Lesson Plan 3d Trig f676

Lesson Planning Sheet Title: 3D Trigonometry Learning Objectives: By the end of the lesson: All students should be able to calculate a length in a 3D shape using 2D representations of right angled triangles Most students should be able to calculate an angle in a 3D shape using 2D representations of right angled triangles.  Some students should be able to calculate a combination of length and angle in a 3D shape using 2D representations of right angled triangles Key words: Trigonometry, Sine, Cosine, Tangent, Right Angled Triangle, 2D Representation, Pythagoras’ Theorem  

Learning Activities

Resources:

Starter/Introduction Recap the three trigonometric ratios and Pythagoras’ Theorem by matching the ratio and equations to the respective right angled triangle. Students should work in pairs to discuss which equation matches the shape. AfL – Discussion is paramount to ensure the students are able to correctly label the sides and recognise which ratio to use.

Calculators, Mini-whiteboards Worksheets Projector

Development Work through the first example involving the cube. Emphasise the need to represent the 3D object two dimensionally using right angled triangles. Vertex notation is key to identifying the paths involved. AfL – Pose questions such as which paths would take us from one vertex to another an includes an right angle? Students should work in pairs for the second example if sufficient understanding is shown, if not, teacher to work through the example whilst posing more questions. Students attempt the first question on the third slide in pairs, presenting their working out and answers on mini-whiteboards. AfL – Discussion about how break the problem down into individual triangles is key. with reference to the student’s discussions. Pose the question on the third slide to consolidate understanding. When ready students should work individually through the questions on the sheet. ing and extending where necessary. Plenary The plenary is intended to consolidate and extend the differentiated learning objective by assessing whether the students can break down the square based pyramids themselves. Part A should be accessible for all students, whereas, Part B should be completed by the most able. Students to work in pairs to attempt the problem on mini whiteboards so that teacher assessment can be made. Differentiation More able:  The strategy of determining the necessary path in order to represent the 3D shape 2 dimensionally should be left open for them to determine.  Students should work on problems involving non cuboid shapes. Less Able  Students may need to have the path of the angles provided and focus on first knowing which trigonometric ratio to use.  Calculating only lengths in the 3D shapes maybe enough for the first lesson so that to progress in the second they move on to calculating lengths and angles.