Maths Subject Knowledge: Understanding Numbers

Learn how numbers really work by understanding the underlying structures of everyday maths with this course for teachers.

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Maths Subject Knowledge: Understanding Numbers
The CPD Certification Service

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

Improve your subject knowledge of numbers as part of the maths curriculum

We use numbers every day, but do we really appreciate how they work?

There are lots of fascinating connections and patterns to explore once you delve into the mathematical structure of how simple numbers work.

On this course, you will develop an understanding of the underlying mathematical structure of everyday mathematics.

You will learn why mathematical methods work and find the connections between different areas of maths so that you can appreciate the interconnected nature of different maths topics.


  • Week 1

    Number systems

    • Understanding numbers

      Over the next four weeks we will explore the properties of a range of numbers, connections between different number types, and delve into different number systems. We start by looking at the origins of our number systems.

    • Place value systems

      The denary number system is the one we most commonly use. Here we look at the underlying principles and the place value system.

    • Other number bases

      We've looked at base 10, now we look at how it's possible to work with other number bases. This is particularly important in computing.

  • Week 2

    Multiples, factors and primes

    • Grouping numbers

      This week we look at how numbers are grouped, in particular through times tables. This leads us into exploration of multiples, factors, and primes.

    • Patterns of divisibility

      In the next steps we explore whether the last digit in numbers shows us whether that number is exactly divisible by another. There are some interesting links to error checking used in real life.

    • Multiples and factors

      Lowest common multiples and highest common factors are used across areas of mathematics. In these steps we clarify what they mean and how they can be used.

    • Prime numbers

      Prime numbers is a group of numbers that many people have heard of. How would you define what a prime number is and how might you find them?

  • Week 3

    Negative numbers and exact numbers

    • Negative numbers

      So far in the course we have only looked at positive whole numbers. How do calculations work with negative numbers and what patterns might there be?

    • Negative numbers: addition and subtraction

      We'll now look at the different ways you can teach addition and subtraction of negative numbers.

    • Negative numbers: multiplication and division

      Moving on from addition and subtraction, you'll now explore a couple of approaches for multiplying and dividing by negative numbers.

    • Order of operations

      The agreed system for processing calculations is the order of operations. Without an order, chaos reigns!

    • Approximation and exact answers

      In the final part of this week we look at representing approximations and different forms of exact answers using irrational numbers.

  • Week 4

    Number sequences

    • Introducing number sequences

      Our final week of the course looks at number sequences and different activities that link numbers together.

    • Types of sequences

      There are two main types of mathematical sequence studied in school: arithmetic and geometric. We start though with a sequence you may have heard of before: Fibonacci.

    • Characterising numbers

      In the final part of this course we look at square, triangle, perfect and happy numbers.

    • 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.

What will you achieve?

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

  • Explore how the number system we use every day actually works
  • Investigate patterns created when exploring factors of numbers, multiples of numbers and prime factorisation of numbers
  • Explain when and why two negatives make a positive
  • Describe the order in which operations are performed
  • Explore a variety of different number sequences

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

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  • 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

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  • 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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