1. Royal Institution Primary Maths Masterclasses
Möbius bands
Cut your sheet of paper into long strips 3cm wide. How many strips can you make?
Title slide, nice pictures to show what’s coming!

2. Welcome to the Royal Institution Primary Mathematics Masterclasses
Welcome to your first Royal Institution Masterclass. We hope that you will enjoy this series of workshops. Each time you will get to explore a different topic, so over the weeks you will get to see a little bit of all the wonderful and exciting things you can do with maths. We hope that at least one of the Masterclasses will make you want to investigate the topic further, and that you will get the chance to play with maths which you have not met before.
You are part of a big family of Masterclass students – Royal Institution Masterclasses have been running for over 35 years with thousands of students taking part each year. If you attend enough sessions in the series you will get a special Royal Institution certificate, and if your Masterclass series is close enough to London you might be able to come and visit the Royal Institution for a special celebration of maths. If there are Secondary Masterclasses running in your area you might even get another chance to attend when you are in secondary school.
Image credits: Tim Mitchell

3. The Royal Institution Our vision is:
A world where everyone is inspired to think more deeply about science and its place in our lives.
The Ri is a science communication charity which has been around since We’ve got a huge amount of history and lots of famous scientists lived and worked at the Ri. Most importantly, we’ve always been about communicating science to the general public – and that’s something we still do today. We do talks and activities for the public as well as with schools all across the UK.
Image credits: Tim Mitchell

4. Royal Institution activities
Online videos & activity resources
National education programmes
Membership
London-based:
Talks and shows
Holiday workshops
Family fun days
Faraday Museum
Here are some of the things that the Ri does today. We especially have lots going on in London, so if you enjoy your Masterclasses there are a range of holiday workshops at the Ri which you might like to take part in.
Image credits: The Royal Institution, Paul Wilkinson, Katherine Leedale

5. The CHRISTMAS LECTURES
The CHRISTMAS LECTURES are the Ri’s most famous activity and are televised on the BBC. The first maths lectures by Prof. Sir Christopher Zeeman in 1978
started off the Masterclass
programme!
Christmas Lecturers include Michael Faraday, David Attenborough, Carl Sagan, Richard Dawkins, Alison Woollard, Saiful Islam & Alice Roberts
Begun by Michael Faraday in 1825, the CHRISTMAS LECTURES are now broadcast on UK television every December and have formed part of the British Christmas tradition for generations. The Lectures have been broadcast on TV since 1936 – we think they were the very first science programme on television. The theme changes every year, with the Lectures delivered by an expert in their field. Many world-famous scientists have given the Lectures since 1925, including David Attenborough, Carl Sagan, Richard Dawkins, and our latest Lecturer Sophie Scott. You can watch all of the recent CHRISTMAS LECTURES on our website, along with many of the older ones – and more are going online all the time. Ri members and UK schools can apply for tickets to see them being filmed live – but no adults can attend without someone aged accompanying them! To find out more about the Lectures (or Ri Membership) visit our website,
The first mathematics CHRISTMAS LECTURES were not until 1978, and were delivered by Professor Sir Christopher Zeeman. They were extremely popular and demonstrated all sorts of mathematical concepts, including mathematical proof – some of which you will see in your Masterclasses. In fact, the lectures were so popular that they started off the Masterclass programme and Christopher Zeeman delivered many of the sessions in the first few series of workshops in London. The most recent maths-themed CHRSITMAS LECTURES were delivered by Marcus Du Sautoy in 2006.
Watch Prof Sir Christopher Zeeman’s 1978 CHRISTMAS LECTURES:
Watch Marcus du Sautoy’s 2006 CHRISTMAS LECTURES:
Image credits: Tim Mitchell, Paul Wilkinson

6. Royal Institution videos
CHRISTMAS LECTURES – on the Ri website
We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

7. Royal Institution videos
CHRISTMAS LECTURES – on the Ri website
Ri on YouTube – experiments, videos & talks for all ages
We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

8. Royal Institution videos
CHRISTMAS LECTURES – on the Ri website
Ri on YouTube – experiments, videos & talks for all ages
ExpeRimental – science experiments at home
We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

9. Title slide, nice pictures to show what’s coming!

10. 7
Title slide, nice pictures to show what’s coming!

11. Title slide, nice pictures to show what’s coming!

12. How many faces?
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13. How many faces? How many edges?
Title slide, nice pictures to show what’s coming!

14. August Möbius Title slide, nice pictures to show what’s coming!
Image source: via Wikimedia Commons

15. Title slide, nice pictures to show what’s coming!
Image credits: Katie Steckles

16. (keep going until you get back to where you started)
Draw a line down the middle
(keep going until you get back to where you started)
Title slide, nice pictures to show what’s coming!

17. (keep going until you get back to where you started)
Draw a line down the middle
(keep going until you get back to where you started)
How many faces?
Title slide, nice pictures to show what’s coming!

18. Draw a line along the edge
Draw a line down the middle
(keep going until you get back to where you started)
How many faces?
Draw a line along the edge
(keep going until you get back to where you started)
Title slide, nice pictures to show what’s coming!

19. How many faces? How many edges?
Draw a line down the middle
(keep going until you get back to where you started)
How many faces?
Draw a line along the edge
(keep going until you get back to where you started)
Title slide, nice pictures to show what’s coming!
How many edges?

20. Title slide, nice pictures to show what’s coming!
Image credits: Katie Steckles

21. Title slide, nice pictures to show what’s coming!
Image credits: Katie Steckles

22. ½ twist
Title slide, nice pictures to show what’s coming!

23. no twists
½ twist
Title slide, nice pictures to show what’s coming!

24. no twists ½ twist one full twist
Title slide, nice pictures to show what’s coming!

25. no twists ½ twist one full twist 1½ twists
Title slide, nice pictures to show what’s coming!

26. no twists ½ twist one full twist 1½ twists two full twists
Title slide, nice pictures to show what’s coming!
two full twists

27. Title slide, nice pictures to show what’s coming!

28. Title slide, nice pictures to show what’s coming!

29. Title slide, nice pictures to show what’s coming!

30. Title slide, nice pictures to show what’s coming!

31. Title slide, nice pictures to show what’s coming!

32. Title slide, nice pictures to show what’s coming!

33. Title slide, nice pictures to show what’s coming!

34. Title slide, nice pictures to show what’s coming!

35. Title slide, nice pictures to show what’s coming!

38. Image credits: Katie Steckles

39. Image credits: Katie Steckles

40. Möbius bands

41. Möbius bands
More twists

42. Möbius bands
More twists
Cutting up

43. Möbius bands
More twists
Cutting up
Other shapes

44. Try these as extra activities in class, or try them at home…
What else can I do to
extend my knowledge?
nrich.maths.org/7530
Cylinder cutting
These are activities they can try at home, or can be given to pupils who finish the main activities.
Try these as extra activities in class, or try them at home…

45. What else can I do to extend my knowledge?
Watch these videos by Vi Hart:
Wind & Mr Ug
bit.ly/wind-mrug
Candy Buttons
bit.ly/candy-buttons
Möbius Music Box
bit.ly/mobius-musicbox
These are activities they can try at home, or can be given to pupils who finish the main activities.

46. What else can I do to extend my knowledge?
And this Ri video:
Levitating superconductor on a Möbius Strip
These are activities they can try at home, or can be given to pupils who finish the main activities.

47. Royal Institution Primary Maths Masterclasses
Möbius bands
Thank you!
Title slide, nice pictures to show what’s coming!
Image credits: Katie Steckles