Square number snakes and rings
Make square number snakes by creating chains of integers where adjacent ones have to sum to a square number. You cannot have any number more than once in the snake. Who can make the longest snake?
Then split your snakes up so that the ends can be placed adjacently so that they sum to a square number. Now you have a square number ring! What is the smallest ring you can make? What is the largest?
Great for getting pupils to learn the square numbers…