# Icosahedron

How Many Triangles?

The image is a spinning icosahedron, made using POV-Ray, it is an animated GIF image. Created by en:User:Cyp and copied from the English Wikipedia. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation;

The animation was adapted from one created by Ramandeep Singh and made available on www.Flashkit.com

## A Mathematics Lesson Starter Of The Day

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Topics: Starter | Shape (3D)

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• Any DnD (Dungeons & Dragons) player will immediately recognize this familiar shape as a d20. A good task is to ask the students to form the net, or better yet, make there own.
• Gopal Singh Porte, Kurukshetra
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• I think there are 20 triangle.
• Best Year Maths Group, King Alfred's College The Best
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• Really hard but a good starter.
• Mr Cansdale, Wintringham Grimsby
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• The majority of 7Y1 think 25 (Juris got 20 instantly).
• Barbara Clark, The Plume School
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• I would like to be able to stop it moving so that students can see where the sides and edges are. The diagram is excellent, but quite hard for students to really see, unless they understand immediately.
• Transum,
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• Thanks for your comments Barbara. Use the freeze button on your projector's remote control to stop the diagram moving.
• Mr Cansdale, Wintringham
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• 7X2 think 25, the corner table think 20!
• Bill Irwn, Knoxville, TN
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• In non-euclidian geometry, the answer is different. 3-d.. Just saying...
• David, King Alfreds
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• I found this starter challenging but I have tried and tried but it is still quite hard I know the answer but I tried it on my sister and she can't figure it out.
• 9k4, West Kirby Grammar School
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• Most people thought 16, but Lucy and Eleanor thought 20!! :-).
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• I worked out how many octagons there were
They have octagons because octagons are made of 4 triangle each and the each have 2 vertices. 2 times 4 = 8
There are 5 octagons
5 times 4 + 20.
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• I think it is 20 because each side there are 5 and there are 4 sides so you need to do 5 times 4 equals 20.
• Aya And Tyra, Yr5 Thomas's Academy
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• We think this answer is 14 becawe counted the faces. 2 were 5 triangles and 2 were 2 triangles.2+2+5+5=14.
• Mckelly, Sats Class
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• I and my class think 20. Is it right?

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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This starter has scored a mean of 3.3 out of 5 based on 881 votes.

Previous Day | This starter is for 1 March | Next Day

## Extension

Can you sketch a net for this shape?

Have you seen the Great Dodacahedron?

Other shape counting starters:

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## Numbers and the Making of Us

I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).

"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=March1

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=3D

For Students:

For All: