In Higher maths, pupils have to be able to find the equation of altitudes, medians and perpendicular bisectors. Previously I have taught each different type of line over three different lessons then spending some time on mixed questions afterwards.
However, this term I have been trying to build in more interleaved practice into my lessons, where appropriate. So rather than teach my pupils about the three types of line separately, we tackled them altogether.
Here is my lesson:
It started with the pupils drawing a triangle and marking on an altitude, median and perpendicular bisector and annotating the diagram with the properties of each line.
Then I challenged the class to discuss in their groups how they could find the equation of an altitude, median and perpendicular bisector. As I listened in, many groups quickly figured out that to find the gradient of an altitude would first require finding the gradient of the perpendicular side. We then discussed each type of line, really focussing on the fact that to find the equation of a straight line you have to know the gradient and a point on the line.
I then gave the class this sheet to stick into their notes and then we worked through the three examples.
This sheet is available here.
After this the pupils were able to go straight to mixed up problems where they had to really think about each problem and use different techniques rather than completing a whole section on one type then another then another.
This has allowed the class to have more time on mixed practice which involves far more thinking and hopefully help when it comes to their final exam.