2. Winter Wonderland Our Natural World Described Mathematically

3. Using Student Responders To respond to a question: Wait for polling to open. Select your response You do not have to turn on your responder, it is ready to go.

4. Here’s one snowflake…

5. Here’s another snowflake…

6. Based on geometry which video shows a possible real snowflake. 1.Snowflake A 2.Snowflake B

7. How do snowflakes form? Why do snowflakes have similar shapes? Are all snowflakes identical?

8. How is snow formed? 1.Water freezes as it falls to the ground. 2.Water vapor condenses directly into an ice crystal. 3.Ice freezes more in cold weather.

9. How does the water become snow? When water vapor condenses directly into an ice crystal. What happens when water freezes as it falls to the ground? SLEET

11. Let’s look at some Euclidean shapes…

12. Some natural shapes to sort…

13. Let’s look at some snowflakes…

14. Why do snowflakes have similar shapes?

15. What shape do these snowflakes have in common?

16. 1.Circle 2.Square 3.Cone 4.Hexagon 5.Pentagon 6.Octagon

17. What is the molecular shape of an ice crystal? H O H

18. Molecular Structure of Ice

20. Are any two snowflakes alike?

21. Temperature Humidity Wind

22. Temperature Warmer air = smooth ends Colder air = sharp ends

23. Humidity Crystals formed in dry air have simpler shapes than those in higher humidity.

24. Why do more complex crystals form in more humid air? 1.The humidity works on snowflakes the same way it does hair (frizz). 2.More humid air has more molecules in it. 3.Dry air is warmer.

25. Wind

26. Fractal Snowflakes

27. Materials: Protractor Marker/Pencil Six-sided die Snowflake template Air Properties Chart

28. Draw a diameter

38. Congratulations! Stage Zero

39. What is the midpoint measurement of each red line segment?

43. What properties determine the growth of a snow crystal? Temperature Humidity Wind Air Properties Chart Click Here

44. Air Properties Chart 3 T = 0°/32° H = 0.10 30° T = -7°/20° H = 0.10 30° T = -12°/10° H = 0.10 45° T = -18°/0° H = 0.10 45° 2 T = 0°/32° H = 0.05 15° T = -7°/20° H = 0.05 15° T = -12°/10° H = 0.05 30° T = -18°/0° H = 0.05 30° 1 T = 0°C/32° H = 0.0 15° T = -7°C/20°F H = 0.0 15° T = - 12°C/10° F H = 0.0 15° T = -18°C/0°F H = 0.0 15° 1234

45. Air Properties Chart 3 T = 0°/32° H = 0.10 30° T = -7°/20° H = 0.10 30° T = -12°/10° H = 0.10 45° T = -18°/0° H = 0.10 45° 2 T = 0°/32° H = 0.05 15° T = -7°/20° H = 0.05 15° T = -12°/10° H = 0.05 30° T = -18°/0° H = 0.05 30° 1 T = 0°C/32° H = 0.0 15° T = -7°C/20°F H = 0.0 15° T = - 12°C/10° F H = 0.0 15° T = -18°C/0°F H = 0.0 15° 1234

46. Air Properties Chart 3 T = 0°/32° H = 0.10 30° T = -7°/20° H = 0.10 30° T = -12°/10° H = 0.10 45° T = -18°/0° H = 0.10 45° 2 T = 0°/32° H = 0.05 15° T = -7°/20° H = 0.05 15° T = -12°/10° H = 0.05 30° T = -18°/0° H = 0.05 30° 1 T = 0°C/32° H = 0.0 15° T = -7°C/20°F H = 0.0 15° T = - 12°C/10° F H = 0.0 15° T = -18°C/0°F H = 0.0 15° 1234 T = -12°C/10°F H = 0.05 g/m 3 30°

53. Stage One!

60. Fractal Snowflake

61. One more time

62. Here’s the other snowflake…

63. Based on geometry which video shows a possible real snowflake. 1.Snowflake A 2.Snowflake B

64. Thank you for visiting Winter Wonderland today.