Royal Institution Primary Maths Masterclasses Off the shelf

Royal Institution Primary Maths Masterclasses Off the shelf Masterclass: Patterns and Sierpinski’s Triangle

The Royal Institution Our vision is: A world where everyone is inspired to think more deeply about science and its place in our lives. 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 Image credits: The Royal Institution, Paul Wilkinson, Katherine Leedale

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 Image credits: Tim Mitchell, Paul Wilkinson

Royal Institution videos • CHRISTMAS LECTURES – on the Ri website

Royal Institution videos • CHRISTMAS LECTURES – on the Ri website • Ri on You. Tube – experiments, videos & talks for all ages

Royal Institution videos • CHRISTMAS LECTURES – on the Ri website • Ri on You. Tube – experiments, videos & talks for all ages • Expe. Rimental – science experiments at home

Royal Institution Primary Maths Masterclasses Off the shelf Masterclass: Patterns and Sierpinski’s Triangle

patterns

Chaos Game

iteration

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 cm 20 5, 6 3, 4

1, 2 cm 0 1 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

1, 2 5, 6 3, 4

Roll the dice Draw a line from the last dot you drew to that corner of the triangle Measure the length of the line and divide by 2 Mark the point half way along the line

Use this link to see the Chaos Game played bit. ly/sierpinski-chaos

Sierpinski Triangle

Use this link to see why no points can land in the middle triangle bit. ly/sierpinski-midpoint

16

Colour in the triangle you remove Use a different colour for each size

fractal

Pascal's triangle

1 1 1

1 1 1 2 1 1

1 1 1 2 1 1 1

1 1 1 2 1 3 1 1

1 1 1 2 1 3 1 1

1 1 1 2 1 3 1 1

1 1 1 2 1 3 1 1

1 1 2 1 1 3 3 1

1 1 2 1 1 3 3 1 1 4 6 4 1

1 1 2 1 1 3 3 1 1 4 6 4 1

1 1 2 1 1 3 3 1 1 4 6 4 1 ?

Add the numbers 1 in the two 1 1 squares above to get the 1 2 1 number 1 3 3 below 1 4 6 4 1 1

1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1

1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1

same = shade different = don't

patterns in numbers

patterns in numbers iteration: drawing dots

patterns in numbers iteration: drawing dots Fractal (Sierpinski's triangle)

patterns in numbers iteration: drawing dots Fractal (Sierpinski's triangle) Pascal's triangle same pattern, different place

We hope you have enjoyed exploring Sierpinski’s Triangle with us! What questions do you have? Any unanswered questions can be written down and emailed to “Ask the Ri Masterclass Team” using this email masterclasses@ri. ac. uk We don’t know all the answers instantly, but we will find out and get back to you before the next Masterclass. Any comments you have about what you enjoyed or what you’d like to do more of can be written on the post-it note and handed in.

What else can I do to extend my knowledge of Sierpinski’s triangle? https: //nrich. maths. org/ 6921 Paper Curves https: //nrich. maths. org/ 1880 Smaller and smaller https: //nrich. maths. org/ 5404 Excel investigation: Pascal multiples Try these as extra activities in class, or try them at home…