Spinning and Flipping a Square

This week’s challenge takes a square (that could look a bit like a face (or layer) of a Rubik’s cube and challenges you to notice which moves produce which change in orientation.

Challenge On Boarding – Analysing the Square

Squares are symmetrical, which means we can flip or rotate one and it will look the same as it did before.

Using a square with one corner and one edge piece coloured in, we can tell when the square’s orientation has been changed.

Different Orientations

You can find the total number of orientations by using seeing how many positions one piece can fit in.

Then for each of those positions, how many possibilities are there for the other piece.

The Transformations

There are 7 different ways to transform this square such that:

  • The outline shape doesn’t change in any way
  • You do not take the square apart at all.

Each transformation changes a particular orientation into a different one.

The Challenges

  • Find all 8 orientations
  • Map the transformations between different orientations

Fill in the orientations and then the transformations between each one.

Download or share all of these challenges with this pdf and let us know how you got on with it by tweeting using #momentofmaths and start to see Every moment is a #momentofmaths

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