What’s the big deal about ‘place value’?

Place Value shown from ones to hundred millions on whiteboard
Have you been told that your child needs more work on place value? What is place value and why does it matter? How can you help your child understand and apply it?

First of all, place value underpins our whole number system. It enables us to count and work with huge numbers, way past millions of millions, and also the tiniest of numbers used to measure organisms visible only through a microscope.

Our number system consists of only ten digits, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each of these digits represents a specific number or quantity of things. For example 7 bananas is not the same as 3 bananas. These digits can be placed together side by side to make a new number such as 73. 73 bananas is not the same as 7 bananas and 3 more bananas. This is because values are given to digits according to where they are placed in a number. This is what is meant by ‘place value’.

So what are the place values we use? Starting with the ones (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), the next place to the left is the tens, then hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, ten billions, hundred billions, trillions and so on. See the photograph above for an example of this. For smaller numbers we place a decimal point to the right of the ones and continue to the right with tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, ten millionths, and so on.

The process of learning to use the number system with larger numbers and decimal numbers is gradual and is built on the understanding that ten of one unit is the same as one of the units immediately to the left in place value, e.g 10 ones is the same as 1 ten, or 10 hundreds is the same as 1 thousand.

Where do you start to help your child understand place value? Begin here:

  • Purchase some ‘icy-pole’ sticks from a bargain or craft shop (200 sticks is best) and a packet of elastic bands
  • Ask your child to count out ten icy-pole sticks and then put an elastic band around them to form a tight bundle.
  • Repeat this process until you have ten bundles or so.
  • Show your child how to count the bundles of ten: 1 ten, two tens, three tens, four tens, etc. If the child can already count in tens (ten, twenty, thirty, forty) that is fine but not necessary.
  • Practice making numbers using bundles of tens and single sticks as ones.
  • Introduce a chart with the headings ‘tens’ and ‘ones’ at the top (use a small whiteboard, cardboard or piece of paper with a line drawn down the middle) and for a given number such as 73, place the bundles of ten on the left (7 bundles) and the single sticks (3 sticks) on the right (see the photograph above).
  • Tell your child to add 3 ones to the number – three ones are placed in the ones column. Now ask what is the new number?
  • Next ask the child to add 2 tens – 2 bundles are placed in the tens column. What is the new number? Take all the sticks away and start again with a new number.
  • When there are more than 10 ones in the ones column, count out 10, bundle them together with an elastic band and move them over to the tens column. If you end up with more than 10 bundles in the tens column, pick up 10 bundles and tell your child that this big bundle is 100 and that you could put a very big elastic band around them and make another column for the hundreds on the left of the tens.

For adding and subtracting numbers with two or more digits, understanding place value is needed. See my post on ‘Icy-Pole Sticks and Early Maths’ Concepts’ for more help with this.