**"Sequences"**

## 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 […]

## Make a von Koch Poster

*By toni On 12 September, 2019 · Leave a Comment*

The curve, also known as the ‘snowflake curve’, was invented in 1904 by the Swedish mathematician Helge von Koch.

Take a large piece of backing paper, and either draw an equilateral triangle with edges of length 27 cm or cut a triangle from coloured paper and stick it on […]

## Table of Tables

*By toni On 3 July, 2019 · Leave a Comment*

What patterns do you notice in this table?

Continue the patterns to fill the empty squares.

Write a list describing all the patterns that you see.

What do you notice about the numbers on squares of the same colour?

Would the patterns […]

## A2 SEQUENCES AND PATTERNS

*By toni On 11 January, 2018 · Leave a Comment*

How to use beans, stones and other objects to form pattern sequences and to develop an understanding of algebraic formulas.

Click here to download a PDF with all you need to run your own professional development workshop.

## Equipattern

*By toni On 12 November, 2017 · Leave a Comment*

Copy this pattern. You could use toothpicks or paper sticks or draw the pattern on isometric paper (download here).

Make or draw the next 3 patterns in the sequence. How would you explain to someone else on the telephone how to do this when you could not point to the diagram?

[…]

## Squares Pattern

*By toni On 4 August, 2017 · Leave a Comment*

This square of squares pattern has edge length 5 squares. You could make this pattern with 48 matchsticks.

Work out the number of edge squares and the number of lines (matchsticks) needed to make the pattern with: side length 6, side length 25, side length 100, side length n.

Click here […]

## Steps

*By toni On 5 November, 2016 · Leave a Comment*

Continue these sequences for the next three terms and continue the sequences backwards to the previous 3 terms:

7, 10, 13, 16, 19, …

15, 18, 21, 24, 27, …

1, -2, -5, -8, -11, …

What do you notice?

The first two sequences come from a multiplication table shifted up. Which […]

## Handshakes or Bows

*By toni On 26 August, 2016 · Leave a Comment*

Everyone in the class must shake hands with everyone else and say hello, or bow to each other in a one-to-one greeting. Everyone must join in. How many handshakes (or bows) will there be altogether?

This will be difficult to count, especially if you have a large class. Try the problem in […]

## Coordinate Patterns

*By toni On 5 January, 2014 · 22 Comments*

Imagine this pattern of squares continuing on and on …

How do you find the coordinates of the centre of square 1 if you know that (0, 3), (3, 4), (4, 1) and (1, 0) are vertices?

What are the coordinates of the centre of the 20th square?

Imagine the sequence of […]

## Loopy

*By toni On 17 January, 2012 · 3 Comments*

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