Application of DOLACEE and ILLIPS

Tang Kam MingT.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 PlanDate Topic Content objectives Language

objectivesProcess Strategies used Resources

17/5/07

3-D Trigonometric 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

A B

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

A B

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

Thank You!