Mathematics Teachers’
Association
of the Northern Territory
Maths over Sunday
Brunch
Sunday 1st August 2010
O’Loughlin Catholic College
Exploring some mathematical ideas
Matt Skoss & Jeanette Venhoek
[email protected] & [email protected]
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 shape: A line can be
drawn between any two
points and not go outside the
shape.
• Convex shapes
• Non-convex shapes
Non-convex shape: A line can
be drawn so that it does go
outside the shape.
Convex v non-convex
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?
Hmmm...How many cubes in
all the non-convex shapes
made with 1, 2, 3 or 4 cubes?
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?
Piet Hein (a Danish
mathematician) thought so in
1936 and invented the ...
Soma Cube
Using an IWB...or bluetooth
mouse/keyboard/slate/iPod
• NLVM’s Space Blocks:Touch
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
RekenWeb’s Cube Builder:
http://www.fi.uu.nl/toepassingen/00338/toepassing_rek
enweb.xml?style=rekenweb&language=en&use=game
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