Fibonacci’s Rabbit Problem-

This problem has been around since the 13th century and is a great way to introduce number patterns.

‘A farmer has a pair of rabbits. It takes a pair two months before it can produce another pair of offspring. How many rabbits are created by one pair in one year?’

Prompt students to use diagrams and explain what they can observe.

Rabbits within a clear circle represent rabbits who are not ready to produce

Rabbits within a green circle represent that the rabbits are one month mature

Rabbits within an orange circle represent that they are ready to reproduce

Some examples of how students can solve the problem using diagrams:

January: First pair of rabbits

February: First pair of rabbits mature

March: First pair of rabbits can reproduce

April: First pair can reproduce again, and the white pair become one month mature

May: First pair reproduce again, the white pair becomes mature, the green pair becomes mature and produces.

June: First pair reproduces again, the white pair becomes mature, the green pair becomes mature and produces, the orange pair produces again, and the white pair becomes mature

Students can continue this diagram all the way through to December. Ask students to count the number of pairs in each month and write the sequence of numbers down ie:

1, 1, 2 , 3, 5, 8, 13, 21, 34, 55, 89, 144,…

As they analyse the numbers they will identify the pattern, namely that they must add the first number to the second number (1 + 1), the second number to third number (1 + 2), the third number to the fourth number (2 + 3), and so forth all the way to the twelfth number. They could go on to see how many in 2, 3, or 4 years and realise that the sequence does not end.