Why Algebra?

It’s the start of the new year, and I’m getting to meet all of my new classes. I’m really excited to be teaching a year 11 General Maths class for the first time, and even more excited to find out that I only have 14 students!

Our first topic is Algebraic Manipulation. Sounds like a whole bundle of fun to a group of kids who just told me that more than half of them don’t like maths, and at least 2/3rds of them think they’re really bad at it. Since I knew that at some point most students in the class would probably groan “wwhyyyy do we even have to learn this?” I decided to pre-empt this and have the discussion before we even started.

I started by asking them “So what is algebra?” expecting to get responses about using the alphabet in maths (there were a few along these lines), but I was surprised when students started to tell me that algebra was all about patterns. A good start!

I told them that algebra is a tool (and I think a few agreed with that statement on its own) – a mathematical tool that’s used for two things: describing patterns and relationships, and proving ideas. We had a look at a few formulas that they know already and talked about the relationship that each one was representing. Then I showed then a magic trick.

Pick a number between 1 and 10
Double it
Multiply it by 5
Divide by your original number
Subtract 7
The number you’re thinking of is 3!

And from that ‘trick’ one of the best classroom discussions I’ve ever seen ensued:

Student 1: Why did it have to be a number between 1 and 10? Would it work with other numbers?
Me: Give it a go with other numbers and see if it works!
Everyone picked a new number – bigger than 10 – and were amazed when the magic still worked
Student 2: What if you pick a negative number?
Me: Try it out, see what happens!
There was even more excitement when these numbers worked too
Student 3: What about if it’s not a whole number? What if I pick, like, a half?
Me: What do you think? Will it work or not?
A few nods and shakes of the head. When these worked as well I posed the question:

Will this always work? How do you know?

After a short silence a student tentatively offered the answer “algebra?”
Me: Yes! So we want to pick a number, but we don’t know the value of that number yet. How do we represent it?
Ss: x!
Me: Do we have to use x?
Ss: Nope, you can use any letter
Me: Good. But it doesn’t have to be a letter – it can be any symbol – I could draw a picture of a fish if I really wanted to

Then we went through the process using x (and fish) and showed that our original number divides out, so it’s completely irrelevant.

One student picked up on the fact that we didn’t need to subtract 7 – we could have finished the trick with one less step, but we decided that it makes the trick look more impressive it there’s an extra step in there.

If this lesson is any indication of the year to come, it’s going to be awesome!

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One thought on “Why Algebra?

  1. Good on you for generating such a good conversation. Here is a place where I think the fact that my students are ‘more accomplished’ already in math makes them less willing to be amazed. I love the fact that your students weren’t (a) disinterested or (b) scared off by the magic of the trick.

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