Shapely Tiling
2 out of 3
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
Problem
Below is a pattern which can be created using a pair of compasses and a ruler, and a photograph of an Islamic Star.
Have a good look at this shape below.
What shapes can you see?
Find shapes that are the same.
Can you name the different shapes you find?
Can you produce the following tessellations:
regular octagons with two different types of triangle?
irregular hexagons with triangles and squares?
Getting Started
Experiment with colouring in different sections to make particular shapes. How could you make a regular octagon?
Try finding as many different triangles as you can - this may help you to see what can be done.
Student Solutions
Amanda from Wallace Hall Academy has sent us a solution to the first part of the question:
You make a regular octagon by making the outline of it with triangles. To do this, you make one quarter of the pattern (i.e. a quarter of the whole interactivity image) orange, so there is an orange square. Then you make the smaller triangles on the edges purple. Then you make the central octagon white, and you will have an octagon outlined by orange big triangles and purple small triangles.
Here is a picture of Amanda's octagon and triangles, using just one quarter of the pattern:
Ling from Beecroft Primary School, Australia has found a way of producing irregular hexagons with triangles and squares. Here is the image she sent:
Let us know if you find any others.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Key questions
Possible extension
Learners could create their own tessellations using this template.
Possible support
The interactivity will be useful for children who don't like making mistakes and those who find colouring difficult.