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 mini-whiteboards. A nice way to differentiate this is to have the less able student do the writing. I check to see whether they can correctly label the sides as this helps to know whether to use Sine, Cosine or Tangent.
When solving 3D problems involving trigonometry, I demonstrate how to identify the right-angled triangle containing the unknown side or angle and sketch it out separately. If there is not enough information given about this triangle, we look for further clues in another triangle involving the same line or angle. Check out the video below for a quick demonstration.
To check the student’s understanding and progress we work through some examples from the Interactive Excel File on mini-whiteboards.
Students are asked to sketch out the necessary right-angled triangles needed to find the length FB and angle FBG. Without explaining how, I ask them to calculate the length FB and show me their working on mini-whiteboards. It is interesting that a couple of students try to apply the Cosine Rule to triangle FBG. We feedback how to use Pythagoras’ Theorem to address the misconceptions.
Next, I ask students to use this new information to calculate angle FBG. Some struggle to use the correct ratio but all students attempt to solve it as a right-angled triangle using either Sine, Cosine or Tangent.
I use the solving 3D problems using trigonometry Interactive Excel File to pose a different, but similar question for the class to attempt again on mini-whiteboards. All students sketch the two relevant right-angled triangles. Some continue to struggle calculating the angle using the correct trigonometric ratio but all students correctly calculate the length FB using Pythagroas’ Theorem.
The plenary challenges the class to identify the necessary right-angled triangles independently. I provide a handout of the shape to some students so they can annotate the drawing. After a couple of minutes of attempting the problem independently we stop the lesson to discuss different approaches. This provides a starting point for some students while reassuring others. The plenary problem normally takes between 10 to 12 minutes. To end the lesson, I ask a willing student to demonstrate their working at the front of the class to their peers. We address any misconceptions as they arise.
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]
Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]