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Make a cube out of straws and have a go at this practical challenge.

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Reasoning about the number of matches needed to build squares that share their sides.

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Tangram Paradox

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Peg Rotation

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Jamie from St John's School told us:

1) It is flipped over from North to South.
2) It is rotated 90 degrees clockwise.
3) It is rotated 90 degrees anti-clockwise.
4) It is flipped over from East to West.

Nik from Radley Primary School agreed with Jamie's answers, but also had some alternative ways of describing the transformations:

The first square can be flipped north-south or flipped east-west and then turned 180 degrees clockwise.
The second square can be turned 90 degrees clockwise or turned 270 degrees anti-clockwise.
The third square can be turned 270 degrees clockwise or turned 90 degrees anti-clockwise.
The fourth square can be flipped east-west or flipped north-south and then turned 180 degrees clockwise.

For the triangular challenges, Callum from St. Patrick's R.C. told us:

"The triangle is turned:
1.Anti-clockwise for one turn, or clockwise for two turns.
2.Clockwise for one turn, or anti-clockwise for two turns."