Each of the problems in this set offers students an opportunity to explore particular numerical cases which give rise to patterns that they may be keen to explain. When they are ready, students can make generalisations, and appreciate the power of algebra to capture the generality in a concise and elegant way.
Multiple Surprises and Square Number Surprises include solutions that have previously been submitted to NRICH, so students may wish to try these problems first and then compare their own approaches with the published ones. Then they could go on to try Tilted Squares and Difference of Two Squares, which are open for them to submit their own solutions.
Multiple surprises
Square number surprises
Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Difference of two squares