Maths over Sunday Brunch
Sunday 1st August 2010O’Loughlin Catholic College
Exploring some mathematical ideas
Matt Skoss & Jeanette Venhoek
[email protected] & [email protected]
Mathematics Teachers’ Association
of the Northern Territory
Mathematicians ask two ‘big questions’...
•How many ways are there of ...
•How do I know I’ve found them all?
Consider 1, 2, 3 & 4 cubes...
•How many distinct arrangements are there?
•Can you make all arrangements with Multi-Link cubes?
Can we sort our arrangements?
•Convex shapes
•Non-convex shapes
Convex shape: A line can Convex shape: A line can be drawn between any be drawn between any two points and not go two points and not go
outside the shape.outside the shape.
Non-convex shape: A line Non-convex shape: A line can be drawn so that it can be drawn so that it
does go outside the does go outside the shape.shape.
Convex v non-convex
Hmmm...How many cubes Hmmm...How many cubes in all the non-convex in all the non-convex
shapes made with 1, 2, 3 shapes made with 1, 2, 3 or 4 cubes?or 4 cubes?
Six are made with 4 cubes Six are made with 4 cubes and one is made with 3 and one is made with 3
cubes. cubes. Is that significant?Is that significant?
Hmmm...How many cubes Hmmm...How many cubes in all the non-convex in all the non-convex
shapes made with 1, 2, 3 shapes made with 1, 2, 3 or 4 cubes?or 4 cubes?
Hmmm...How many cubes Hmmm...How many cubes in all the non-convex in all the non-convex
shapes made with 1, 2, 3 shapes made with 1, 2, 3 or 4 cubes?or 4 cubes?
Six are made with 4 cubes Six are made with 4 cubes and one is made with 3 and one is made with 3
cubes. cubes. Is that significant?Is that significant?
Piet Hein (a Danish Piet Hein (a Danish mathematician) thought so mathematician) thought so
in 1936 and invented in 1936 and invented the ...the ...
Soma Cube
Using an IWB...or bluetooth mouse/keyboard/slate/iPod
Touch•NLVM’s Space Blocks: http://nlvm.usu.edu/en/nav/frames_asid_195_g_3_t_3.html?open=activities&from=category_g_3_t_3.html
•Virtual isometric drawing: http://www.teacherled.com/resources/isodraw/isoshapeload.html and http://www.teacherled.com/resources/isodotty/isodottyload.html
•RekenWeb’s Cube Builder: http://www.fi.uu.nl/toepassingen/00338/toepassing_rekenweb.xml?style=rekenweb&language=en&use=game
More Soma Cube challenges
Other tasks to extend the Soma Cube...•Try to do it blindfolded•Do it within a certain time...A minute to win it!•Make other shapes•Using isometric paper or interactive web applets to draw the Soma Cube pieces
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