• NATIONAL STEM LEARNING CENTRE

Maths Subject Knowledge: Fractions, Decimals, and Percentages

Improve your mathematics understanding and learn methods for teaching fractions as a non-specialist maths teacher.

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Maths Subject Knowledge: Fractions, Decimals, and Percentages
The CPD Certification Service

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

Make learning fractions, decimals and percentages easier for your students

Often, when teachers are asked which maths topic they find the most difficult to teach and for their students to learn, teachers say fractions.

On this course, you will explore why they find fractions difficult and consider new approaches and methodologies for teaching them that are easier to grasp for your students.

You will learn how to avoid teaching the subject in isolation as you approach fractions, decimals and percentages as three interconnected topics. This will help to give your students context and give them a deeper understanding of the maths structure behind fractions.

Syllabus

  • Week 1

    What is a fraction?

    • Introduction to fractions, decimals and percentages

      Welcome to the course. We begin by explaining how this course will support your mathematical reasoning, and then set our starter problem which we’ll refer to throughout the week.

    • Introducing fractions

      How do you define what a fraction is? We’ll look at what we mean by a fraction of an amount and some of the terminology to use when teaching fractions.

    • Equivalent fractions

      To help us compare fractions, we now look at where different fractions represent the same amount. In the next few steps we look at different ways to create equivalent fractions.

    • Fractions greater than a whole

      For the final part of our introduction to fractions, we look at fractions representing numbers greater than one. Where might you have seen mixed numbers and top heavy fractions before?

  • Week 2

    Expressing fractions as decimals and as percentages

    • Fractions as decimals

      This week we look at how to express fractions as both decimals and percentages. We start with decimals and what the difference is between a terminating decimal and a recurring decimal.

    • Decimals as fractions

      In these two steps, we’ll convert decimal numbers into fractions. That might seem easy with terminating decimals, but how can we do this with recurring decimals?

    • Percentages

      We’ve looked at fractions and decimals, now it’s time to look at percentages. What is the difference between a percentage and a fraction?

  • Week 3

    Multiplying fractions, decimals and percentages

    • Multiplying decimals

      We often need to find a fraction or percentage of something. These are multiplication problems. We start with multiplying decimal numbers.

    • Multiplying fractions

      In this part of the week you’ll practise multiplying fractions. We’ll also recap simplifying fractions and how cancelling down is a useful technique to use before multiplication as well as with the final answer.

    • Multiplying percentages

      In the final part of this week we look at multiplying numbers by percentages. We also introduce a ‘goal free’ teaching approach to build confidence with finding percentages of amounts.

  • Week 4

    Adding and subtracting fractions, decimals and percentages

    • Comparing fractions, decimals and percentages

      We start this week by making comparisons between fractions, decimals and percentages, to work out not just which of two numbers is larger, but also by how much.

    • Adding and subtracting

      Next, we explore methods which develop conceptual understanding as well as procedural fluency. What simple, common mistakes do you think occur when students add and subtract fractions or add and subtract decimals?

    • Further problems

      Selecting the ‘right’ denominator is key to any questions where we are asked to compare, to add, or to subtract fractions. This is a good opportunity to apply some basic number skills to a fraction topic.

  • Week 5

    Dividing with decimals and fractions

    • Dividing decimals

      This week we look at division, starting with a reminder about remainders, and the different methods of division you may have used. How might these approaches help us with dividing with fractions and decimals?

    • Dividing fractions

      When dividing fractions, you’ll need to first understand what we mean by reciprocals. This then leads us into an approach known as the KFC method.

  • Week 6

    Delving deeper into percentages

    • Increasing and decreasing amounts

      This week we look at the application of percentages with examples you will see commonly outside the classroom. We start with a recap and then explore percentage increases and decreases.

    • Expressing amounts

      Here we recap how we express amounts as percentages and representing an amount as a fraction or decimal to help us express an amount as a percentage.

    • Finding increases and decreases

      Percentage increases and decreases are often used to compare results across different amounts, for example profit or exam scores. In these steps you’ll draw upon everything from the course to tackle common real-world problems.

    • 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 why students find the concept of fractions demanding.
  • Develop strategies to enable students to demonstrate their understanding, and use, of fractions.
  • Explore the links between fractions, decimals and percentages and become fluent in their application in differing contexts.
  • Demonstrate an understanding of the mathematical structure and not just teach the ‘tricks’.
  • Solve mathematical problems in context.

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.

Learning on FutureLearn

Your learning, your rules

  • Courses are split into weeks, activities, and steps, but you can complete them as quickly or slowly as you like
  • Learn through a mix of bite-sized videos, long- and short-form articles, audio, and practical activities
  • Stay motivated by using the Progress page to keep track of your step completion and assessment scores

Join a global classroom

  • Experience the power of social learning, and get inspired by an international network of learners
  • Share ideas with your peers and course educators on every step of the course
  • Join the conversation by reading, @ing, liking, bookmarking, and replying to comments from others

Map your progress

  • As you work through the course, use notifications and the Progress page to guide your learning
  • Whenever you’re ready, mark each step as complete, you’re in control
  • Complete 90% of course steps and all of the assessments to earn your certificate

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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
  • Download and print your Certificate of Achievement anytime

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