BEE-EAUTIFUL PATTERNS
"HIVE MAP"
USE THE "HIVE MAP" ABOVE TO HELP BUDDY THE POOR
LOST BEE FIND HIS WAY!
Assume that "Buddy" the bee can only move in a generally
left to right direction, and that he does not backtrack and does not skip
over any cells. Using these guidelines, can you answer the following:
- If "Buddy" needed to get from a starting cell to a neighboring
cell "A", how many paths could he take to get to "A"
If you can print or copy the map, draw Buddy's path on your "hive
map".
- What if Buddy needed to get from the starting cell to cell "B"?
Draw the different paths he could take. How many are there?
- How many paths to cell "C"? Draw each path on the "hive
map".
- How many paths to cell "D"? Draw each possible route.
- Draw the possible paths to cell "E". How many are there?
- How many paths would lead Buddy from the starting cell to cell "F"?
(Make more "maps" if you need them.)
- How many possible paths are there for Buddy to get from the starting
cell to cell "Z"?
- How did you get the answer to that last question? (Is there an easier
way to figure this out than drawing maps?
- Make a table or chart to show the number of paths there are for
each cell from cell "A" to cell "M" (or "A"
to "Z" for an extra challenge!)
MORE BEE-EAUTIFUL PATTERNS
CHINESE TRIANGLE
LOOK AT THE NUMBERS IN THIS TRIANGLE. CAN YOU TELL
WHAT NUMBERS SHOULD GO IN THE LAST 2 ROWS? HOW MANY ROWS COULD YOU ADD
TO THIS TRIANGLE? WHAT PATTERNS DO YOU SEE? ARE THE FIBONACCI NUMBERS IN
THIS TRIANGLE? IF SO, WHERE?
OR, LOOK AT...
PASCAL'S TRIANGLE
WHAT PATTERNS DO YOU SEE IN THIS TRIANGLE? HOW IS IT
LIKE THE CHINESE TRIANGLE? HOW ARE THEY DIFFERENT? CAN YOU FIND THE FIBONACCI
NUMBERS IN PASCAL'S TRIANGLE?
See if you can find more information on the Chinese
Triangle or Pascal's
Triangle. Or, look for another triangle called "Sierpinski's Triangle".
Do other shapes besides triangles have patterns in
them? Maybe you can find some.
Back to Fun with Fibonacci.