Coperative Learning

5

(ii) Prepare the worksheets.

*The no. of worksheets = The no. of

concepts

(iii) Highlight the worksheet no. according to
student’s capability.

(iv) Prepare one review quiz.

STEP 1 (i) Ask your students to be in their HG.
INTRODUCTIO (ii) Distribute each set of worksheets to

N students.
(5 minutes) (iii) Ask students to read over the worksheet

questions that have been highlight at
least twice and become familiar with it.
No discussion and no need for them to
memorize it.

STEP2 (i) Ask students to get into their EG. At this stage,
DEVELOPMENT (ii) Encourage students to discuss the best students with
similar concepts
(25 minutes) ways to teach particular concept to their meet together.
HG members. Hence, they become
student teachers who are interested to After they have
deliver content as many creative ways finish discussing,
as possible. lecturer can give
(iii) Lecturer can float around in the them solutions.
classroom, listening, assessing and
evaluating the preparation of the EG
members to teach their HG members.
(iv) Lecturer can help students to become
expert by providing additional
information, example and also
challenging them with open ended
questions that would allow students to
examine the concept from a more
comprehensive perspective.

STEP 3 (i) Once they have gained the expertise, Lecturer could float
CLOSURE/ asked them to return to their HG. around, observing
CONCLUSION the process.
(20 minutes) (ii) Students are asked to teach other
member in their HG.

(iii) Discourage students from reading the
matter from the paper rather they should
teach, explain, give example and ask
questions.

(iv) Every student is given the time and
opportunity to teach his/her portion to
his/her group members.

(v) Encourage others to ask questions for

47

Developing Independent Learning in Vibrant Environment
clarification.

STEP 4 (i) Students are given quiz to check how Can do this on next
EVALUATION/ well they have taught and learned from class.
each other and how much learning has
FEEDBACK taken place as a result of the jigsaw
lesson.

(ii) This can be done in variety of creative
ways too.

48

WORKSHEET LECTURERS’
WORKSHEET
Question 1

Find the solution set for the inequalities 2  4x  6  18 .
Solution 1
2  4x  6  18
8  4x  12
2  x  3

x : 2  x  3

Question 2
Find the solution set for the inequalities 3x 1  6  2x  5x  20 .
Solution 2

3x 1  6  2x  5x  20

3x 1 6  2x and 6  2x  5x  20

5x  5 -7x  14

x 1 x  2

x : 2  x  1

Question 3

Find the solution set for inequality 3x 2  2x  x 2  3x  3

Solution 3

3x2  2x  x2  3x  3

2x2  5x  3  0 1 3
2 x>3
2x  1 x  3  0

By using graph or number line or table method

Answer :  x : x   1  or x : x  3
2

Question 4

Find the solution set for inequality 3x 1  2.

x3

Solution 4

3x  1  2
x3

3x  1  2x  3  0

x3

x7 0
x3

By using graph or number line or table method

Interval / factor x ≤-7 -7 < x < 3

49

Developing Independent Learning in Vibrant Environment

(x + 7) ─ + +
(x-3) ─ ─ +

x7 0 + ─ +
x3

Answer : x  7 or x  3

Question 5

Find the solution set for inequality 3  2 .
x4 x1

Solution 5

32
x4 x1

3  2 0
x4 x1

3 x  1  2 x  4  0
 x  4 x  1

 x  x  5  1  0
4 x


By using graph or number line or table method

Interval / factor x ≤-5 -5 ≤ x < 1 1<x<4 x>4
+ +
(x + 5) -+ + +
- +
(x - 1) --

(x - 4) --

x7 0 -+ -+
x3

Answer : x : x  5 or 1  x  4

50

TOPIC : 2.0 EQUATIONS, INEQUALITIES AND ABSOLUTE VALUES

SUBTOPIC : 2.2 INEQUALITIES

LESSON : WORKSHEET

LEARNING OUTCOME : Students are able to
(a) Relate the properties of inequalities.

(b) Solve linear inequalities.
(c) Solve quadratic inequalities by algebraic or

graphical approach.
(d) Solve rational inequalities involving linear

expressions.

MATERIAL : Question 1 is for students Grade E or below
Question 2 is for students Grade D+ to D below
Question 3 is for students Grade C to C+
Question 4 is for students Grade B- to B+
Question 5 is for students Grade A and A-

DURATION : 1 HOUR

STEP 1 INSTRUCTION
(5 minutes)
Get into your home-group and review the
questions.(Worksheet 1) Each person takes one (1) question.

