Follow this recipe for sieving numbers and see what interesting patterns emerge.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Which numbers can we write as a sum of square numbers?

How would you judge a competition to draw a freehand square?

Here we look back at the year with NRICH and suggest mathematical summer holiday activities for students, parents and teachers.