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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.

August 22, 2019

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way. Mathematics Teaching and Learning Folder All teachers receive a folder […]

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

## LukeandJim says:

This is a mindboglingly weird activity. The fact that you’re using area to represent the product of two terms makes one feel that the situation ought to make some kind of mathematical sense, but rather than providing purpose or utility the situation seems to be there solely as a pretext for practising algebraic manipulation.

Out of what kind of situation might your area formula in two independent variables have arisen?? Why might it involve differently shaped rectangles?? How does it help to represent these different rectangles by identical rectangles??

I’ve written a GeoGebra file that compares rectangles 1 and 5. It provides a degree of purpose and intrigue, but not a lot… I will email it to you.

Regards

Luke&Jim