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! rigb.org @Ri_Science

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

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 1799. 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

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

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 11-17 accompanying them! To find out more about the Lectures (or Ri Membership) visit our website, www.rigb.org. 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: http://www.rigb.org/christmas-lectures/watch/1978/mathematics-into-pictures Watch Marcus du Sautoy’s 2006 CHRISTMAS LECTURES: http://www.rigb.org/christmas-lectures/watch/2006/the-num8er-my5teries/lecture-1   Image credits: Tim Mitchell, Paul Wilkinson

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.

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.

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.

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

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

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

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

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

August Möbius Title slide, nice pictures to show what’s coming! Image source:http://www.portraitindex.de/documents/obj/33213645 via Wikimedia Commons

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

(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!

(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!

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!

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Image credits: Katie Steckles

Image credits: Katie Steckles

Möbius bands

Möbius bands More twists

Möbius bands More twists Cutting up

Möbius bands More twists Cutting up Other shapes

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…

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.

What else can I do to extend my knowledge? And this Ri video: Levitating superconductor on a Möbius Strip https://www.youtube.com/watch?v=zPqEEZa2Gis These are activities they can try at home, or can be given to pupils who finish the main activities.

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