What are Square Numbers?
Square numbers are a special group of numbers. Let’s find out what makes them unique.
Square numbers (or ‘perfect squares’) are a special type of number.
What makes them special?
Well, a square number is the product of a number multiplied by itself.
So, for example, four is a square number because it is equal to 2 x 2. 16 is a square number because it’s equal to 4 x 4, just as 529 is a square number because it’s the product of 23 and 23.
At the elementary level, we tend to be most familiar with the smaller square numbers, so here they are from 1 (1 x 1) to 225 (15 x 15):
Interesting things about square numbers
There’s lot of interesting features when it comes to the square numbers. Let’s take a look:
1. Square numbers are square in more than just name
When shown as a multiplication array, these square numbers, as you can see below, take the shape of a square (hence the name square numbers).
You can see below that for square numbers, each array has the same number or rows as it does columns.
2. The square numbers alternate odd and even.
Another interesting fact about the square numbers is that they are alternately odd and even.
1 = odd
4 = even
9 = odd
16 = even
25 = odd…
… you get the idea.
2. The square numbers run diagonally across the multiplication chart.
When we mark square numbers on the multiplication chart, you can see that they form a diagonal line from 1 in the top left corner, to 100 in the bottom right corner.
If you look carefully at the numbers either side of that diagonal line, you’ll see that the numbers in one half of the chart are reflected in the other half.
Does my child need to learn the square numbers and their corresponding multiplication facts?
If your child is learning their multiplication facts then one square number math fact will appear in each multiplication table. For example 3 x 3 = 9 will be included when your child is working on their 3 times table, just as 9 x 9 = 81 will be covered as they work through the 9s.
By the time they have learnt all their facts up to 10 x 10 they will have already learnt the square number math facts for all the square numbers from 1 up to 100.
However, I like to focus on the square number facts as one special group of numbers and give them a bit of extra individual attention.
It’s a nice way to check for understanding of what a square number is, plus trickier facts like 8 x 8 and 9 x 9 always need a bit more attention and so a bit of repetition never hurts.
