It all began when a line met a circle…

I got a bit nervous this week. I had to teach my high-flying year 11s how to solve simultaneous equations algebraically when one is a circle and another is linear. This was the first time I’d taught this topic and one I foresaw as having many potential obstacles to them gaining a good understanding. It links so many areas of maths: substitution, rearranging equations, expanding brackets and solving quadratic equations. Whilst I was reasonably confident they could do all these things individually, using them all in one question was going to be a real challenge for them I thought.

I decided to produce a ‘model answer’ for them to stick in their revision notebooks. That way they could concentrate on understanding the concepts and process rather than have to do that and also copy down the example. I chose the equations carefully so the x and y solutions were whole numbers. This kept it neat and tidy for the example which needed to emphasise the method for solving these problems rather than the calculation skills.

To my surprise they totally got it! It was a resounding success and when I set them a question with decimal number solutions they were very comfortable with it.

A great success for planning and thinking beforehand about what the obstacles to learning are likely to be and doing your best to smooth over or bypass them. If only I had the time to plan every lesson like this…!

You can download the model solution below to use as notes for your students. I would suggest that you solve the equations graphically first to illustrate the principles involved. That seemed to add purpose to the algebraic substitution method that followed…

Click here to download the notes

Click here to download a homework activity

Enhanced by Zemanta

You may also like...

1 Response

  1. Pak Liam says:

    Thanks for sharing. I often find that I use model answers after I have had students wrestle with the concept first, that way the model answer has more meaning to them.

Leave a Reply

Your email address will not be published. Required fields are marked *