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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Proportion, Ratio and Scaling. Join the course to learn more.

Skip to 0 minutes and 1 secondHello, I'm Michael Anderson, mathematics subject specialist at the National STEM Learning Center. I'm Paula Kelly, I'm a secondary maths teacher, so welcome to this course on proportional reasoning. [Michael] Proportional reasoning appears everywhere in the curriculum; including enlargements, fractions, ratios and more. But often, proportionality can be taught in a few standard, unconnected ways or treated implicitly. [Paula] The aim of this course is to provide you with some clear approaches to proportional reasoning that you can apply to a range of different contexts. In this first week, we're going to have a look at some different methods to proportional reasoning questions, and explore the underlying structure that these questions have in common.

Skip to 0 minutes and 51 seconds[Michael] We'll look at scaling up, scaling down, the unit method, and how to calculate value for money problems. Each week includes videos, examples, worked questions and questions for you to have a go at yourself. We hope you enjoy the course.

Welcome to maths subject knowledge: proportion, ratio and scaling

Welcome to Proportional Reasoning, a maths subject knowledge course from the National STEM Learning Centre. This course is designed for non-specialist teachers, teaching assistants, parents and other educators who wish to improve their subject knowledge.

In this course, Paula Kelly, secondary mathematics teacher, and Michael Anderson, mathematics specialist at the National STEM Learning Centre, guide you through the mathematical topic of proportional reasoning.

Proportionality pervades many areas of mathematics and is widely used in other subjects such as science and technology. The ability to master the skill of proportional reasoning is key to understanding many areas of mathematics.

Proportion reasoning, sometimes referred to as multiplicative reason, is the ability to scale up and scale down by multiplying by a common ratio. This skill is important in topics such as enlarging shapes, fractions, percentages and ratios.

The aim of this course is to provide some clear approaches to developing your proportional reasoning skills which can be applied in a range of different contexts.

Weekly activities

Each week you will have access to:

  • Videos explaining key concepts and worked examples.
  • Problem sheets for each week to accompany the videos.
  • End of week ‘practice questions’ applying the techniques you’ve learnt.

Problem sheets are linked at the bottom of the first step in each week. Answers for problem sheets are available at the bottom of the final step for each week.

Throughout the course we encourage you to engage with other learners, sharing your ideas about how to solve the problems. The important thing to remember is that on this course we encourage you to post your explanations, even if you think you might get things wrong. It’s mathematical thinking that we’re hoping you’ll develop.

Support on this course

This course has three main ways to get support:

  • Course educators, Michael Anderson and Steve Lyon, will be available in the discussions between 8 June 2020 and 10 July 2020.
  • Learn from other course participants, asking questions and supporting their understanding.
  • Join the STEM Learning Community Group to post questions for Q&A sessions with course educators that will take place twice a year.


Start the course by sharing who you are, what you teach, and what brought you to this course.

Take a look at other learners’ posts. If you find someone who works in a similar context, you can use the Follow feature to keep track of what they’re sharing in the course and perhaps support each other.

Mark complete

When you complete a step on the course, click Mark as Complete at the bottom right. This helps you keep track of your progress. Mark over 90% of the course steps complete, get at least 70% on the end of course test, and you’ll be eligible for a Certificate of Achievement when you Upgrade.

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This video is from the free online course:

Maths Subject Knowledge: Proportion, Ratio and Scaling

National STEM Learning Centre