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For brilliant puzzles, follow Catriona Agg who regularly posts new puzzles. As you can see from her tweet above, she has made her collection of screenshots freely available.
Following each puzzle, you can find a discussion on the puzzle. Have a look at this puzzle and discussion for example.
In response to this puzzle, you can see various solutions including an Autograph file created by Rob Smith. Rob has this up to change both squares and you can move also move a point on the smaller square.
Another brilliant puzzle author is Ed Southall who has made 40 puzzles available to celebrate his 40th birthday; he has also provided slides for teachers. Check his Geometry Cheat Sheet.
Try these brilliant GeoGebra puzzles from Daniel Mentrard, also his 64 geometric puzzles.
Perhaps try Tangram on Mathigon.
How many of the different shapes can you make?
rich also have a Tangram activity for students age 7 – 11 or for 5-14 years olds try Tangram Pictures.
On Nrich try Penta Colour.
Estimating Angles (NRICH game)
Play alone or challenge a friend – 10 goes each. Score points depending on how close you are.
Alien Angles – an alternative angle estimation game from Math Playground.
Board Block (NRICH)
As a child, my Spirograph was definitely a favourite toy so I was delighted to find this digital version, Inspirograph by Nathan Friend. Try altering the gears so that the fixed and rotating gears are the same size, or make one size a factor of the other, make the two sizes have a common factor, or not! Investigate. You can change the colours too and create a work of Art!
Spiro Graphic Art has a reference section, including a Spirograph Pattern Guide. Note the references to ring 144/96 and 150/105, you can select these on the digital version.
The Nrich problem ‘Making Maths: Planet Paths‘ challenges students to draw some planet paths using a Spirograph.