Fibonacci sequences with simultaneous linear equations

The second of two lessons on Fibonacci sequences with the 9-1 GCSE specification in mind. Please see my other resources for the first lesson, although this also works as a stand-alone lesson. Inspired by a sample exam paper question where pupils had to work out the first two terms of a Fibonacci sequence, given the 3rd and 6th terms.

Activities included:

Starter:
A set of simultaneous linear equation questions, to check pupils can apply the basic method.

Main:

• A nice puzzle to get pupils thinking about Fibonacci sequences.
• Examples and a set of questions with a progression in difficulty, on the main theme of finding the first terms using simultaneous linear equations.
• A lovely extension puzzle where pupils investigate a set of Fibonacci sequences with a special property.

Plenary:
A brief look at some other curious properties of the 1, 1, 2, 3, 5, … Fibonacci sequence, ending with a few iconic images of spirals in nature.

Slides could be printed as worksheets, although lesson has been designed to be projected.

Answers included throughout.

Please review if you buy as any feedback is appreciated!