I was introducing how to expand single bracket to a class this week and it got me thinking. I have taught this hundreds of times and in many different ways but what is the best way? Recently I have used an area model to demonstrate. The examples I might use are:
I really like this method as it shows very clearly why 12(x + 1) = 12x + 12 and leads nicely into using a grid for expanding brackets.
So why did I want to change to a different method?
Whilst exploring Open Middle I came across this problem.
I then thought about exploring expanding brackets using the distributive property of numbers. I tried to think about how I could get my pupils to play around with some numbers and consider how to expand brackets. The trouble was that I did it in a bit of a hurry and this is what I came up with:
To start with it worked really well. There was good discussion around the room and they came up with two things:
What I had failed to include was the link to brackets. We then discussed the link as a whole class and then looked at the relationship to algebra. What I wonder is how to create a better task so that the pupils investigate the relationship rather than me show them. I have had a few thoughts and will show them below.
- change the questions to include the brackets
- include the opportunity for pupils to create their own to see if they understand the rule
- make the link to algebra within the original set of problems
I would really appreciate some feedback so that I can create a better task for pupils the next time I am introducing expanding single brackets.