The Fibonacci Sequence

#TheCompleteSeries5lessons

During the five lessons included in this complete unit of work, your pupils will be challenged to apply the prior knowledge and understanding of algebra, ratio, proportion and problem solving to identify, generate and describe number sequences. They'll find examples of the Fibonacci sequence and the golden ratio in real life, use simple formulae to extend number sequences and solve problems involving scale factor.

#Lesson1TheFibonacciRabbitsProblem

Introduce your class to Fibonacci's original 'rabbit problem', which led to his creation of the Fibonacci sequence as a way of describing changes in a rabbit population. Once they've examined a variety of number sequences—including the famous Fibonacci sequence—children may design mathematical 'golden spiral' pictures using the sequence to describe the shapes they will draw. This Maths lesson plan pack is the first of five in 'The Fibonacci Sequence': a Year 6 unit of work with five complete lessons all about using number patterns and sequences, algebraic formulae and ratio.

#Lesson2InvestigatingConsecutiveNumbers

Take a closer look at the patterns found in consecutive numbers within the Fibonacci sequence, and challenge children to work systematically to prove what they find. This challenging Year 6 Maths lesson is the second of five in 'The Fibonacci Sequence' unit of work. Children will use problem-solving skills, long multiplication and division to investigate, then prove if patterns they identify are always, sometimes or never true of other consecutive numbers in the sequence.

#Lesson3FindingthenthTerm

Explain how to find the nth term in a linear number sequence, including the Fibonacci sequence, using an algebraic formula. This challenging Year 6 lesson includes detailed slides with lots of number sequences for children to describe, along with very clear explanations of how to use a formula to find any other number in a sequence. They will learn to use the acronym 'DiNO' to help them write formulae for a sequence, then find the 10th, 20th and 100th terms in various linear number sequences.

#Lesson4FibonacciandtheGoldenRatio

Take a mathematical look at aesthetically pleasing 'golden rectangles', and how their proportions are defined by the Golden Ratio of Phi (ϕ). This enjoyable and challenging lesson shows your pupils the link between the Fibonacci sequence and the Golde ratio. Children are challenged to use multiplication and division to identify and make golden rectangles. This is the fourth of five lessons in 'The Fibonacci Sequence', a complete Maths unit of work for Year 6.

#Lesson5TheGoldenRatio

Explore how the golden ratio is found in design as well as in art and nature. After discovering Phi and its significance in the previous lesson (this is the last of five lessons in 'The Fibonacci Sequence' unit of work for Year 6), explore how artists and architects use the Fibonacci sequence, the golden spiral and the golden ratio to make their work more aesthetically pleasing. Can your class spot examples of the golden ratio in design, in different artwork, in buildings – or even in human facial features?

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Curriculum Objectives covered

• Year 6 - solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• Year 6 - solve problems involving addition, subtraction, multiplication and division
• Year 6 - use simple formulae
• Year 6 - generate and describe linear number sequences