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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.

March 10, 2019

When calculating the volume of a pyramid we can substitute the values of the length, width and perpendicular height into the formula V = 1/3 lwh. In my experience this is often provided for the students with little explanation as to why a volume of a pyramid is exactly one third the volume of a […]

March 4, 2019

When teaching solving 3D problems using trigonometry we begin the lesson with a recap of Pythagoras’ Theorem and the three trigonometric ratios. We do this by matching the ratio and equations to the respective right-angled triangle. Students are encouraged to work in pairs and to show the diagrams as part of the working out on […]

January 29, 2019

When I teach rounding to a significant figure, I ask the class to discuss in pairs or small groups a definition for the word significant. It is a word that all the students have heard before but not all are able to define. After 2 or 3 minutes of conversation I ask the students to […]

## 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