Last week i read a blog post on pondering planning about teaching corresponding angles. The post is here i an highly recommend that you read it.
It really made me think about other topics where maybe i haven’t spent the time really delving into the fundamentals. One of the topics that came to mind was Pythagoras. In the same way that the author felt frustrated that students drop marks on corresponding angles how often do our students drop marks when finding a shorter side of a right angled triangle? So often our students just want to square and add the sides together regardless of what those sides represent. It made me question do i spend enough time getting to grips with the hypotenuse?
When i have taught Pythagoras i have always dedicated a part of my lesson to students labelling triangles and switching orientations and getting them to say which part is C but is this really enough? If my students really understood the concept of a hypotenuse would they be able to understand and apply Pythagoras better.
With all of this in mind i decided to plan a full lesson on the hypotenuse and getting to grips with what that is.
I decided to start with an adaptation of a frame model:
I want my students to understand what the hypotenuse is and that it only applies to right angled triangles so i thought this would be a good starting point.
From there i decided to go into labelling right angled triangles that did not have values assigned to their sides but letters. This is to see if they understand that the hypotenuse can also be identified due to it being opposite the right angle. After a few quick questions on whiteboards i took some inspiration from some question i had seen i decided to create a worksheet dedicated to identifying the hypotenuse:
You will notice how i move away from using actual right angled triangles into just their lengths. Again I wanted to be certain that my students understood that the hypotenuse is always the longest side of a right angled triangle.
Now that there is some grounding on the hypotenuse i introduced Pythagoras’ theorem. I wanted the students to understand why being able to identify the hypotenuse was important. However, this lesson does not look at finding a length of a hypotenuse, instead i decided to look at Pythagorean triples.
This question once again relies on my students knowing that the hypotenuse is the longest side of the right angled triangle. They have to use this knowledge and Pythagoras’ theorem to decide if this triangle does indeed create a triple.
Once a discussion has taken place, and modelling if needed, students can go into embed these skills by looking at more triples:
Reading the blog on corresponding angles and now planning a lesson on the hypotenuse has certainly made me think. I will be making sure in the future that i think carefully about key concepts and if more time needs to be dedicated to them.
If you would like to use any of these resources please feel free to do so.
They are all below: