Category Archives: equations

Simultaneous Equations using real life examples

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Students need to sort the cards into matching pairs and then use the information on each card to find the price of each item (2 equations, 2 unknowns). Introduces simultaneous equations using some concrete examples as a way into the algebra. There are 3 different levels, on the spreadsheet here.


A simple circle problem

My high attaining Year 9 class didn’t quite get this on their own yesterday but they enjoyed the challenge and were able to follow the explanation.

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The crux of the problem is getting a right angle triangle with sides 1, (1+x) and (2-x).  It is the (2-x) side which is hardest to spot.  There were groans when I finally showed them.

Then it requires some algebra – namely expanding (1+x)² and (2-x)² which Year 9 hadn’t had much practice in, so it was good to show them why (1+x)²≠1²+x²

I gave them the problem printed out, here they are 2 to a page.

Here is link to the Geogebra file that I created this on.

I had a few Twitter responses to this including @ProfSmudge who kindly set us an extension question:

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It’s an example of an Apollonian gasket, apparently (thanks to @mathforge for pointing that out!).  That gets properly hard, involving Cosine Rule.  Certainly not something I’d give to my students, but I’ve got a few teachers working on it!


Solving Linear Equations

This is a pretty old flash-based resource hosted on (requires a log-in but it’s free).  It is still my favourite tool for practising solving linear equations. I’m worried that I haven’t found anything better yet and that as Flash become less and less supported, I’m not going to be able to use it much longer.  Let me know if you know of others!

I use it to really reinforce the idea of “doing the same to both sides”.  It can be used both in whole class explanations / discussions and also with students using it themselves.  The process of “getting it wrong” is really productive as they can see what would happen if they did that.  I also like the fact that there is no “undo” button. They need to work out that “undo” just means do the inverse operation so it reinforces that idea too.



Think of a number, but how does it work?

This is a nice development of the classic “Think of a Number” problems that are a good way of introducing algebraic equations.  Nrich covers this introductory activity with Your Number Is… and other linked activities.

This one takes it a stage further.  Proving algebraically why this works would be a nice extension activity. Note that with the numbers below, this will only work in 2015.  I’ll leave you to work out what you need to change for subsequent years!

Work this out as you read.

Be sure you don’t read to the bottom until you’ve worked it out.

First, pick a number 1 to 7

Multiply this number by 2.

Add 5.

Multiply it by 50.  (Come on, you can do that without a calculator).

If you have already had your birthday this year, add 1765

If you haven’t, add 1764

Now, subtract the four digit year that you were born.  e.g. 1984

You should have a 3 digit number:

The first digit of this was your original number.

The next two numbers are your age.