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Numeracy problems to solve for Key Stage 1, 2 and 3

Key Stage 1 & 2    Solve it...!    
Sam gets Tessellated

We are all familiar with tiling. We find it in the bathroom, kitchen, fire places, on the floors. The Romans called the small tiles they used for pavements and walls 'tessellations'. Repeating designs made with tiles that fit together without any gaps are called tessellations. This tile of sam can be used to make a tessellation like the one below.

A 'Sam' tessellation

Task A

Make your own Sam tile like this

This 'Sam' tile slots together to make a tessellation. Starting with a square, pieces are cut out from one side and added to the opposite site to make his nose and hair.

Click here for the squared paper

You can colour your 'Sam' tiles as you wish and make your own tessellation.
If you are in KS1 you may need an adult or older brother, sister or friend to help you make your Sam tile and Sam tessellation.

Task B

Try making a fish tile and using it to make a fish tessellation. Make your tile from a square.

An extra challenge

  • This bird tile can be made from a rectangle. Can you work out how? (the dotted lines might help you) Can you design your own bird tessellation.
  • Try making other tiles to tessellate from either a square or rectangle by
taking a piece from the left or right side and fitting it to the opposite side. Then take a piece from the top and fit it to the bottom.

Key Stage 3   Solve it...!    
Mysterious Geometry

Crop circles are flattened or swirled areas which are found in fields where wheat, barley or other cereal crop is growing.

How are they made? Superior alien technology? Or geometry that would have been easy for the Ancient Egyptians?

The fascination of crop circles is that large geometric designs appear overnight as if no human has had a hand in them but...

The designs are usually made by hoaxers - people who enjoy creating apparently mysterious happenings. However, some of the simpler crop circles may be caused by unusual weather conditions.

The crop circle in the drawing above appeared in Wiltshire, as if by magic, in August 2000. The inside design is a repeat of the outside one and only the circular outline are flattened in a clockwise direction. Although it looks complicated, using a length of rope and flattening boards.

How the crop circle could be made by two hoaxers with a length of rope:


Can you draw your own crop circle design with two pencils and a piece of string? Or use a pair of compasses for a more accurate drawing. You might wish to use rope and chalk in a playground or other appropriate place.



Links on this page:
Key Stage 1
Key Stage 2
Key Stage 3


The answers are variable

































































These problems were sourced by
North East Lincolnshire's Numeracy Team

Thanks to CIRCA Maths Magazine for their Ideas.

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