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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!
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