Exercise 1
Sharing into a ratio
Share the following numbers into a ratio:
a) Share £15 into a ratio of 1:2
b) Share £10 into a ratio of 4:1
c) Share £18 into a ratio of 2:1
d) Share £12 into a ratio of 5:1
Exercise 2
Unlike fractions
Exercise 3
Percentages of a number
a) 50% of £50
b) 10% of £20
c) 20% of £80
d) 25% of £200
Lesson
Title: Entry Point
Challenge Question
Is there a way of telling whether a shape will tessellate?
Learning Targets
Beginning
Will be able tessellate simple shapes.
Developing
Will be able to investigate which shapes can tessellate and which cannot (and why not).
Mastering
To justify which shapes can tessellate and how many different tessellation are possible.
Resources
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
MangaHigh - Week 2