STEP 2 Get into your expert group and discuss the best way to solve

(20 minutes) the question.

STEP 3 Get back to your home group and ‘teach’ the members of

(25 minutes) your home-group how to solve the problem.

51

Developing Independent Learning in Vibrant Environment

WORKSHEET STUDENTS’
Question 1 WORKSHEET
Find the solution set for the inequalities 2  4x  6  18 .
Solution 1

Question 2
Find the solution set for the inequalities 3x 1  6  2x  5x  20 .
Solution 2

Question 3
Find the solution set for inequality 3x 2  2x  x 2  3x  3
Solution 3

Question 4
Find the solution set for inequality 3x  1  2 .

x3

Solution 4

Question 5

52

Find the solution set for inequality 3  2 .
x  4 x 1

Solution 5

5.4 THE LESSON PLAN USING COOPERATIVE LEARNING APPROACH : LT

TOPIC : 4.0 MATRICES AND SYSTEMS OF LINEAR EQUATIONS

SUBTOPIC : 4.4 System of Linear Equations with Three Variables

LESSON : WORKSHEET

LEARNING OUTCOME : Students are able to:
(a) write a system of linear equations in the form of
AX = B .
(b) find the unique solution to AX = B using
(i) Inverse Matrix
(ii) Elimination Method

MATERIAL : Question Sheets, Answer Sheets, Cooperative Group Role
Cards, Mind Map (prepared by the student)

DURATION : 1 HOUR

PHASES SUGGESTED SUGGESTED
INSTRUCTION/ACTIVITY COMMUNICATIO
PREPARATION
(A day or a Divide the students into their N
week before discussion group. Call for a (By facilitator/
class) discussion among teammates by
each discussion group. students)
Summarize the topic by using mind Elect a group
map. Each teammate must have the leader in each
mind map. group.
Make sure everyone in the group Set a date for the
understand every concept in the topic discussion.
discuss. Cooperative
learning done by
ACTIVITY DAY students in their
own groups with
or without lecturer.

INTRODUCTIO STEP 1 : SET UP ACTIVITY GROUP Group leaders
N help to arrange
a) Arrange the tables according to the tables.
(5 minutes) the number of groups involved. Group 1 go to
table 1, group 2
b) According to the list prepared,
allocate the students into their

53

Developing Independent Learning in Vibrant Environment

individual groups. Students will be go to table 2 and
placed in groups of three/four and so on.
seated around a table.
In each group, everyone is given
1 worksheet and 1 cooperative
group role card.
c) Each teammate is assign to one
role
Role 1 : Reader (Leader)
Role 2 : Recorder
Role 3 : Time keeper
Role 4 : Presenter
Role 5 : Errand monitor

d) To start the activities :
They need to place their mind
map or summary on the table for
references

Follow the instruction given by
lecturer/instruction sheet, and start
the activity.

STEP 2 First 20 minutes : Answer Lecturer facilitates
DEVELOPMEN Question 1 by moving from
Leader one group to
T (a) Read the question. Highlight the another group and
(40 minutes) ask question that
important key words. stimulate their
STEP 3 (b) Plan the working by asking critical thinking.
CLOSURE/ Example :
CONCLUSION suggestion from each teammate. “Can we use other
(5 Minutes) (c) Start writing the answer. approach to find
(d) Double check the answer by the answer?
Explain how. ”
referring to the lecturer. Lecturer can also
(e) After the lecturer check the monitor each
group so that each
answer, proceed teammate
with the next question. participates in the
Another 20 minutes : Answer discussion.
Question 2
(Repeat steps from the first
question.)
(a) If the students have a problem
solving question in the allocated
time, make sure they approach
the lecturer for guidance.
(b) If they finish early, they can
proceed answering the last
question.

Students are asked to state the
method used in each question and
explain the differences of each
method

54

STEP 4 Ask students to try to complete the

EVALUATION/ worksheet and submit their work for

FEEDBACK evaluation.

COOPERATIVE GROUP ROLE CARDS

LEADER RECORDER
 Makes sure that every voice is heard  Compiles group members’ ideas on

(all participate). collaborative A4 papers or writing
 Focuses work around the learning task pad.
 Writes on the board for the whole
or activities. class to see during the presentation
Examples : (if ask by the lecturer).
Examples :
 “Let’s hear from ____ next.”
 “That’s interesting, but let’s get back to our  “I think I heard you say________; is that
right?”
task.”
 “How would you like me to write this?”

