**"Geometric patterns"**

## Years 7 to 12 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 […]

## Grades 6 to 12 Sierpinski Number and Shape Patterns

*By toni On 11 September, 2019 · 2 Comments*

In March 2014 and February 2015 Bubblz the Mathematical Clown and the Pyraloons built Guinness World Record breaking Balloon Model Sierpinski Pyramids to raise funds for AIMSSEC. The photo shows the triumphant team in a shopping mall in Cambridge, UK and their 6.5 metre high pyramid.

The smallest pyramid is made from […]

## Years 6 to 12 Flower of Life

*By toni On 16 July, 2019 · Leave a Comment*

Describe the picture? What do you notice? Talk with your friends about it. What shapes can you see in it?

Describe the different symmetries. Draw the picture yourself. Draw your own designs using this idea. Can you explain how this 2-dimensional picture appears to show a 3-dimensional object?

You could use paperclip […]

## Grades 5 to 9 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?

[…]

## Grades 4 to 7 Tangram Pattern

*By toni On 3 June, 2017 · Leave a Comment*

Arrange the 7 tangram pieces to make the shape in the grey picture.

What do you notice about this shape?

Describe the shapes of the tangram pieces.

What is the same and what is different about the shapes of the tangram pieces?

Make a pattern of your own using all 7 pieces.

[…]

## Grades 7 to 12 Mystic Rose

*By toni On 24 February, 2017 · 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 […]

## Grade 12 GP Geometrically

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

The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .

## Grades 5 to 9 Path to the Stars

*By toni On 24 June, 2015 · Leave a Comment*

Is it possible to draw a 5-pointed star without taking your pencil off the paper?

When you turn this star around it looks exactly the same in 5 different positions so we say it has ROTATIONAL SYMMETRY of order 5.

Is it possible to draw a 6-pointed star in the same way […]

## Grades 9 to 12 – Trisquares

*By toni On 2 June, 2015 · 6 Comments*

These ‘trisquares’ are made up of three squares and each has an area of 3 square units.

Can you fit them together to make an enlargement of the shape? What is its area?

Can you fit trisquares together to make enlargements of scale factors 3, 4 and 5? What are their areas?

Is it […]

## Grade 10 to 12 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 […]

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