11+ Maths
Recognising and calculating square numbers — and using them in sequences and area links.
Square Numbers appears in 53 of our 571 ready papers (77 tagged questions). It averages 1.5 questions a paper worth about 1.58 marks each. The typical question allows around 54 sec.
Square-number questions reward instant recognition of 1, 4, 9, 16, 25 and beyond. Papers ask “which is a square number”, for the square of a value, or for the next term in a square sequence. Children who multiply by 2 instead of squaring, or who confuse square with prime, drop easy marks. Memorise squares to at least 15×15 and practise linking squares to area of a square shape. Independent papers sometimes combine squares with algebra (“n²”). A quick check — “is there an integer whose square is this?” — catches many false candidates in multiple-choice lists. Keep a tiny written list of squares from 1 to 15 at the top of rough paper in the first minute of the exam if recall feels shaky. Area-of-a-square questions are square numbers in disguise — side×side — so cross-check with your squares list when the side is an integer. If a multiple-choice list mixes squares with near-misses (48, 50, 51), test candidates by asking what integer times itself produces each option. Under timed 11+ conditions, children who pause to name the method before they calculate — and who check the form of the final answer — keep more marks than those who rush the first approach that comes to mind. Build that habit with short, mixed sets from real papers rather than endless textbook drills of one type.
A real tagged question from our catalogue — method included, not paywalled.
Ranked from our tagged catalogue — open a paper to practise the questions that actually test this topic.
Not sure whether square numbers is the problem? Mark any past paper on 11plusSolved and the report tells you which topics are costing marks — and how many.
