Year 6

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We understand what square numbers are and know the squares of numbers to 12 × 12

We can work out the squares of multiples of 10

We can work out the square roots of numbers up to 144

Year 6 Unit 14

What we are learning:

  • A square number is the product of multiplying a number by itself. In other words, if 3×3=9 then 9 is a square number because we have multiplied the number 3 by itself to make 9. We call them square numbers because we can lay out a pattern of dots for that number in the form of a square. In this case there would be three rows of three dots to make a square of nine dots altogether.
  • We say ‘three squared is nine’ and write this as 3²= 9. The use of the small number 2 indicates that we are multiplying the number 3 by itself.
  • Your child should understand that all square numbers can be laid out as squares and know the square numbers to 144.
  • They are 1 (1X1), 4 (2×2), 9 (3×3), 16 (4×4), 25 (5×5), 36 (6×6), 49 (7×7), 64 (8×8), 81 (9×9), 100 (10×10), 121 (11×11), and 144 (12×12).
  • Try some quick fire quiz questions like, What is the square of 8? What is the square of 4?
  • We can use our tables knowledge to work out the squares of larger numbers if they are multiples of 10. For example, the square of 20 is 400 because 2×2=4, so 20×20 = 400. Try exploring the squares of larger numbers like this.
  • A square root is the number that, multiplied by itself will give you the target number. In other words we are reversing the process of finding the square of a number.
  • If 3×3=9 and we know that 9 is the square of 3, then we also know that 3 is the square root of 9. In the same way, 4 is the square root of 16, 5 is the square root of 25 and so on.
  • You can always work out the squares and square roots of large numbers on a calculator and ask your child to estimate the answer. If they talk through their thinking out loud this will give a good demonstration of how
    they understand and are solving the problem.

Activities you can do at home:

Now you can mix the questions together:
What is the square of 6?
What is the square root of 144?
What is the square of 40?
What is the square root of 2500?

Good questions to ask:

What is a square number?
How do we know whether a number is square?
Is 5 a square number? Why can’t it be square?
What is a square root?

If your child:

Cannot explain or understand the concept of a square number
Take some objects and lay them out in a square pattern, e.g. 9 objects make a 3×3 square. See what happens if you add one more object to the pattern – you cannot make a square. Build other square numbers in this way.
Grasps the concepts of squares and square roots easily Try finding the squares of larger numbers or of numbers with decimals in them. Do the same for square roots.


Activity sheet PDF

Extension Activity

Please use this activity when you think your child understands the unit of work. It will deepen and extend your child’s understanding of this unit.


Extension activity (PDF)