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 & jvenhoek@gmail.comjvenhoek@gmail.com Mathematics Teachers’ Association of the Northern Territory

2. Mathematicians ask two ‘big questions’... How many ways are there of... How do I know I’ve found them all?

3. Consider 1, 2, 3 & 4 cubes... How many distinct arrangements are there? Can you make all arrangements with Multi-Link cubes?

4. Can we sort our arrangements? Convex shapes Non-convex shapes Convex shape: A line can be drawn between any two points and not go outside the shape. Non-convex shape: A line can be drawn so that it does go outside the shape.

5. Convex v non-convex

9. Hmmm...How many cubes in all the non-convex shapes made with 1, 2, 3 or 4 cubes? Six are made with 4 cubes and one is made with 3 cubes. Is that significant?

10. Hmmm...How many cubes in all the non-convex shapes made with 1, 2, 3 or 4 cubes?

11. Six are made with 4 cubes and one is made with 3 cubes. Is that significant? Piet Hein (a Danish mathematician) thought so in 1936 and invented the...

12. Soma Cube

13. 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 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/isoshap eload.html and http://www.teacherled.com/resources/isodotty/isodottyl oad.html http://www.teacherled.com/resources/isodraw/isoshap eload.html http://www.teacherled.com/resources/isodotty/isodottyl oad.html RekenWeb’s Cube Builder: http://www.fi.uu.nl/toepassingen/00338/toepassing_rek enweb.xml?style=rekenweb&language=en&use=game http://www.fi.uu.nl/toepassingen/00338/toepassing_rek enweb.xml?style=rekenweb&language=en&use=game

14. More Soma Cube challenges

15. 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