After some initial practice on expanding double brackets, in the second part of the lesson I wanted to encourage the students to behave mathematically. I wanted them to conjecture, to try it out and to reflect on the outcome.
I came up with this really simple task.
I modeled the task, however, rather than model success, I made a point of modelling failure to give the students the confidence to begin the task.
I wrote (x+3)(x+8) and expanded it.
I then put on a bit of a pantomime act of "oooh how frustrating that I'm only 1x away from what I want! but guys - I'm quite close to getting what I want so it'd be silly of me to start from scratch when I am so close. What I'll do instead is try just changing one of my expressions and see where that gets me."
I then wrote (x+3)(x+6) and expanded it, highlighting that I'd just changed one expression.
The dramatics then returned "Oh this is even worse! Now I've not got enough x in my expanded expression. Well I better try again".
I didn't try again. I let the students get on with it having shown them that failure to arrive at 10x was okay because we were using failure to inform our future endeavours.
All students started straight away, some had spotted what they'd need to do to change my second attempt in order to get there. Some hadn't but were happy to just choose two expressions and go for it.
Most students managed to find several ways of making the statement true. Plenty of faces lit up as they put their hand up to ask me if there was a pattern. Other students' hands went up to ask if they could have subtractions inside their brackets so they could check if the pattern continued. Some students even asked about decimals inside their brackets.
Once students arrived at the idea that constants in the expressions needed to sum to 10 they were pushed to try it when one bracket had to contain (2x....).
I came out of this lesson absolutely buzzing at the quality of work the students had produced. The way they made predictions, tested them out, evaluated the outcome and changed their expressions accordingly.
I'll admit lacking confidence in delivering these types of tasks that push the students to behave more mathematically but I'm determined to continue trying them as I can see the benefits they bring.