Cut out and reassemble the pieces. Can you explain what happens?
What's the greatest number of sides a polygon on a dotty grid could have?
Take a look at the video showing squares drawn on dotty grids...
Have a go at this 3D extension to the Pebbles problem.
What is the shape of wrapping paper that you would need to completely wrap this model?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?