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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 seconds MICHAEL ANDERSON: Over the last four weeks, we’ve explored many interesting facets of numbers and their properties. We’ve seen the properties of numbers, the connections between different types of number, and methods for working with a variety of numbers.

Skip to 0 minutes and 21 seconds PAULA KELLY: In week one, we looked at the history of numbers, how they developed in different civilizations, and we introduced a different number basis.

Skip to 0 minutes and 29 seconds MICHAEL ANDERSON: In week two, we found patterns in the times tables. We discovered the visibility rules and delved into factors, multiples, and prime numbers.

Skip to 0 minutes and 37 seconds PAULA KELLY: In week three, we worked with a range of different numbers, including negatives, [? sets, ?] and pi. We also explained the order in which you perform operations.

Skip to 0 minutes and 47 seconds MICHAEL ANDERSON: In this final week, we looked at Fibonacci sequences, arithmetic and geometric sequences, square and triangle numbers, and we also found happy numbers and perfect numbers.

Skip to 0 minutes and 57 seconds PAULA KELLY: We hope we’ve provided you with clear classroom-based teaching approaches that will help your students to develop a deeper understanding of the topics we explored.

Skip to 1 minute and 6 seconds MICHAEL ANDERSON: The course was written for newly qualified teachers, trainees, non-specialists, and math teachers who wanted to brush up on their subject knowledge. If this is you, we wish you the very best in your mathematics teaching career.

Skip to 1 minute and 18 seconds PAULA KELLY: Each week, we’ve had questions to help you consolidate your learning and teaching resources to incorporate what you’ve learned into your teaching. If you haven’t already done so, please remember to download these now.

Skip to 1 minute and 31 seconds MICHAEL ANDERSON: Do take a moment to complete your self-audit in order to identify where you will go next your professional development. We really hope you’ve enjoyed this course.

Course summary: understanding number

Well done! You have reached the end of the course all about numbers. Throughout the course we explored methods to help develop a deeper understanding of this topic.

We hope you have picked up some clear, classroom-based teaching approaches and explanations that will help your students to get to grips with, and develop links between, the different aspects of number.

We’ve looked at different types of number, found patterns in times tables, discovered divisibility rules and delved into factors, multiples and prime numbers. We have worked with a range of different numbers, including negatives, surds and pi. We also explained the order in which we perform operations and how these skills are applied across the wider mathematics curriculum.

Mathematical fluency

One of the aims of the English national curriculum is that students become fluent in the fundamentals of mathematics. This statement may be interpreted as requiring students to practise techniques by completing long exercises of questions until fluency is achieved. The aim of the steps on perfect numbers and happy numbers is to highlight that there is an alternative to just doing exercise in order to gain fluency.

Further resources

Dr Colin Foster from Loughborough University is leading the Mathematical Etudes Project which aims to find creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures.

Q&A with the National STEM Learning Centre

Twice a year we will run an online Q&A with the Maths Subject Specialists at the National STEM Learning Centre. We will take your questions and record our answers to a selection of the most common or unusual problems!

The video will be posted to the STEM Learning Community Group for this course. You can post your questions to the community group before the deadlines advertised on the group.

Further professional development

Watch the video below to learn about the STEM Learning Impact Journey: our approach to supporting your continuing professional development as a teacher, teaching assistant or technician.

This is an additional video, hosted on YouTube.

Find out more about subject-specific CPD led by the National STEM Learning Centre:

*CPD is made affordable through Project ENTHUSE and ENTHUSE Bursary which are available for many of our CPD activities, and can be used towards the cost of CPD fees, expenses and resources. ENTHUSE Bursary is available to individuals from all UK state funded schools, including maintained schools, academies and free schools.

Free online learning and teaching resources

The National STEM Learning Centre’s website houses the largest open collection of resources for teachers of science, design and technology, engineering and mathematics in the UK.

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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre