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Winter WonderlandWinter Wonderland
Our Natural World Described Mathematically
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Using Student RespondersUsing 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.
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Here’s one snowflake…Here’s one snowflake…
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Here’s another snowflake…Here’s another snowflake…
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Based on geometry which video Based on geometry which video shows a possible real snowflake.shows a possible real snowflake.
50%50%
Snowflake A Snowflake B
1. Snowflake A
2. Snowflake B
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How do How do snowflakes snowflakes
form?form?
Why do snowflakes have Why do snowflakes have similar shapes?similar shapes?
Are all Are all snowflakes snowflakes identical?identical?
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How is snow formed?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.
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How does the water become snow?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
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Let’s look at some Euclidean Let’s look at some Euclidean shapes…shapes…
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Some natural shapes to sort…Some natural shapes to sort…
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Let’s look at some snowflakes…Let’s look at some snowflakes…
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Why do snowflakes have similar Why do snowflakes have similar shapes?shapes?
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What shape do these snowflakes What shape do these snowflakes have in common?have in common?
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What shape do these snowflakes What shape do these snowflakes have in common?have in common?
Circ
le
Squar
e
Cone
Hex
agon
Pen
tagon
Oct
agon
17% 17% 17%17%17%17%1. Circle
2. Square
3. Cone
4. Hexagon
5. Pentagon
6. Octagon
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What is the molecular shape of an What is the molecular shape of an ice crystal?ice crystal?
HO
H
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Molecular Structure of IceMolecular Structure of Ice
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Are any two snowflakes alike?Are any two snowflakes alike?
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Temperature Humidity
Wind
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Temperature
Warmer air = smooth ends
Colder air = sharp ends
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Humidity
Crystals formed in dry air have simpler shapes than those in higher humidity.
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Why do more complex crystals Why do more complex crystals form in more humid air?form in more humid air?
The
humid
ity w
orks
...
More
hum
id a
ir has
...
Dry
air
is w
arm
er.
33% 33%33%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.
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Wind
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Fractal SnowflakesFractal Snowflakes
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Materials:Materials:
• Protractor
• Marker/Pencil
• Six-sided die
• Snowflake template
• Air Properties Chart
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Draw a diameterDraw a diameter
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Congratulations!Congratulations!
Stage Zero
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What is the midpoint measurement What is the midpoint measurement of each red line segment?of each red line segment?
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What properties determine the What properties determine the growth of a snow crystal?growth of a snow crystal?
Temperature Humidity
Wind
Air Properties ChartClick Here
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Air Properties ChartAir 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°FH = 0.0
15°
T = -12°C/10°
FH = 0.0
15°
T = -18°C/0°FH = 0.0
15°
1 2 3 4
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Air Properties ChartAir 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°FH = 0.0
15°
T = -12°C/10°
FH = 0.0
15°
T = -18°C/0°FH = 0.0
15°
1 2 3 4
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Air Properties ChartAir 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°FH = 0.0
15°
T = -12°C/10°
FH = 0.0
15°
T = -18°C/0°FH = 0.0
15°
1 2 3 4
T = -12°C/10°F
H = 0.05 g/m3
30°
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Stage One!Stage One!
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Fractal SnowflakeFractal Snowflake
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One more timeOne more time
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Here’s the other snowflake…Here’s the other snowflake…
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Based on geometry which video Based on geometry which video shows a possible real snowflake.shows a possible real snowflake.
50%50%
Snowflake A Snowflake B
1. Snowflake A
2. Snowflake B
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Thank you for visiting Winter
Wonderland today.