How to teach square numbers
Grade 4 to Grade 6
A square number is the result of multiplying a whole number by itself, so 6 squared (6²) is 6 × 6 = 36. They are called square numbers because that many dots or tiles form a perfect square. Recognising them fluently helps with area, factors and later work with square roots.
How to teach it
- Make it visual: build squares of tiles (2×2, 3×3, 4×4) and count the total, that total is the square number.
- Introduce the notation: 6² means 6 × 6, not 6 × 2.
- Learn the first perfect squares to 144 (1, 4, 9, 16, 25 …) by heart, like times-table facts.
- Practise both ways: work out a square (7² = ?) and find which number was squared (which number squared is 49?).
- Link it to area, the area of a square with side 6 is 6² = 36 square units.
Common mistakes
- Reading 6² as 6 × 2 = 12 instead of 6 × 6 = 36.
- Confusing a square number with doubling.
- Forgetting the units are 'square' units when linking to area.
Frequently asked questions
What is a square number?
A square number is the result of multiplying a whole number by itself. So 6 squared, written 6 with a small 2, is 6 times 6, which equals 36. They are called square numbers because that many tiles form a perfect square, such as a 6 by 6 grid.
What age or grade are square numbers taught?
Square numbers are usually taught from Grade 4 to Grade 6, once multiplication facts are secure. Students learn the notation, memorise the first perfect squares, and link them to area, which prepares the way for square roots in later years.
What does 6 squared mean, 6 times 6 or 6 times 2?
Six squared means 6 times 6, which is 36, not 6 times 2. The small 2 in the notation tells you how many times the base is multiplied by itself, not what to multiply by. Reading it as 6 times 2 to get 12 is the most common error.
Why are they called square numbers?
They are called square numbers because that many dots or tiles can be arranged into a perfect square. For example 16 tiles form a 4 by 4 square, so 16 is a square number. The name comes directly from this geometric picture.
Which square numbers should children memorise?
It helps to learn the first perfect squares up to 144 by heart, like times-table facts: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. Quick recall of these makes work on area, factors and later square roots much faster.
How do square numbers link to area?
The area of a square with a side of 6 units is 6 squared, which is 36 square units, because area is side times side. This is exactly why the numbers are called squares, and linking the two makes both the notation and the meaning stick.
What comes after square numbers?
Once square numbers are fluent, students often meet square roots, which reverse the process by asking which number was squared to give a result, such as the square root of 49 being 7. Square numbers also support work on area, factors and later algebra.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.