maths over sunday brunch sunday 1st august 2010 o’loughlin catholic college exploring some...

Maths over Sunday Brunch

Sunday 1st August 2010O’Loughlin Catholic College

Exploring some mathematical ideas

Matt Skoss & Jeanette Venhoek

matt@skoss.org & jvenhoek@gmail.com

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