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FE Magazine - Issue 3: Mathematics and numeracy

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 01 May 2009 by ncetm_administrator
Updated on 26 May 2009 by ncetm_administrator

FE Magazine - for post-16 mathematics and numeracy educators
FE - work-based learning - adult numeracy - offender learning

Mathematics and numeracy - exploring digital devices

We are all familiar with the decimal system of numbers, where we use the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent any number by placing it appropriately in the H, T, or U column:

HTU Table

Let's suppose we had only two digits, 0 and 1. In a similar way, we can represent numbers like this:

Decimal Table

Very interesting, but so what?

Well, from a teaching point of view, many learners don’t fully understand how decimal numbers work. Perhaps by asking them to do base 2 arithmetic with ‘easy’ numbers, the structure could be easier to understand and manipulate.

In the ‘real’ world, using binary (base 2) arithmetic enables us to model situations where there are just two possible states, e.g:

  • on or off
  • smooth or bumpy
  • present or absent. 

A major application of this occurs in the computer industry. Computers are made up of lots and lots of tiny electronic switches, whose state can be represented by 1 or 0.  Each piece of information held by the switch is called a bit (short for Binary digIT).

Using an 8-bit binary number (a byte) gives us 256 combinations of instructions or information which can be stored. Suddenly we are into bigger numbers.

A hard disk on a three-year-old laptop is 55.8 gigabytes, which is small by today’s standards. What does this actually mean, in terms of units of information stored?

‘Giga’ means the original number multiplied by 1 000 000 000, so this computer can hold 5 580 000 000 bytes of information, which is approximately equal to 230 pieces of information.

Why do modern computers have so much more memory? One reason is because we now use them to download and store music which contains a great deal of information.

For our final piece of number crunching, let’s look at a single CD and how it is made:

  • An analogue recording is chopped into 44 100 pieces per second, each of which requires 2 bytes to hold the information
  • The sound is recorded on two channels
  • 44 100 x 2 x 2 bytes so far….per second
  • x 60 …………………………..per minute
  • x 74 …………………………..for a 74 minute CD
  • A total of 783 216 000 bytes, all contained in a spiral 5 km long!

How could you use some of this information in your teaching?
How many mathematical topics could it link to?
What other everyday contexts could you use in your lessons in a similar way?

Further reading (from howstuffworks.com)

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04 June 2009 21:08
Never forget that old Christmas cracker "magic trick" with the numbers from 1 to 63 on 7 cards.. a lovely way to inspire students to think about binary!

Another calculation involves pixels and the number of colours in a digital image. How many different colours can we have in a "24 bit" image? How much disk space does a 5 megapixel, 24 bit image need? (I believe "bitmap" format requires this space because it doesn't compress the image like jpeg etc. so students can look at the actual filesize on a computer.)
By stoofus
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