## Monday, 23 September 2013

### What is x?

How do you introduce "x" to your students?

I'm guessing you start teaching informal algebra in this kind of way:

10 + ? = 20

Where the question mark obviously represents the mysterious-sounding "unknown". Except it's not really unknown, because it's obviously 10.

Eventually you replace the question marks (or empty boxes) with letters. Not just the letter x, obviously, but you have to admit x is a popular one.

In this number sentence, what is x? I don't mean what is it's value, I mean, what is it?

2x + 4 = 12

It's an unknown. It is a number that definitely exists and has one particular value which at this very moment is unknown to us but in a matter of seconds will be completely known. Two quick steps and we and x will be on first-name terms.

In this number sentence, what is x?

2x + 4 = y

Suddenly, x is no longer an "unknown". It is a "variable". Meaning, its identity is still a secret, but it's not one specific number, it could be any (any any?) number in the world.

2x + 4 = y and y = 5.

Now, suddenly, although x is a variable, it has been forced to stop varying, and simply be unknown.

Can you see how the dual nature of x (or any letter really) could be very confusing for students? If students think of a letter as representing one particular number (even if they realise that number can change on a daily basis), this might hinder them when it comes to studying linear graphs, or functions.

Maybe we should try to introduce x as a variable instead of an unknown. Think about how you could do this, perhaps with your brand new, untainted year sevens with their clean-blanket-of-snow brains.

Let me know how you get on,

Emma x x x

1. Hi Emma,
I decided to try this with my bottom set year 7 last week, I started by writing the following on the board:

a + 2 = b

I paused for a few seconds while I worked out exactly how I was going to phrase a question for them, then turned to face the class again to find that, to my surprise, over half of them had their hands up before I had even said anything. Clearly what I had written on the board does not have an "answer" but they were all very keen to add their opinion,
One said with great confidence that "a is 3 and b is 5", another was then sure the answer must be 2 and 4. This then lead to an excellent discussion that sometimes the value of letters can change, and sometimes their value is fixed.
Thank you for helping me to get my math-phobic class to talk about maths.

Charlie V.

2. x is a letter.