This document discusses how maps can be used to enrich math tasks. It provides examples of using maps to measure the height of structures by comparing shadows, calculating speed from distance and time measurements in a "speed trap" activity, and exploring zoom levels and dilation factors in map images. Other tips mentioned include finding creative reference sources and measuring objects in multiple ways to improve accuracy. Potential map websites for similar activities are also listed.

1. Maps and Math: Using maps to enrich tasks
David Sabol | Saint Ignatius High School in Cleveland, Ohio
tweeters: @dave_sabol

2. Thales of Miletus
c. 620-546 BCE
!
“Western philosophy began with Thales.”
– Bertrand Russell

3. Thales measures the pyramids http://projectionsystems.wordpress.com/

4. -Plutarch
“…without trouble or the assistance of any
instrument [Thales] merely set up a stick at the
extremity of the shadow cast by the pyramid and,
having thus made two triangles by the impact of
the sun’s rays, … showed that the pyramid has to
the stick the same ratio which the shadow [of the
pyramid] has to the shadow [of the stick].”

5. Thales measures the pyramids http://projectionsystems.wordpress.com/

6. Main Building Tower
Constructed in 1891

10. …from GeoGebra…
Tower shadow (on science building): 4.28
Science building shadow: 1.6
Goal post shadow: 1.04
Goal post height: 30 feet

11. …from GeoGebra…
Tower shadow (on science building): 4.28
Science building shadow: 1.6
Goal post shadow: 1.04
Goal post height: 30 feet
30
1.04
=
x
1.6 + 4.28
x ≈169.62

12. Main Building Tower
Constructed in 1891
Tower Height: 159 feet
Error: approx 6.3%

13. Not bad.
!
Maybe?
!
What could we have done to make it better?

14. Tips
• Look around
• Bing
• Yahoo
• ???
• Find creative sources for the reference.
• Try to find an object you can measure several ways.

15. What say you, Youngstown?

19. Closest team credit: Deadspin

20. Most liked team per county credit: Facebook

21. Media markets credit: Facebook

23. Voronoi Diagrams
Named after Georgy Voronoy
1868-1908

24. source: wikipedia

26. source: jasondavies.com

27. source: jasondavies.com

28. source: Reddit.com user asbusinessmagnet

29. Zooming and Dilation

30. Factor ≈ 0.7009

31. Factor ≈ 0.7148

32. Factor ≈ 0.6995

33. Factor ≈ 0.4783

34. Factor ≈ 0.4831

35. Factor ≈ 0.5171

36. Factor ≈ 0.4872

37. Factor ≈ 0.4278

38. Factor ≈ 0.4448

39. Zoom
Level
Factor
1 -
2 0.7009
3 0.7148
4 0.6995
5 0.4783
6 0.4831
7 0.5171
8 0.4872
9 0.4278
10 0.4448
Zoom Factors

40. Speed Trap Let’s watch.

41. Any questions?

43. approx 123 feet

44. Speed Trap Let’s get some speeders.

45. Car ∆d ∆t AROC
Red sedan 123 ft 3.37 sec
Black SUV 123 ft 3.17 sec
Red truck 123 ft 3.30 sec
Grey sedan 123 ft 2.97 sec

46. Car ∆d ∆t AROC
Red sedan 123 ft 3.37 sec 24.89 mph
Black SUV 123 ft 3.17 sec 26.45 mph
Red truck 123 ft 3.30 sec 25.41 mph
Grey sedan 123 ft 2.97 sec 28.23 mph

47. So how long would the trip take if
they weren’t speeding?
Anyone?
123 feet
15 mph

49. Some nice maps sites
• http://www.jonathancrowe.net/maps/
• Strange maps: http://bigthink.com/blogs/
strange-maps
• http://www.reddit.com/r/maps

57. Maps and Math: Using maps to enrich tasks
David Sabol | Saint Ignatius High School in Cleveland, Ohio
tweeters: @dave_sabol