# Use of alphabet codes to help understand equivalent fractions

I have been using alphabet codes - A=1 to Z=26 - probably for over 45 years. It allows you, for example, to use different levels of questions for each number / letter. The letter P, that’s 16, can go from (8 + 8) to 4^{2} to 2^{4} to √256 to ^{3}√4096. Why I find it useful is that students don’t feel they’re learning about numbers, they just think of themselves as solving a puzzle.

Over the past decade or so volunteering in my local primary school I have also found that I can “teach” something the students don’t know simply by using it in a code question. The powers and roots above are classic examples.

A variation of that code that I started using at some point was obtained by dividing each number by 24. That meant I went from A = ^{1}/_{24} and B = ^{1}/_{12} (because I cancelled all fractions) to X = 1, Y = 1^{1}/_{24} and Z=1^{1}/_{12}. I wrote a first sheet putting A to Z in fractions at the top of the sheet and using exactly those fractions for each letter hoping that, for some students, its use might simply help them to understand, for example, that ^{5}/_{6} is bigger than ^{3}/_{4} or that ^{25}/_{24} can be expressed as 1^{1}/_{24}.

The second sheet contained the same codes for A to Z, but I explained to students that I had used some different fractions to those at the top – though they had the same value. So, for example, I might have used ^{2}/_{4} for ½ and ^{6}/_{9} for ^{2}/_{3}. The depth of explanation would depend on which year they might be in and how confident they had seemed with the topic on the first sheet.

Just recently, for the first time, I decided to go a step further with a small group in the primary school. To be honest, being an OAP, I had forgotten that the group I was seeing that session had already done most of the first two sheets and I was still expected to be dealing with fractions! I told the students that they would be writing to me in code and that they would have to use the fraction code. However, I stipulated that they would not be allowed to use the code that appeared at the top of the sheet, but would have to use equivalent fractions like those which appeared in questions in the second sheet.

I have offered students the opportunity to write code messages from my early teaching days. At times there were sessions in which students weren’t allowed to speak but could pass a code message to anyone in the class. Naturally, I made it very clear from the beginning that I could walk round and read all code messages very quickly – and the one thing which would make it stop was if a student wrote something unpleasant to another student. Students were encouraged to make the degree of difficulty suit the recipient, so students learned at times to write complex codes themselves. If a student spoke during the session, I held up a piece of paper with **19, 8, 8, 8** on it in large print!!

There is actually one more stage I am thinking about but haven’t used yet. I still have – so old that it is hand-written – a third sheet with fraction calculations using addition and subtraction to create codes. Such a sheet could be rewritten, for example, to explain why addition and subtraction of fractions is not as obvious as some primary students might think. By asking them, for example, what is ^{1}/_{2 }+ ^{1}/_{3} , you could point out that ^{1}/_{2} represents the 12th letter and ^{1}/_{3} represents the 8^{th} letter, so the sum should give us the 20^{th} letter, which is ^{5}/_{6} . That might prompt a discussion with students who haven’t yet added fractions as to how we can reach that answer. Why, for example, is 6 the denominator? What did we do on sheet 2 that could help?

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