD Certification Service
The CPD Certification Service:

The CPD Certification Service was established in 1996 and is the leading independent CPD accreditation institution operating across industry sectors to complement the CPD policies of professional and academic bodies.

When would you like to start?

Start straight away and learn at your own pace. If the course hasn’t started yet you’ll see the future date listed below.

Learning on this course

You can take this self-guided course and learn at your own pace. On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.

What will you achieve?

By the end of the course, you‘ll be able to...

  • Identify problems that can be solved using proportional reasoning
  • Solve problems of scaling up and scaling down using the unitary method
  • Solve problems of ratio with two and three quantities
  • Apply proportional reasoning to conversion and compound measure problems
  • Apply proportional reasoning to scaling of area and volume

Who is the course for?

This course is specifically designed for secondary school teachers and educators who are not specialised in maths, but who are wanting to learn mathematical methods and improve their understanding of the subject.

It’s particularly suitable for new teachers and those studying teaching as a profession. Primary school teachers may find this course useful to understand how the mathematics curriculum progresses further in secondary school.

Who will you learn with?

Mathematics Subject Specialist at the National STEM Learning Centre, York.

I have taught mathematics for over 30 years, as a head of department, an advanced skills teacher and as maths lead at STEM Learning. I am the level 3 lead for the Yorkshire Ridings maths hub.

Secondary maths teacher.

Who developed the course?

National STEM Learning Centre

The National STEM Learning Centre provides world-class professional development activities and resources to support the teaching of STEM (science, technology, engineering and mathematics) subjects.

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What's included?

This is a premium course. These courses are designed for professionals from specific industries looking to learn with a smaller group of like-minded individuals.

  • Unlimited access to this course
  • Includes any articles, videos, peer reviews and quizzes
  • Tests to validate your learning
  • Certificate of Achievement to prove your success when you're eligible
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