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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.

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

March 26, 2019

Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]

## 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