Argh! Algebra!

Every year, with every class, in every school, it's there on the scheme of work: Into to Algebra. A lesson of review or true introduction, depending on the class, and how much they've forgotten from last year. There's rarely any guidance or ideas provided for this lesson, even though it's crucial to how the students perceive algebra. I haven't taught it the same way twice yet, but this is where I'm at so far.

We talk about how sometimes, either we don't know what a number is (how many pencils in this box), or the number can change (how many siblings someone has, will change depending on the person). This is when we use letters. We go straight from there into simplifying - one jar of sweets, plus another jar of sweets, is 2 jars of sweets. j + j = 2j

I haven't seen other teachers do this, but I think it's important to get straight into manipulating the letters, rather than using numbers straight away (substituting or solving), so the students get used to using the letters. We use the simplifying to explain the hidden multiplication signs in expressions like 2j, and then think about why we write 2n not  n2. I ask the students to tell me a thing that begins with n - the best so far is ninjas. If, I ask, Sophie and Charlie suddenly revealed that they were ninjas, what would we say? We'd say 'Look, there's....' I repeat this short pantomime until the whole class are shouting at me 'Look, there's 2 ninjas!' Would we say 'Look, there's ninjas 2!'? Clearly not!

That's enough abstract algebra for most 11-13 year olds to handle, so back to the numbers. Everyone pick their favourite number. Yes, go on, do it! You can call that number by the first letter of your name. Alex's favourite number is 7, so he's going to use A for 7. Then, using their favourite numbers, the students have to make a list of numbers that I give them, writing the rules using the letter. So if Alex was making 20, he could write A + 13. Students like to feel clever, so soon they start coming up with more complicated ways, as I encourage them to write multiple methods for the same answer. 2A + 6, for example, using their simplifying knowledge. It's a good lesson in equivalence too.

We review this exercise by asking people for what they wrote, and I write one 'answer' next to every target number on the board. For 20, I might write Alex's answer: 2A + 6. Then we try to guess Alex's number.

The great thing about this lesson is that, after some explanation of simplifying, the kids can figure everything else out by themselves. I go slowly on the simplifying, taking maybe half an hour, so that everyone can follow. Then they're off! They can make the problems as complicated as they like. I'd like to make the simplifying half of the lesson less teacher-led, and mind-mapping might work for older students, but when they haven't seen algebra before, there needs to be some instruction. Possibly a card sort could replace some of it?