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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.

April 15, 2018

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]

April 11, 2018

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis. Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]

March 23, 2018

Students learn how to generate and describe arithmetic and geometric sequences on a position-to-term basis. Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]

## 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