Sheep Talk In sheep talk the only letters

Sheep Talk In sheep talk the only letters used are B and A. BAAA BABAA Sequences of words are formed as follows: The first word only contains the single letter A. To get the next word in the sequence change each A in the previous word into B and each B in the previous word into AB. Write down the first ten words in this sequence.

Sheep Talk In sheep talk the only letters used are B and A. BAAA BABAA Count the number of A's in each word in the sequence. Then count the number of B's in each word in the sequence. Finally count the number of letters in each word in the sequence. You now have three sequences of numbers. What do you notice? Will the same patterns continue if you generate longer sequences of words?

Leonardo’s Leaps Hello, my name is I love up Howwalking many ways Leonardo, but most steps. Sometimes I could up these people. I walk call me walk up one at awild When I’m feeling steps? Fibonacci. time, buta when I’mof 1 I go up mixture very I like to stephappy and two steps! jump up two at a time

5 ways

Leonardo’s Leaps Can you investigate this for different numbers of steps? Can you find a pattern? How many ways could I walk up 15 steps?

Number of steps Number of ways

Making a Beeline 2 1 4 3 6 5 7 This bee is making its way through the cells in this beehive. It can enter from cell 1 or cell 2. It can only move to the right, and one cell at a time. How many ways can it get to cell 2? It can go 2 or 1 -2 That is, 2 ways How many ways can the bee get to each number?

Cell Number of ways

Sheep Talk Leonardo’s Leaps Making a Beeline All produce the same sequence. This is the Fibonacci sequence. Can you explain why they are the same?