For the Love of Spatial Thinking
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1 For the Love of Math and Computer Science Happy 50th! For the Love of Spatial Thinking Slide Show: goo.gl/lr8umw Website With Links: goo.gl/ryfqlj Kevin Shonk, Baden P.S. Currently at CEMC 7 & 8 Math Courseware kshonk@uwaterloo.ca
2 What is the fewest number of colours required to colour each challenge? *Spaces that share an edge may not be the same colour. Play Challenge 1 Challenge 2 Challenge 3
3 What is the fewest number of colours required to colour each challenge? *Spaces that share an edge may not be the same colour Colours 3 Colours 4 Colours 1
4 4 Colour Map Theorem
5 Extend
6 International Mathematicians Salute Oct , million Students James Tanton Mathematician in Residence Mathematical Association of America
7 The 1 Information Slide Spatial Thinking Spatial Reasoning Location and movement of objects in space Spatial Sense Developed by visualizing, drawing and comparing figures in various positions
8 Spatial thinking can be fostered with the right kind of instruction
9 Transformations Number Lines Cubes
10 Games, Theorems, & Open Problems Spatial Thinking
11 Good Will Hunting
12 Good Will Hunting
13 Draw all the Homeomorphically Irreducible Trees with n=10. Network of dots and lines (No Cycles) Play (Numberphile: James Grime) Number of dots (10)
14
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17 Extend Good Will Hunting How many trees for other n s? n=6, 7, 8, 9, 11, 12? Is there a pattern?
18 No Rectangles Problem (Larry Guth, MIT) Play How many dots can you place in a 3x3 grid without creating a rectangle?
19 Play
20 Extend No Rectangles Problem Larger N x N grids Open problem in mathematics
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
22 Euler Characteristic: V - E + F = 2 Using the Euler characteristic, # moves = starting vertices + free ends - 2 # moves = # moves = 8 Even # moves = player 2 win!
23 Brussel Sprouts Cheat Sheet Crosses (n) Moves Winner 1 3 Player Player Player Player 2 Number of Moves = 5n - 2
24 Extend Brussel Sprouts Vary starting positions Sprouts
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 on the same finish?
26 Amida-Kuji Challenges Challenges Start Position ABCD ABCD ABCD ABCDEF Finish Position BADC DCBA CDAB BFACED Play
27 Extend Amida Kuji More variables Are all outcomes possible? A B C D
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
29
30 Extend Grid Paths Smaller grids Larger grids Rectangle grids
31 The Utilities Puzzle (ancient) Goal: Connect each house to each utility (9 lines) without crossing any lines. Play
32 Extend The Utilities Puzzle On a sphere? On a torus?
33 A B C D A C D B
34 Shameless Plugs cemc.uwaterloo.ca 7 & 8 Math Courseware CEMC Math and Computing Contests Gauss in May Problem Set Generator! Beaver Computing Challenge: November
35 For the Love of Math and Computer Science Happy 50th! For the Love of Spatial Thinking Kevin Shonk, Baden P.S. Slide Show Link: goo.gl/lr8umw Website with Links: goo.gl/ryfqlj Currently at CEMC 7 & 8 Math Courseware kshonk@uwaterloo.ca
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