**Student-led inquiry**

**Daniel Walker **describes how the inquiry developed in his year 9 classroom:

"I used the new prompt today and it went really well with a class that have done *y *= m*x + *c but not simultaneous equations.It proved to be a really organic way of introducing the topic. Once the two equations were on the board, I gave pupils a minute or two to discuss what they might do with them. Some pupils used this a chance to describe gradient and intercept (and observe that gradient and intercept had been swapped) whilst others immediately realised that two lines would lead to an intersection, which all pupils set about finding on grids.

"Once the result (1, 1) had been verified, pupils picked their own values of a and b to investigate. Some stuck to the same format of a + b = 1 (although this wasn't discussed, I like to think they made a conscious decision to do this!), others used positive values for both a and b. All pupils realised that the *x*-coordinate is always 1 and a few spotted the fact that the *y*-coordinate is always a + b. A few pupils made mistakes that meant not all of their graphs agreed with this, but this gave them the motivation to re-check their work.

"With 15 minutes to go, I got pupils to feed back, taking a selection of their choices of equations and using Autograph to quickly show and verify their results on the projector. I put a table of their equations and coordinates of intersection on the board (so that all pupils could understand the findings of those who identified patterns). I spent the last 5 minutes showing them an algebraic proof of the result. The investigative element really motivated pupils and those who spotted all the patterns were excited by their discoveries. I'll definitely use this lesson to introduce this topic in the future. Probably the best Friday afternoon lesson I can remember!"