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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.
Transformations
Mirror, Mirror...
Age 11 to 14
Challenge Level 
Explore the effect of reflecting in two parallel mirror lines.
Growing Rectangles
Age 11 to 14
Challenge Level
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Reflecting Squarely
Age 11 to 14
Challenge Level
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Attractive Rotations
Age 11 to 14
Challenge Level
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Shady Symmetry
Age 11 to 14
Challenge Level
How many different symmetrical shapes can you make by shading triangles or squares?
Transformation Game
Age 11 to 14
Challenge Level
Why not challenge a friend to play this transformation game?
...on the Wall
Age 11 to 14
Challenge Level
Explore the effect of reflecting in two intersecting mirror lines.
Who is the fairest of them all ?
Age 11 to 14
Challenge Level
Explore the effect of combining enlargements.
Fit for Photocopying
Age 14 to 16
Challenge Level
Explore the relationships between different paper sizes.
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.