2023: The Year of the Rabbit

The year 2023 is the Year of the Rabbit in the Chinese Zodiac. Media4Math would also like to make this the Year of Fibonacci. If you recall, Fibonacci investigated his famous number pattern by looking at the number pattern generated by the increase in the number of rabbits from month to month. The Fibonacci Sequence is one of the most important number patterns found in nature.

So, every month this year we will be investigating different aspects of the Fibonacci Sequence and we’re creating some visually-based instructional resources to investigate this pattern. Here is our first.

The Fibonacci Sequence

The Fibonacci sequence looks at the number of pairs of rabbits each month, and it observes these two rules:

• It takes one month for two baby rabbits to grow to adulthood.
• It takes one month for a pair of adult rabbits to have a pair of baby rabbits.
• An adult pair has one pair of rabbits, one male, one female.

These rules are used to generate a number pattern. It doesn’t necessarily represent how actual rabbits reproduce.

Let’s start the Fibonacci Sequence in January with one pair of baby rabbits. The baby bunnies have a distinctive look, and this first pair of bunnies is labeled with the letter a.

 

It takes one month for these two rabbits to grow into adulthood. So in February, we have one pair of adult rabbits.

Notice how the adult rabbits have a distinctive look from the baby bunnies. Also, the letter label goes from a lowercase a to an uppercase A, indicating adulthood. In February, these adult bunnies can have their own bunnies, but it will take a month. 

This is what it looks like in March. 

Notice that the letter A is now underscored, indicating that these rabbits will now have a new pair of baby bunnies each month, starting with the current month. The first such pair is shown with the label b. There are now a total of two pairs of rabbits in March.

This is what it looks like in April.

The rabbits labeled A have another pair of rabbits, while the rabbits labeled B are now adults and can have bunnies in a month. The new pair of baby bunnies is labeled c. There are now a total of three pairs of bunnies.

This is what it looks like in May.

Here you can see that A had a  pair of bunnies, labeled d, while B had a pair of bunnies, labeled e. There are now five pairs of rabbits.

We now have enough data to look at the beginnings of a number pattern. Take a look.

 

 

Do you see that beginning in March, the pairs of rabbits are equal to the sum of the previous two months. Do you see that? This means that the number of rabbits in June should be 8, or the sum of April and May.

 

Let’s look at the diagram to verify.

As you can see there are, in fact, eight pairs of rabbits in June. Will this pattern continue?

Now it’s your turn. Use the following cut-out sheets for adult rabbits and baby rabbits to continue the pattern. How many rabbits will there be in July? What about August?

Complete the table below.

 

 

Write a description of the Fibonacci Sequence in your own words.