If there is one idea that holds primary maths together, it is place value. It explains why 42 is not four and two, why we “carry” and “borrow”, and why a zero matters. Children who understand it find addition, subtraction, multiplication, decimals and even money easier. Children who do not often rely on tricks that stop working.
What place value means
The value of a digit depends on where it sits. In 352, the 3 means three hundreds (300), the 5 means five tens (50) and the 2 means two ones. We can write it in expanded form: 300 + 50 + 2. The same digit 5 would mean 500 in 512 or just 5 in 205. Our number system uses ten digits, 0 to 9, and each place is worth ten times the place to its right.
Start with objects
Make ones with small counters or dried beans, bundle ten of them with a rubber band to make a ten, and put ten tens in a bag to make a hundred. Children see that ten ones really are one ten. Base-ten blocks do this neatly, but beans, sticks and coins work just as well. Our tens and ones pages use pictures of exactly these bundles.
Regrouping: carrying and borrowing
Adding 47 + 38: the ones are 7 + 8 = 15, which is one ten and five ones. We write 5 and regroup the ten into the tens column. Subtraction reverses the process: to subtract 8 from 3 ones, we exchange one ten for ten ones. Children who have handled bundles understand this as a fair swap rather than a magic trick. Practise with addition with regrouping and subtraction with borrowing.
The zero as a placeholder
Zero often confuses children. In 405, zero tells us there are no tens. Without it, 45 would be a very different number. Ask children to make numbers like 407 with place value cards and to explain why the zero is there. Subtracting across zeros, such as 300 − 148, becomes easier when they think of 300 as thirty tens.
Bigger numbers and decimals
The same pattern continues in both directions. Thousands, ten thousands and millions continue to the left. To the right of the decimal point, tenths, hundredths and thousandths are each one-tenth of the place before. Money is a handy example: 4.25 is four dollars, two dimes and five cents, or whichever coins your country uses. Our place value pages run from tens and ones to millions, and the decimal pages pick up from there.
Quick games to build place value
- Digit cards. Draw three cards and make the largest and smallest numbers possible.
- What is 10 more? Ask “What is 10 more than 47? 10 less? 100 more?” Do it daily for a minute.
- Number of the day. Choose a number and write it in words, in expanded form and with a picture.
Frequently asked questions
At what age do children learn place value?
Tens and ones are introduced around ages six and seven, with hundreds and thousands over the next two years.
Why does my child ‘borrow’ differently from how I learned?
Methods vary between schools and countries. Ask the teacher which one is taught and follow it to avoid confusion.
What if my child counts on fingers?
That is a normal stage. Gradually encourage number bonds and place value ideas so they need fingers less.
