DAILY LESSON PLAN

Class 403Date 3 August 2013Time 11.05 – 12. 15Venue ClassAttendance

Topic / Theme: Lines and Planes in 3- Dimensions.

Learning Objectives:

Students will be taught to :Understand and use the concept of angle between lines and planes to solve problems.

Learning Outcomes:

Students should be able to :i. Identify normal to a given plane.ii. Determine the orthogonal projection of a line on a plane.iii. Draw and name the orthogonal projection of a line on a plane.iv. Determine the angle between a line and a plane.v. Solve problems involving the angle between a line and a plane.

Activities:

STEPS T&L ACTIVITIES FORMATIVE

EVALUATION NOTES

TEACHING AIDS

A. Opening Activities

1. Teacher enters to class on time.

2. Teacher greets and prepares the lesson.

3. Teacher prepares physically condition

of students in order to ready for joining

- Marker- Eraser- Book

and Pen

learning process.

a. Teacher checks the attendance list.

b. Teacher asks students to prepare

the tools which are used for

learning.

4. Teacher delivers the title of main

material which want to be explained

and writes on the white board.

5. Teacher delivers the learning

objectives.

6. Teacher motivates students.

B. Core Activities

1. Teacher reviews about materials in

meeting before uses software Cabri 3D

for

a. showing about line and plane.

b. showing some space geometry

object such as cube, cuboid, prism,

and pyramid by Cabri 3D.

Teacher : Students, I will show you about line and plane.

H G

E F

D C

A B

H G

E F

D C

A B

c. showing normal to plane.

d. showing orthogonal projection of

line.

Teacher : do you still remember about normal line?Students : (hopefully answer ) Yes..Teacher: what is a normal from point E to plane ABCD? who knows?One of students : EA.

Teacher : do you still remember about orthogonal projection of line?Students : (hopefully answer ) Yes..Teacher: what is a orthogonal projection of space diagonal HB to plane ABCD? who knows?

H G

E F

D C

A B

H G

E F

D C

A B

e. Showing the angle between a line

and plane based on the figure

before.

2. Teacher gives problem to students to

determine normal line, orthogonal

projection, and the angle size.

One of students : (answer by explaining) because the normal line is HD then the orthogonal projection is DB.

Teacher : from that figure, can you determine what is angle between line HB and plane ABCD?One of students : The angle is HBD.

The angle between the lines perpendicular to the line of intersection of two planes is the angle between the two planes.

Teacher : Please look at following figure.

Given that TABC is regular triangular pyramid. Point D at the middle of AC. The length of each edges is a cm. Determine the size of angle between TD and plane ABC.One of students:

i) Draw the line TD.

T

AB

CD

ii) Determine the centre point of plane ABC by finding intersection point medians.

iii) Determine the normal line.

Students : normal line is TSiv) Determine the orthogonal projection of

T

AB

CD

T

AB

CD

S

T

AB

CD

S

3. Teacher explain that would be held a

model named CRH (Course Review

Horray).

4. Teacher makes groups that consist of 2-

3 persons.

5. Teacher gives Horray Cards

(attachment 2) and explains the how to

use it.

line TD on the plane ABC.Students : the orthogonal projection is DS

v) Determine the the angle between TD and plane ABC.

Students : The angle is TDS

vi) Determine the size of angle Finding the length of TD Finding the length of DS Finding the size of angle TDS

Teacher : “Students, for enhancing your

understanding about algebraic operation of

roots and rationalizing, We will apply a model

named CRH (Course Review Horray).

Teacher : “ Before we start our activity, I give

this Horray Card and please write 1-9 randomly

in these nine fields.

Teacher : “Next, I will show a question in a

α

T

AB

CD

S

6. Teacher gives the explanation about the

rule.

7. Teacher start by giving a problem.(

attachment 3).

8. Teacher lets one of the students to solve

the problem in front of class,

slide, then all of you please do detail in group

for solve it in a piece of paper. After that I give

chance for one of you by rise your hand first.

And then, he/she come to in front of class for

writing the solution.

When he/she has finish the answer and it’s

correct, I will give you know, what number is it,

but when the answer is not correct yet, I want the

other one does it in front of class bravely. And

please circle the number when you have answer

correctly,

The group who is answer correctly in horizontal

or diagonal, can speak out “ HORRAY” loudly

and I give you reward. There is a big reward for

the group with the most collector HORRAY

reward.

And for the last, there is individual assessment in

this game.

9. When it is correct; teacher gives them

to know what number is it. But, if it is

not correct yet, teacher will continue to

the next number.

10. Steps in 6 and 8 are repeated until the

time is up for game in 10 minutes

Teacher gives quiz to be done by

themselves without sharing each

others. ( attachment 4).

