Summary
Multiplying by 10 can be confusing for learners with Dyscalculia or maths difficulties. Many children describe multiplying by 10 as just ‘adding a zero’ and dividing by 10 as ‘taking a zero off’. This can be particularly true for children with dyscalculia and other maths difficulties, as they may have learnt a process without understanding the reason why. Whilst this description is true when multiplying and dividing whole numbers by 10, it can’t be applied when multiplying and dividing decimals.
Why do we seem to ‘add a zero’ when we multiply a number by 10?
The answer to this lies in the place value of our decimal number system. Using Dienes or other place value manipulatives, we can see that:
10 ones is the same as 1 ten
10 tens is the same as 1 hundred 10 hundreds is the same as 1 thousand
So:
4×10=40 because 4 ones multiplied by 10 becomes 4 tens
40×10=400 because 4 tens multiplied by 10 would become 4 hundreds
400×10=4000 because 4 hundreds multiplied by 10 would become 4 thousands
We can show this on a place value grid, starting with 4 in the ones column. Each time we multiply by 10, the 4 moves one space to the left and we need to use a zero as a placeholder in the column it moved from.
When we divide by 10, the movement is reversed, because dividing a thousand into 10 equal pieces results in hundreds, dividing a hundred into 10 pieces results in tens, and dividing a ten into 10 pieces results in ones. This time the digit moves one column to the right, which means that one of the placeholders is no longer needed.
4000÷10= 400
400÷10= 40
40÷10= 4
Understanding this movement of digits will allow children to apply the process successfully to working with decimals.
You can find links to place value grids to download or to use online here:
https://www.fixitmaths.com/place-value-grids.html
Check out more Fixit with Karen videos for learners with dyscalculia or maths difficulties in our ‘Blogs’ here – https://dyscalculianetwork.com/insights-events/
or on our Youtube Channel here –
