Students will learn how to extend the Fibonacci numbers to negative values. At this point, students know a Fibonacci number is generated by adding the two previous Fibonacci numbers. Knowing this, ask students to figure out how a Fibonacci number can be determined from the two Fibonacci numbers which follow it. For example, 2 + 3 = 5, so 5 - 3 = 2. Knowing this, the sequence can be extended. 1 - 1 = 0, 1 - 0 = 1, 0 - 1 = -1, 1 - (-1) = 2, etc. Have students generate 20 or so Fibonacci numbers that precede the usual Fibonacci sequence, which is 1, 1, 2, 3, 5, etc.

Next, give your students these challenges:

- A Romantic Riddle by NRICH

Hidden Equation Puzzle 3 by Math Equals Love: The black circles are multiplication signs, not decimals.

Conclude by leading this investigation:

Cannibal Fish

by MathPickle