C. Closing Activity

1. Students and teacher make the

conclusion together. Then, choose

some students for presenting it.

2. Students are given motivation to learn

again the material and always share

when there is any difficulties.

3. Do the reflection about the activity

which has done.

4. Teacher presents about the next

meeting.

5. Teacher closes the lesson punctually.

Language Focus: Malay, English

Pedagogy:Contextual √ Multiple Intelligent √ Inquiry -Discovery

(ID)√

Learning how to learn Mastery learning Self excess Thinking skill √ Future study Constructivism √

TechniqueGroup work Simulation Finding informationDiscussion Lecture Watching TVExperiment Reference Role playQuiz Taking note √ Explanation √ A visit cooperative learning Demonstration √Problem solving √ Teaching aids Teaching using

moduleBrain storm √ Information

communication technology (ICT)

Research

Exercise √ OHP machine Project

Values:Confident & independent

√ Kind & loving Honest

Rational Responsible √ Cooperative √Fair and impartial √ Hardworking & patient √ SystematicFlexible and open-minded

Community spirit Dare to try √

Moderate Patriotism ObjectiveRespect each other √ clean physical & mental Appreciating &

Thankful√

Courteous

Reflection:

Remarks:

Attachment 2

HORRAY CARDS

Group :

Member : 1. 2. 3.

Attachment 3

Problem :

1. Given a cube ABCD.EFGH with the length of edges are 4 cm. Determine the size of angle between line AC and plane BDG!

2. Given a model below. State :

a. Normal of line GD to the plane EJCD.

b. Orthogonal projection of line GD to the plane EJCD.

c. The angle between line GD and the plane EJCD

H G

E F

D C

A B

L

K

H I J

G

E F

3. Pyramid V.PQRS with the base PQRS is a square. The edges of base have 4 cm in length and UM = 5 cm. Determine the angle size between line

VQ and PQRS.

4. A pencil case in the shape of cuboid beside. What is the length of the longest pencil that can be placed in the pencil case?

V

P Q

S R

P Q

S R

T U

W V

5. Look at the following pyramid with its base is square.

Find the cosine of angle between TA and ABCD.

6. The figure shows cuboid. T and U are midpoints of QR and BC respectively. Calculate the angle between AT and ABCD.

T

8 cm

D C

6 cmA B

S R

D C T

P Q U

A B

7. The figure shows a prism. Q is a point on PR where QR = 4 cm. Given UT = 7 cm, TS = 11 cm and R = 6 cm, calculate the angle between line UQ

and PSRV.

8. The figure shows a prism. Calculate the length of the space diagonal HB.

9. Given cube ABCD.EFGH. Determine the size of angle between line AH and diagonal plane of BFHD.

P R

V S

U T

H G

E F

D C

A B

H G

E F

D C

A B

Attachment 4

Problem Solving :

1. Given a cube ABCD.EFGH with the length of edges are 4 cm. Determine the size of angle between line AC and plane BDG!

The way for determining the size of angle between line AC and plane BDG as follows.

i) Draw the line AC and plane BDG

ii) Find the normal line of AC to the plane BDG.

H G

E F

D C

A B

H G

E F

D C

A B

So the normal line is CP

iii) Fine the orthogonal projection of line AC to plane BDG.

The orthogonal line is OP

iv) Find the size of angle.

GC = 4 cm

GO =

2. Given a model below. State :

H G

E F

D C O

A B

C

A

GO

P

d. Normal of line GD to the plane EJCD.

e. Orthogonal projection of line GD to the plane EJCD.

f. The angle between line GD and the plane EJCD

3. Pyramid V.PQRS with the base PQRS is a square. The edges of base have 4 cm in length and UM = 5 cm. Determine the angle size between line

VQ and PQRS.

4. A pencil case in the shape of cuboid beside. What is the length of the longest pencil that can be placed in the pencil case?

L

K

H I J

G

E F

V

P Q

S R

5. Look at the following pyramid with its base is square.

Find the cosine of angle between TA and ABCD.

P Q

S R

T U

W V

6. The figure shows cuboid. T and U are midpoints of QR and BC respectively. Calculate the angle between AT and ABCD.

7. The figure shows a prism. Q is a point on PR where QR = 4 cm. Given UT = 7 cm, TS = 11 cm and R = 6 cm, calculate the angle between line UQ

and PSRV.

T

8 cm

D C

6 cmA B

S R

D C T

P Q U

A B

8. The figure shows a prism. Calculate the length of the space diagonal HB.

9. Given cube ABCD.EFGH. Determine the size of angle between line AH and diagonal plane of BFHD.

P R

V S

U T

H G

E F

D C

A B

H G

E F

D C

A B