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

Skip to 0 minutes and 7 secondsMICHAEL ANDERSON: Hello. I'm Michael Anderson, mathematics subject specialist at the National STEM Learning Centre.

Skip to 0 minutes and 12 secondsPAULA KELLY: I'm Paula Kelly. I'm a secondary maths teacher. Welcome to online number course.

Skip to 0 minutes and 18 secondsMICHAEL ANDERSON: Over the next four weeks, we'll explore the properties of numbers, the connections between different types of number, and methods for working the variety of numbers.

Skip to 0 minutes and 27 secondsPAULA KELLY: Our course has been developed for nearly qualified teachers, trainees, non-specialist teachers, or math teachers that want to brush up on their subject knowledge.

Skip to 0 minutes and 37 secondsMICHAEL ANDERSON: We'll provide you with clear classroom-based teaching approaches that will help your students to develop a deeper understanding of the topics that we explore.

Skip to 0 minutes and 46 secondsPAULA KELLY: In week one, we take a brief look at the history of numbers, how they developed in different civilizations, consider the number system used today, and explore how different number bases work.

Skip to 0 minutes and 57 secondsMICHAEL ANDERSON: In week two, we'll search for patterns found in the times tables. We'll take a closer look at factors and multiples and introduce the mysterious and fascinating world of prime numbers.

Skip to 1 minute and 8 secondsPAULA KELLY: In week three, we were at the range of different numbers, including negatives, sets, and pi. We also consider the order in which we perform operations.

Skip to 1 minute and 18 secondsMICHAEL ANDERSON: Week four is all about number sequences. We'll get to grips with some of the usual, and some of the more unusual patterns found in number. We'll explain how they are generated, how you can spot them, and develop the rules behind certain sequences.

Skip to 1 minute and 34 secondsPAULA KELLY: Each week would include videos, examples, word questions, and questions to help you consolidate your learning and incorporate what you've learned into your teaching.

Skip to 1 minute and 45 secondsMICHAEL ANDERSON: Please feel free to introduce yourself in the comments section below.

Skip to 1 minute and 48 secondsPAULA KELLY: We hope you enjoy the course.

Welcome to understanding number

Welcome to Understanding Numbers from the National STEM Learning Centre. We’ve designed this course for teachers as subject knowledge enhancement as part of your professional development. If you are not a teacher, you are still very welcome to complete this course to improve your own understanding of mathematics.

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.

By the end of this subject knowledge course you will 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.

Learning on this course

You will experience classroom-based teaching approaches designed to help your students to develop a deep understanding of these three interconnected topics. Teaching resources are included throughout the course (for licensing reasons, you will need a free STEM Learning account should you wish to access these resources).

We will introduce each section and then you’ll see examples and worked solutions in the videos on each step. After you’ve watched the videos, complete the questions we set and the discussion tasks throughout the course.

You’ll discover that we place a lot of emphasis on being able to explain your reasoning, more on this in the next step.

Problem worksheets

Each week is accompanied by a worksheet of questions to help consolidate your learning. You can download the weekly worksheets from the bottom of the first step of each week (under Downloads). Answers are provided at the end of each week.

Course support

This course has been written by Steve Lyon and Michael Anderson, Maths Subject Specialists at the National STEM Learning Centre. It is presented by Michael Anderson who will be online between 9 March - 10 April 2020 for this run of the course. We also provide a Q&A with Michael twice a year, available through our online community for Maths Subject Knowledge. Take a look at step 4.14 for more information.


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: Understanding Numbers

National STEM Learning Centre