Multiplying and dividing by 10, 100 and 1000 has to be one of the most misunderstood concepts in Maths. It's definitely one, as a teacher, I spend time unpicking every year with Year 4, 5 and 6 pupils.
I totally understand how the advice, 'just add a zero' has come about and I was probably taught this myself in school, however this hack doesn't always work and here's why:
2.3 x 10 = 23
No zero in the answer
The essence of a good foundation in maths is understanding Place Value; the value of every digit in a number (e.g. 235 is made up of 200 + 30 + 5). When multiplying a digit by 10, the value of each digit increases by 10 and we can model this using a place value chart (see the diagram below). When we multiply 235 by 10 each digit changes value to 2000 + 300 + 50 = 2350.
Some may argue that 'adding a zero' is just a short term method to help children on their way. However, once children are told that there is a shortcut they rely on their answer to be true. When children suddenly find they are no longer successful at multiplying or dividing by 10 (in Year 4 working with decimals), confusion and frustration sets in.
Good mathematicians evaluate their answers and can identify when they don't make sense, using the principles of Place Value. The example below is a common mistake I see children apply time and time again. As teacher, it shows me that the child hasn't understood that multiplying a number changes the value of each digit.
Common Mistake:
8.5 x 10 = 8.50
This can't be true as 8.5 is the same as:
8.50
8.500
8.5000
Adding zeros in this example does not change the value of the number: 8.5 = 8 whole ones + 5 tenths.
When this occurs, I take children back to basics to experiment with numbers and see for themselves what happens to the value of each digit. This helps children to understand how to multiply by 10 correctly, no matter whether they are working with a whole number or a decimal number. Using the knowledge of place value, children learn to understand that 8 multiplied by ten is 80 and 5 tenths multiplied by ten becomes 5 whole ones.
Once children have understood multiplying by 10 they can then progress to calculating with the inverse operation (dividing by 10). They can then apply this to multiplying and dividing by 100 and 1000 too. This concepts also leads to using efficient mental methods to calculate questions involving multiples of 10, 100 and 1000 e.g. 40 x 300 = 12000.
Maths is a jigsaw of concepts. If we don't give children the full picture and confuse them with shortcuts, they can't put the pieces together correctly and move on with the bigger picture.
Joanne Adams
