The little two does not mean times two
The Short Answer
A square number is a whole number multiplied by itself, written with a small two beside it. That small two does not mean times two: seven squared is forty-nine, not fourteen, and that single confusion costs more marks than anything else on this topic. A cube number is multiplied by itself twice, so five cubed is a hundred and twenty-five.
What is a square number?
A whole number multiplied by itself. Seven times seven is forty-nine, written as 7².
And here is the sentence that matters most in this whole topic:
The little two does not mean times two. Seven squared is forty-nine, not fourteen.
That single mistake costs more marks than anything else here, and it comes from something entirely reasonable — a child reads the small two as an ordinary number, because nobody has told them it is an instruction.
What the small number is telling you
It says how many of them are multiplied together.
7² — two sevens multiplied: 7 × 7 = 49. 5³ — three fives multiplied: 5 × 5 × 5 = 125.
Said that way, cubes need no separate explanation, and the notation stops being arbitrary.
The numbers worth knowing cold
Squares to 144: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Cubes to 125: 1, 8, 27, 64, 125
Seventeen numbers. They are worth learning properly because they pay off in four topics rather than one — sequences built on squares are invisible to a child who does not recognise 1, 4, 9, 16; the area of a square is a square number; and in algebra a² is the same notation doing the same job.
Both a square and a cube
Where do pupils lose marks?
Reading 7² as 7 × 2, which is the whole reason for this post.
Confusing squares with doubles in a sequence — 1, 4, 9, 16 read as an odd sort of doubling.
Not recognising a square when it appears inside another question.
Try it yourself
Say what the small number is telling you to do before you calculate.
- What is 7²?
- List the square numbers up to 144.
- What is 5³?
- Which numbers under 200 are both square and cube?
- A child answers 14 for 7². What have they done?
- 49. Seven multiplied by itself. Not 14.
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. Twelve of them, and they are worth knowing by heart because they turn up inside sequence, area and algebra questions as well as their own.
- 125. Five multiplied by itself twice — 5 × 5 × 5. The cubes worth knowing are 1, 8, 27, 64 and 125.
- 1 and 64. One is 1 × 1 and also 1 × 1 × 1. Sixty-four is 8² and also 4³. It is a favourite question because it looks as though it needs searching and only has two answers.
- Multiplied by two instead of by itself. It is the commonest error on this topic and it comes from reading the small two as an ordinary number rather than as an instruction.
How much practice does this type need at home?
Seventeen numbers, learned the way times tables are learned — out loud, in the car, repeatedly, until they are recall rather than calculation.
Then one game worth playing: say a number and ask whether it is a square, a cube, both, or neither. Sixty-four. Both. Twenty-seven. Cube. Eighty-one. Square. It takes seconds and it is the exact question the paper asks.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why do children answer 14 for 7 squared?
Because they read the small two as a number to multiply by, which is a reasonable thing to assume if nobody has said otherwise. The fix is to say what the notation means out loud: the little two tells you how many sevens are being multiplied together, not what to multiply by. Two sevens multiplied together is 7 × 7. Saying it that way makes cubes obvious as well.
Which squares and cubes should be known by heart?
The squares to 144 — that is 1 through 12 squared — and the cubes to 125, which is 1, 8, 27, 64 and 125. That is seventeen numbers, they recur constantly, and recognising 81 as 9² or 64 as 4³ instantly saves time in sequences, area questions and algebra as well as in questions about squares themselves.
Why does 64 come up so often?
Because it is both a square and a cube — 8 × 8, and also 4 × 4 × 4 — and it is the only one under 200 apart from 1. That makes it perfect for a question asking which number is both, since it looks as though a search is needed and there are only two answers. Knowing that pair turns the question into recall.
Where else do squares turn up?
Everywhere. The area of a square is a square number. Sequences built on squares — 1, 4, 9, 16 — appear regularly and are invisible to a child who does not recognise the numbers. And in algebra, a² means a × a, which is the same notation doing the same job. Learning the seventeen numbers pays off in four topics rather than one.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
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