Crib Sheet

Our guide to educational jargon, teaching methods and the strange things children may bring back from school as homework. If there is a particular aspect of your child's education you wish explaining, use the POL Ask an Expert service.
 Mathematics - Bases  
 In mathematics, this is the number of single digits allowed by a system of counting. Although this is a simple concept, it forms the basis of all of the rest of arithmetic, so it's important children understand it thoroughly.
Counting on your fingers

In most everyday mathematics, we use Base 10 - this means we use the digits 0,1,2,3,4,5,6,7,8,9 - almost certainly because we have ten fingers and thumbs. However, certain other bases are also used (though some of them are being phased out). For instance, computers use base 2 - binary - in which the only digits are 0 and 1. In telling the time, we use base 60 (for the number of seconds in the minute and the number of minutes in the hour) and either base 12 or 24 (for the number of hours in a day by the a.m./p.m or the twenty-four hour system); in measuring angle, we use base 60 and base 360 to express degrees of arc; in measuring using Imperial weights, we use base 16 and 14 (ounces to pounds and pounds to stones); and the old fogies among us are used to using base 12 and even base 3 for measuring inches to the foot and feet to the yard.
 Bases higher than 10 In theory, for bases above 10 it's necessary to invent extra symbols for the single digits over nine. Hexadecimal - base 16, used in computer programming - does this by using the letters of the alphabet to represent them. In practice, though, most everyday bases larger than 10 don't bother with special symbols.

It can help children a lot to have these other bases pointed out to them. In fact, practicing counting anything that comes in sets of a given number will help your child grasp the concept. If you want a simple example, try showing them boxes of eggs (either in half dozen or dozen sizes - base 6 and base 12); or you could count gloves, shoes, or socks in base 2 - 'I've got five socks, so that that's two pairs and one left over'.
Place Values Remember Hundreds, Tens and Units?
The concept of bases leads naturally to that of place value - that is, the idea that you can make the single digits allowed by the base stand for bigger numbers depending on where they are.
For instance, if you're counting in Base 10, once you have ten items you no longer write them down as ten 'units' (because there is no single digit that means 'ten'). Instead, you have 'one lot of ten and no units'.
You might have seen this notation in
your child's maths exercise book:		 TU
10
or TU
12 which means 'one ten and two units'.

or

 TU
35 which means 'three tens and five units'.
Similarly, once you have ten lots of ten, they move along a place - and we call them hundreds: HTU
1 2 3
'One hundred, two tens and three units'.

This works all the way up the numbering system. The number on the left is always worth the number on its right times the number of the base.		  So for example, in base 10, you get:
10,000 1000 100 10 Units

And in binary: 16 8 4 2 Units		  

It's absolutely vital for your child to get this straight, since it's impossible to understand arithmetical operations (such as adding, subtracting, dividing and multiplying) properly, and to do them correctly, without.
 The Value of Nothing  Place value depends on having a symbol for zero - literally, a 'place holder' to use when there's nothing else to put in that space. This is a more difficult concept than it sounds (the Romans were great engineers, but they didn't have a symbol for zero - and therefore, didn't have a system of mathematics that used place value; instead they had a different symbol for every number).


Not surprisingly, some children find the idea of zero hard to grasp. Some leave it out altogether, others take a more the merrier approach. For instance, sometimes you'll find a child who writes 'one hundred and one' 1001 - literally, a 'one hundred' and then 'an extra one'. Or you might see the same figure written as 11 (because, 'there's nothing in the middle so it doesn't count').

If your child seems to be having difficulty with arithmetic, it's worth doing a bit of detective work to try and discover if they might not have grasped the idea of zero - and how to use it - properly.