**"Sequences"**

## Farey Sequences

*By toni On 23 November, 2021 · Leave a Comment*

It is not difficult to put a list of decimals in order of size. But what about ordering fractions?

John Farey introduced sequences of sequences of fractions in order of size, now called Farey sequences. Can you discover his method from the following examples?

## Mystic Rose

*By toni On 31 January, 2021 · Leave a Comment*

What can you see in this diagram?

Could you draw it? Could you draw a similar diagram with just 5 or 6 points around the outside? Try it?

How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out […]

## Fibonacci’s Rabbits

*By toni On 20 August, 2020 · Leave a Comment*

Fibonacci (in the year 1202) investigated a problem about how fast a population of rabbits would grow in the following circumstances, starting with just one pair of rabbits:

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of […]

## Sheep Talk

*By toni On 19 August, 2020 · Leave a Comment*

In sheep talk the only letters used are B and A.

Sequences of words are formed as follows:

The first word only contains the single letter A.

To get the next word in the sequence change each A in the previous word into B and each B in the previous word […]

## Elephant Dreaming

*By toni On 17 August, 2020 · Leave a Comment*

Start to explore ideas of Fibonacci numbers and the golden ratio by copying the picture and drawing this spiral which is made up of quarter circles. Watch this inspirational video.

Then create your own elephant. The numbers in the centres of the squares give the radii of the quarter circles […]

## Frogs Puzzle

*By toni On 18 July, 2020 · Leave a Comment*

Five red-eye frogs and five orange frogs line up in a row with a space between them.

They have to change places but they can only hop, one frog over another frog or slide to an empty space next to them.

Red-eye frogs can […]

## Shifting Times Tables

*By toni On 8 May, 2020 · Leave a Comment*

Count in 4’s to give the 4 times table: 4, 8, 12, 16, 20, … 80, 84, 88, …

Now shift the 4 times table up 3 to give 7, 11, 15, 19, 23, … 83, 87, 91, …

Which tables were shifted to give the following sequences? By how much? Explain […]

## Quadratic sequences

*By Kwethemba Moyo On 30 April, 2020 · Leave a Comment*

A sequence is defined by the formula an = n2 – 2n + 1.

(a) Calculate the first 8 terms of the sequence.

(b) Calculate the first difference between the terms.

(c) Calculate the second difference between the terms.

(d) What can you say about the results you obtained?

Please click Guide for Home […]

## Linear Sequence

*By Kwethemba Moyo On 21 February, 2020 · Leave a Comment*

1.1 The square grids below the continuous line depict negative numbers and those above the line positive numbers. Study the square grids shown above with black squares forming a pattern. How is the pattern growing? Create square grids 9, 10 and 11; complete them with black squares to further develop the […]

## Squareflake Fractal

*By toni On 14 September, 2019 · Leave a Comment*

1. If the red square has area 1 square unit. What is the area enclosed by the stage 1 squareflake?

2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?

3. If replacing each line segment on the edge with the zig-zag is […]

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