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Resources tagged with Fibonacci sequence similar to Ordered Sums:

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Broad Topics > Sequences, Functions and Graphs > Fibonacci sequence

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Ordered Sums

Age 14 to 16 Challenge Level:

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .

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The Golden Ratio, Fibonacci Numbers and Continued Fractions.

Age 14 to 16

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

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Fibonacci Surprises

Age 11 to 14 Challenge Level:

Play around with the Fibonacci sequence and discover some surprising results!

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Paving Paths

Age 11 to 14 Challenge Level:

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

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1 Step 2 Step

Age 11 to 14 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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Fibs

Age 11 to 14 Challenge Level:

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

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Gnomon Dimensions

Age 14 to 16 Challenge Level:

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

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Building Gnomons

Age 14 to 16 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

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Fibonacci's Three Wishes 2

Age 7 to 14

Second of two articles about Fibonacci, written for students.

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First Forward Into Logo 11: Sequences

Age 11 to 18 Challenge Level:

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

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LOGO Challenge - Circles as Bugs

Age 11 to 16 Challenge Level:

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

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Cellular

Age 7 to 16 Challenge Level:

Cellular is an animation that helps you make geometric sequences composed of square cells.

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Got a Strategy for Last Biscuit?

Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

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Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

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Continued Fractions I

Age 14 to 18

An article introducing continued fractions with some simple puzzles for the reader.

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Spirals Instead of Sunflowers

Age 11 to 16 Challenge Level:

Using logo to investigate spirals

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Leonardo of Pisa and the Golden Rectangle

Age 7 to 16

Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.

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Whirling Fibonacci Squares

Age 11 to 16

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.