Numbers

This website has been designed as an educational resource for number work, especially for projects and work outside the conventional curriculum. There is information for research purposes. There are also interactive elements which should work under any computer system.

The index page can be used to step through numbers from one upwards in various number systems. This is partly for fun, but it does show how different numbers can be.

There are separate pages for various historic number systems: Egyptian, Babylonian, Chinese, Greek, Roman and Mayan, ending with Arabic numbers, the conventional system. Each one allows you to convert a decimal number to the system version, or count through the numbers. Then there is a description of the system and how it works.

Any one of historic number systems could be used in a cross-curriculum project, perhaps as the mathematical element of a history project (or the history element of a mathematics one!) However, they have a serious mathematical element as well. All these systems work in a different way, they don't just having different symbols. Click here for a comparison of the different systems. Understanding how a number system is different from our numbers is the start to understanding our own system more profoundly. Perhaps different groups of children could try to understand different systems and then explain them to each other. They could also try to do arithmetic in the different systems, to see their advantages or disadvantages. Finally, they may realise that numbers are not 1,2,3 or even one, two, three. These are one way of writing something called a number, but the real number exists outside all human representation of it. This is the way that mathematicians think!

The Arabic numbers are handled in a different way, as most people know these numbers. The first part of this section is probably the most boring part of the website. I really designed it for parents or adults who can't remember how to do simple arithmetic, but want to help their children, or even learn it for themselves. There is a short history, and a page on how numbers are represented. Then there are pages on addition, subtraction, multiplication and division. Each has a straight-forward description on how to do it, including long multiplication and division. There is also interactive practice, which tells you immediately when you type in the wrong digit, rather than waiting until you have finished the number. I find that this helps less able children, as they can correct the mistake immediately.

In the Arabic numbers section, there is also interactive mental arithmetic against time. It sets you ten sums to do, and tells you at the end how many you got right, wrong, or ran out of time, and a number of stars based on how well you did. It can be used for a very wide range of abilities by setting the limit and the time to be possible but challenging - or rather very challenging for able children and easy for less able until they get more confidence. Surprisingly enough, I have found that if the limits are set right, children enjoy seeing their own performance improve.

The Arabic numbers section also has a page on rational or partial numbers called Less than one (although such numbers may be bigger than one, of course). This gives some simple demonstrations of fractions, some work with decimals and a description of percentages. Finally the three systems are compared, to draw home the point that these are not different numbers, but merely different ways of describing the same number. There are several interactive exercises and demonstrations.

The final part of the Arabic numbers section is more challenging. This describes the main types of numbers, explaining how they are necessary, and giving their correct names. There are several links into the interesting numbers which go into more depth. Obviously this is for children more interested in Mathematics.

The finger systems cover several different ways of using your fingers for number work. These include signing numbers, Chisenbop counting (which is a way to count to a hundred on your fingers), multiplying by 6,7,8 and 9 and a Chinese method which counts to 100,000 on your fingers! It is interesting to figure out why these systems work, and it may help some children with their number work. Not everyone manages to deal with numbers inside their heads, and using your fingers seems to be easier. Or, of course, these could be used as a 'fun' exercise, when a teacher needs a lesson filler.

The calculating machines tackles abacuses, Napier's bones, slide rules and calculators. The abacus page has various interactive elements. It can help in understanding the units, tens and hundreds columns in addition if you actually see them as beads on an abacus. Napier's bones are a historic way of doing multiplication. They are easy to make, and might help children with their multiplication. The slide rule has no real purpose except as a historical curiosity. It is assumed that calculators are easy to use, but I'm not too sure. So the calculator page has suggestions to improve use of the calculator, plus exercises in using it and in estimation. Finally all these calculating machines are available as stand-alone pages, which could be pulled up on the screen and used when doing calculations on the computer. They include two calculators, a simple one and an arithmetic one which does calculations in the correct way (for example 1+2x3=7 not 9). I'm not too sure that the interactive slide rule will be much help, though!

There are pages on binary and other bases. The binary pages include a game, and a binary counter which uses the children themselves! The other bases page has a counter in any base up to 36, and a convertor from one base to another.

The section on numbers as words is not really part of mathematics. However, it may make children realise that when they talk about numbers, they use words rather than symbols. There are songs with numbers in, and a comparison between English, French and German counting. There is even a page for counting sheep!

The section on interesting numbers is the most challenging part of the site, although a teacher may find part of it suitable for younger children. It discusses various mathematical numbers, such as zero, one, pi, the golden ratio and even infinity. There are interactive formulae which give you increasingly accurate values of some of these numbers (although only to about 8 digits). There is a certain amount of their history, or their use. If you want to know how to count the Fibonacci spirals on a pine cone, or what is the difference between the golden rectangle and a sheet of A4, then it's all here.

Finally, there is a section on handling data. There is an interactive pictogram graph where you can make a simple graph online. There is a short section on gathering data to use in such a graph, including using tallies. There is a page on median, mode and mean. And there is a page on sort techniques. The sorts are not part of any school curriculum that I know of, but they are logical, visual, and a good thing for occupying the sort of child that finishes their work early!

There are several ways to navigate the site. This page gives links into the different sections. There is the main index page. There is the site map which not only lists every page but also the sections within a page. Finally, there is the alphabetical index for looking things up. There isn't a website search. If you can't find it on those pages, then it probably isn't on the site!

Here are some websites which go into the history of number systems in more detail: