Ice, snow, and frost, oh my! In this Family Math Puzzle, you’ll glide your way through mathematical paths and patterns with these wintry words. You’ll explore the geometry of snowflakes and learn some amazing record-breaking winter statistics. Bundle up for the adventure!
Plenty of Great Ski Trails
The Winter Wonderland Ski Resort has opened its slopes for the season. The ski school uses four hills to help skiers build their skills, each one having its own network of trails to choose. The marketing department for the resort would like to advertise the number of different trails they offer. Your mission is to calculate this information.
The slopes are as follows:
- BR, the beginner slope: Skiers start at B at the top of the hill and then choose either path, R1 or R2.
- ICE, the intermediate slope: Skiers start at I, choose either path, C1 or C2, then choose one of the E paths that is connected. C1 is connected to E1 and E2, and C2 is connected to E2 and E3.
- SNOW, the schussing slope: Skiers create their desired trail by choosing connected paths that spell the word snow.
- FROST, the freestyle slope: Skiers create their desired trail by choosing connected paths that spell the word frost.
How Many Trails Are Possible?
Find the total number of different trails that are possible on each of the ski slopes. Discuss strategies for solving the puzzle.
|
Ski Slope |
BR |
ICE |
SNOW |
FROST |
|
Number of Possible Trails |
|
|
|
|
Olympic Ski Team
The Olympic training ski team uses the most challenging slope, WINTER.
No Two Snowflakes Are Identical
Although no two snowflakes are exactly alike in every detail, their shapes have something in common. All snowflakes are basically a hexagon. The shape is determined as water turns to its frozen form, and it is related to the molecules.
Abominable Snow Statistics?
H2O is the make-up of water.
Do some online research to find out more about these U.S. snow-related statistics:
- 1,140 inches (95 feet) is the most snowfall recorded in a single day.
- The largest snowman (actually a snow-woman) on record was 122' 1" high.
- The typical width of a snowflake varies from less than 0.5 inch to 2 inches.
- The largest snowflake on record was 15 inches in diameter.
ANSWERS
|
Ski Slope |
BR |
ICE |
SNOW |
FROST |
|
Number of Possible Trails |
2 trails BR1, BR2 |
4 trails IC1E1, IC1E2, IC2E1, IC2E2 |
8 trails SN1O1W1, SN1O1W2, SN1O2W2, SN1O2W3, SN2O2W2, SN2O2W2, SN2O3W3, SN2O3W4 |
16 trails FR1O1S1T1, FR1O1S1T2, FR1O1S2T2, FR1O1S2T3, FR1O2S2T2, FR1O2S2T3, FR1O2S3T3, FR1O2S3T4, FR2O2S2T2, FR2O2S2T3, FR2O2S3T3, FR2O2S3T4, FR2O3S3T3, FR2O3S3T4, FR2O3S4T4, FR2O3S4T5 |
To find the possible strategies, follow these steps:
- Trace each path with a pencil on the pyramid drawing.
- Make a separate copy of the pyramid for each path or use a different color when tracing.
- List the letters as shown in the table.
Olympic Ski Team
There are 32 possible trails on the WINTER ski slope.