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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.

January 13, 2019

When calculating instantaneous rates of change students need to visualise the properties of the gradient for a straight line graph. I use the starter activity to see if they can match four graphs with their corresponding equations. The only clue is the direction and steepness of the red lines in relation to the blue line […]

January 4, 2019

Fractions, decimals and percentages are ways of showing a proportion of something. Any fraction can be written as a decimal, and any decimal can be written as a percentage. In this blog I discuss how to use the place value table and equivalent fractions to illustrate how fractions, decimals and percentages are connected. You can […]

October 26, 2018

In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. 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