SLIDE 1 For the Love of Math and Computer Science
For the Love of Spatial Thinking
Kevin Shonk, Baden P.S.
Currently at CEMC 7 & 8 Math Courseware kshonk@uwaterloo.ca
Happy 50th!
Slide Show: goo.gl/Lr8Umw Website With Links: goo.gl/ryfQLJ
SLIDE 2 What is the fewest number of colours required to colour each challenge? *Spaces that share an edge may not be the same colour.
Challenge 1 Challenge 2 Challenge 3
Play
SLIDE 3 1 1 1 1 1 2 2 2 2 2 2 1 1 3 3 3 3 1 4 4 1 2
What is the fewest number of colours required to colour each challenge? *Spaces that share an edge may not be the same colour.
2 Colours 3 Colours 4 Colours
SLIDE 4
4 Colour Map Theorem
SLIDE 5
Extend
SLIDE 6 International Mathematicians Salute
James Tanton
Mathematician in Residence Mathematical Association of America www.jamestanton.com @jamestanton
1.3 million Students
SLIDE 7
The 1 Information Slide Spatial Thinking Spatial Reasoning Spatial Sense Location and movement of objects in space Developed by visualizing, drawing and comparing figures in various positions
SLIDE 8
Spatial thinking can be fostered with the right kind of instruction
SLIDE 9
Transformations Number Lines Cubes
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Games, Theorems, & Open Problems Spatial Thinking
SLIDE 11
Good Will Hunting
SLIDE 12
Good Will Hunting
SLIDE 13 Draw all the Homeomorphically Irreducible Trees with n=10.
Network of dots and lines (No Cycles) Number of dots (10)
Play
(Numberphile: James Grime)
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How many trees for other n’s? n=6, 7, 8, 9, 11, 12? Is there a pattern?
Extend
Good Will Hunting
SLIDE 18
No Rectangles Problem
(Larry Guth, MIT)
How many dots can you place in a 3x3 grid without creating a rectangle?
Play
SLIDE 19
Play
SLIDE 20
Larger N x N grids Open problem in mathematics
Extend
No Rectangles Problem
SLIDE 21
Brussel Sprouts
(Numberphile: Teena Gerhardt) Each turn: 1. Player must connect any 2 free ends without crossing another line. 2. Put a slash in your new line to create 2 new free ends. Winner is the last person to make a legal move!
Play
SLIDE 22 Euler Characteristic: V - E + F = 2
Using the Euler characteristic, # moves = starting vertices + free ends - 2 # moves = 2 # moves = 8 Even # moves = player 2 win! + 8
SLIDE 23
Number of Moves = 5n - 2
Crosses (n) Moves Winner 1 3 Player 1 2 8 Player 2 3 13 Player 1 4 18 Player 2 Brussel Sprouts Cheat Sheet
SLIDE 24
Vary starting positions
Sprouts
Extend
Brussel Sprouts
SLIDE 25 Amida Kuji - (Network Lottery)
(Making Mathematics)
A B C D Add as many horizontal lines as you would like. Horizontal lines may NOT touch. Will 2 letters ever end up
SLIDE 26
Amida-Kuji Challenges
Challenges 1 2 3 4 Start Position
A B C D A B C D A B C D A B C D E F
Finish Position
B A D C D C B A C D A B B F A C E D
Play
SLIDE 27
More variables
Are all outcomes possible?
Extend
A B C D
Amida Kuji
SLIDE 28
Grid Paths
(James Tanton)
Draw a path that goes through all squares once.
To move from one square to another, the squares must share an edge.
Play
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Grid Paths
Smaller grids Larger grids Rectangle grids
Extend
SLIDE 31
The Utilities Puzzle
(ancient)
Goal: Connect each house to each utility (9 lines) without crossing any lines.
Play
SLIDE 32
On a sphere?
On a torus?
Extend
The Utilities Puzzle
SLIDE 33
A B C D A C D B
SLIDE 34
Shameless Plugs
7 & 8 Math Courseware CEMC Math and Computing Contests cemc.uwaterloo.ca Gauss in May Problem Set Generator! Beaver Computing Challenge: November
SLIDE 35 For the Love of Math and Computer Science
For the Love of Spatial Thinking
Kevin Shonk, Baden P.S.
Currently at CEMC 7 & 8 Math Courseware kshonk@uwaterloo.ca
Happy 50th!
Slide Show Link: goo.gl/Lr8Umw Website with Links: goo.gl/ryfQLJ
