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![Page 1: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/1.jpg)
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
![Page 2: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/2.jpg)
Mathematicians ask two ‘big questions’...
•How many ways are there of ...
•How do I know I’ve found them all?
![Page 3: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/3.jpg)
Consider 1, 2, 3 & 4 cubes...
•How many distinct arrangements are there?
•Can you make all arrangements with Multi-Link cubes?
![Page 4: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/4.jpg)
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.
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Convex v non-convex
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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?
![Page 10: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/10.jpg)
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?
![Page 11: Maths over Sunday Brunch Sunday 1st August 2010 O’Loughlin Catholic College Exploring some mathematical ideas Matt Skoss & Jeanette Venhoek matt@skoss.orgmatt@skoss.org.](https://reader036.fdocuments.in/reader036/viewer/2022062314/56649e8a5503460f94b8ed2b/html5/thumbnails/11.jpg)
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 ...
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Soma Cube
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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
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More Soma Cube challenges
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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