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
Date
Topic
Content objectives
Language
objectives
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
Process
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
Strategies used
(A) & (B)
Simpler tasks:
more teacherdirected.
(C) Teaching
and Learning
Cycle and
Scaffolding
concepts.
Students work
more
independently
for Act. 2(b)
Resources
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
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.
B
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
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
.
B
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
Teaching—Learning Cycle
Building the field
constructing
the genre independently
developing control of
the genre
jointly constructing the
genre
modelling and
deconstructing the genre
Teaching—Learning Cycle
Building the field
constructing
the genre independently
developing control of
Solving
the 3D
genre
problems
jointly constructing the
genre
modelling and
deconstructing the genre
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
• Listening
meaning
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!