To start a lesson on factorising quadratics with my top set year 10 class I wanted to recap the learning of last lesson through an algebra investigation. My year 10 group are quite bright and respond well to a challenge. So I presented the rectangle shown below as asked them to investigate possible perimeters given the fixed area.
They were asked to work in pairs or small groups using a single mini-whiteboard. The only condition for their work was they had to agree on their workings and be able to explain each other's decisions.
As the groups worked together to factorise the area there were two prominent solutions.
Some decided to factor out the 8 so the dimensions became which produced a perimeter of. However, the majority of the class, based on their learning the previous lesson, chose to fully factorise the expression to to give the perimeter.
After a little encouragement all groups considered factorising with terms such as or 4. A short while later most of the groups had created the following perimeters.
I was impressed with their progress and ability to link together the various aspects of mathematics. A couple of the most able students decided to take this a little further by considering non integer factors and negative powers.
I was really pleased with the momentum this starter gave the lesson as it helped to recap prior learning, link to other aspects of maths and encourage group work.
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