Application of DOLACEE and ILLIPS Tang Kam Ming T.W.G.Hs. Kap Yan Directors’ College

Contents Lesson Plan The Process Design philosophy

Subject : Mathematics Level: S4 Topic: Trigonometry Focus: Intersection of Straight lines in 3D

Lesson Plan DateTopicContent objectivesLanguage objectives ProcessStrategies usedResources 17/5/ 07 3-D Trigonome tric Problems 1. Understand the angle between two intersecting straight lines; 2. Students learn to deconstruct a 3D problem into a 2D problem. Students can - consolidate the concepts of “plane”, “intersecting lines”, through speaking and writing A. Teacher introduces key words: “plane” and “intersect” (2 min) B. Teacher introduces the definition of angle between two straight lines (3 min). Remind students the angles could be found by solving the triangles formed by the 2 straight lines. C. Activity 1 Group work: angle between 2 straight lines lying on one face of model. (10 min) Activity 2(a) Teacher and students jointly attempt to find angle between 2 straight lines lying on two different faces of model. (5 min) Activity 2(b) Group work to find angle between 2 straight lines lying on two different faces of model. (10 min) (refer to notes for activities) D. Conclusion (A) & (B) Simpler tasks: more teacher- directed. (C) Teaching and Learning Cycle and Scaffolding concepts. Students work more independently for Act. 2(b) Models Worksheets

Content Objectives 1. Understand the angle between two intersecting straight lines; 2. Students learn to deconstruct a 3D problem into a 2D problem.

Language objectives Students can - consolidate the concepts of “plane”, “intersecting lines”, through speaking and writing.

Process Part A Teacher introduces key words: “plane” and “intersect”. Part B Teacher introduces the definition of angle between two straight lines in 3D. Teacher reminds students the angles could be found by solving the triangles formed by the 2 straight lines.

Process (cont’d) Part C. Activity 1 Group work: angle between 2 straight lines lying on same face of the model. Activity 2(a) Teacher and students jointly attempt to find angle between 2 straight lines lying on two different faces of model. Activity 2(b) Group work to find angle between 2 straight lines lying on two different faces of model.

Looking triangle: Activity One AB Looking for Triangle: Activity One Instruction for Student A: Step I : Please select two lines. The two lines are lying on the same plane (face) of the model. Line 1: Line 2: Tell Student B the above information. Do not let him/her read your writing. (e.g. I will give you two lines. Line 1 is BG, Line 2 is XG) Step II: Observe the work of B. Help Student B if he/she asks for help. Looking for Triangle - Activity One Instruction for Student B: Step I: Student A will tell you the information of two lines: Line 1: Line 2: Step II: Refer to the solid, what is the acute angle between the two straight lines? The required angle is ∠ (e.g. ∠ ABC) Draw the triangle here. Label the triangle clearly. Also measure the lengths of the 3 sides of the triangle. Step III: (For Step III, you may ask for help from A) Calculate the angle between the two lines. Show your work here.

Looking triangle: Activity Two AB Looking for Triangle: Activity Two Instructions for Student A: Step I: Student B will tell you the information of two lines: Line 1:, Line 2: Step II: Refer to the solid, what is the angle between the two straight lines? The required angle is ∠ (e.g. ∠ ABC) Draw the triangle here. Label the triangle clearly. Step III:(For Step III, you may ask for help from B) Measure/ calculate the lengths of the 3 sides of the triangle. Calculate the angle between the two lines. Show your work here. The answer for the required angle is. Looking for Triangle - Activity Two Instructions for Student B: Step I: Please select two lines according to the following requirements. (a) There must be a common point. (e.g. line AC and line CD, C is the common point) (b) The two lines are lying on two different planes(faces) of the model. Write down the lines here: Line 1:, Line 2: Tell Student A the above information. Do not let him/her read your writing. (e.g. I will give you two lines. Line 1 is BG, Line 2 is XG) Step II: Observe the work of A. Help Student A if he/she asks for help.

(A) & (B) Simpler tasks: more teacher-directed. (C) Teaching and Learning Cycle and Scaffolding concepts. Students work more independently for Act. 2(b)

Scaffolding Work Part A Part B Part C More Teacher Directed Student work more Independently

jointly constructing the genre Building the field Teaching—Learning Cycle developing control of the genre modelling and deconstructing the genre constructing the genre independently

jointly constructing the genre Building the field Teaching—Learning Cycle developing control of the genre modelling and deconstructing the genre constructing the genre independently Solving 3D problems

Teaching- Learning cycle This cycle proposes that any given series of lessons should move through four broad stages: building the field for the learning, modelling and deconstruction, joint construction and finally independent construction.

1. Building the field raise students’ awareness and interest in the topic establish what students already know about the topic establish the scope of the topic

2. Modelling and deconstruction A key element of this stage is preparing students to do the task that will be deconstructed.

3. Joint construction In this third broad stage, teacher and students jointly construct the work.

4. Independent Construction In this final stage, students are now ready to construct their own example of the focus task.

Making meaning with language Writing Speaking meaning Listening

Other considerations and Evaluation Prepare the students with group work Pre-requisite knowledge Language process – “speaking out” abstract concepts + checking of understanding Sense of Ownership

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