Challenge Questions
Is there a way of telling whether a shape will tessellate using the angle rules of polygons?
Learning Objectives
Is there a way of telling whether a shape will tessellate using the angle rules of polygons?
Learning Objectives
Beginning
To investigate and then remember the rules for calculating internal angles in polygons.
Developing
To understand how to solve puzzles using the external angles of a polygon.
Developing
To understand how to solve puzzles using the external angles of a polygon.
Mastering
To justify which shapes can tessellate and how many different tessellation are possible.
Resources
Beginning
Mastering
Regular tessellations use identical regular polygons to fill the plane. The vertices of each polygon must coincide with the vertices of other polygons.
This is an example of a regular tessellation - how many others can you find?
Can you convince yourself that there are no more?
Semi-regular tessellations (or Archimedean tessellations) have two properties:
- They are formed by two or more types of regular polygon, each with the same side length
- Each vertex has the same pattern of polygons around it.
Here are two examples:
In the first, triangle, triangle, triangle, square, square {3, 3, 3, 4, 4} meet at each point.
In the second, triangle, hexagon, triangle, hexagon {3, 6, 3, 6} meet at each point.
Can you find all the semi-regular tessellations?
Can you show that you have found them all?
Printable worksheets with simple regular shapes are available here - 3 4 5 6 8 9 10 12
Book Review
Homework
Your homework this week will be on MyMaths - Angles in Polygons
You can now use MyMaths on your iPad using Puffin Academy
