Going back to front to embed understanding

I love designing questions.  In fact I find it therapeutic.  After attending the Designing Good Questions session at #MathsConf13 on Saturday, presented by Ed Southall (@solvemymaths) it spurred me into some action.  I teach a single lesson for a high ability Y11 group and three out of 4 lessons for a high ability Y10 group this year and, by luck, in both we are looking at quadratics.

We’ve done the main work on quadratics with Y11 – this is more about revisiting and embedding.  With Y10 I want to be able to embed a deeper understanding.  Giving the students the end point of a question and then sort of working out where we started is an interesting approach and I believe really gets the students to understand the processes involved rather than just being able to mechanically process an algorithm.

The first couple of types I’ve seen in GCSE questions (near the end of the higher papers!).  Firstly we have the type where you’ve been using the quadratic equation…


Next, you are given the simplification of an algebraic fraction and you need to work out what the original algebraic fraction looked like (works when the denominator is the difference of two squares type)…

One issue I find with students is an understanding of what the solutions of a quadratic equation actually tell you and the use of the words ‘roots’ and ‘factors’ in this context.  The next few questions try to scratch the surface of this.  Firstly a straight forward question where you have the roots – clearly there are a different number of possible equations but all should be multiples of one in particular…

I’ve done this with a cubic as well to also test multiplication of multiple brackets.

Next you are given the graph of the function and different information.  Firstly the roots…

Then move on to being given the coordinate of the minimum point to really stretch the understanding of completing the square…

Finally simultaneous equations where you are solving a linear and non-linear equation but this time you have the coordinates of intersection and are looking at generating the original equations…

You can download the whole set of questions below – there are 2 of each type.

Quadratic Questions (PDF version)

Quadratic Questions (Word version – editable)

If you use them let me know and please give me some feedback on any issues that arose.

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Mr Chadburn