TIME KEEPER PRESENTER

 Encourages the group to stay on task .  Presents the group’s finished work to
the class.
 Announces or alert the teammates
when time is halfway through and when  Answer question that are ask from
the audience.
time is nearly up.
Examples :
Examples :  “How would you like this to sound?”
 "We only have five minutes left. Let’s  “Do I need to explain _______ in

see if we can wrap up by then.” details?
 “Five minutes before times up, we need

to wrap up everything.”

ERRAND MONITOR

 Briefly leaves the group to get supplies
or to request help from the teacher
when group members agree that they
do not have the resources to solve the
problem.

Examples :
 “Do you think it’s time to ask the

teacher for help?
 “I’ll get an extra paper or writing pad

from the shelf.”

Role 1 : LEADER
(NAME) ______________________________________________

Role 2 : RECORDER

(NAME) ______________________________________________

Role 3 : TIME KEEPER

(NAME) ______________________________________________

Role 4 : PRESENTER

(NAME) ______________________________________________

55

Developing Independent Learning in Vibrant Environment

Role 5 : ERRAND MONITOR
(NAME) ______________________________________________

WORKSHEET (QUESTIONS) LECTURERS’
WORKSHEET

1. Solve the following system of linear equations by using inverse matrix .

+ 2 + 3 = 5

7 + + 6 = 3

− + 2 = 7

(20 MINUTES)

2. (a) Matrices A and B are given as follows:

2 1 3 4 5 2 
A  1 0 2 ,  -1
2 1  B   5 -7
3
 2 -1 -1 

Find AB and deduce A1 .

(b) A rice mill produces three grades of rice, namely A, B and C. The total profits
obtained from the sales of 2 kg of grade A rice, 1 kg of grade B rice and 3 kg
of grade C rice are RM24. The total profits obtained from the sales of 1kg of
grade A rice and 2 kg of grade C rice are RM11. The total profits obtained
from the sales of 3 kg of grade A rice, 2 kg of grade B rice and 1 kg of grade
C rice are RM31.

(i) If x, y and z represent the profits, in RM, per kg obtained from the sales of
grade A, grade B and grade C rice respectively, determine a system of
linear equations based on the information given.

(ii) Write down the system of linear equations in the form of a matrix equation
AX  B . Hence, find the values of x, y and z.
(20 MINUTES)

3. In a local football league, the prize money for a win is RM5000, a draw RM3000
and a loss RM1000. A team has played 12 matches and the total amount of
prize money won is RM40 000. The number of wins is equal to the sum of the
draws and losses.
If x represents the number of wins, y the number of draws and z the number of

losses, write the system of linear equations for the above information in the
matrix form AX  B.

(a) Use the Gauss-Jordon Elimination Method to solve the system of linear
equations.

(b) Hence, if the participation fee is RM2000 for each match, and for each win,
the fee is refunded. What is the net income of the team?
(20 MINUTES)

56

WORKSHEET (ANSWER)

1. =

1 2 3 5
[7 1 6] [ ] = [3]
0 −1 2 7

| | = 1 |−11 62| − 2 |70 62| + 3 |07 −11|
= (8) − 2(14) + 3(−7)

= −41

|−11 26| − |07 26| |70 −11| = 8 −7 9
= −|−21 23| |10 23| − |01 −21| [−14 2 15 ]
− |71 36| 12| ] 1 −13
[ |21 36| |71 −7

−1 = − 1 8 −7 9
41 [−14 2 15 ]
1 −13
−7

−1 1 8 −7 95 1 82 −2
41 [−14 2
= = − 1 15 ] [3] = − 41 [ 41 ] = [−1]
−7 −13 7 −123 3

= − , = − , =

2.

2 1 3 4 5 2 
a AB  1 2  -1
0  5 -7

3 2 1   2 -1 -1 

-8  5  6 10 - 7 - 3 4-1-3 
 4  0  4 502 2  0  2
15 - 14 - 1 6 - 2 - 1 
-12  10  2

3 0 0 
 0 3 0

0 0 3

57

Developing Independent Learning in Vibrant Environment

AB  3I

A1  1 B
3

1 4 5 2
3  -7 -1
  5 -1 -1 

 2

543 5 2
3 3 
3 

 - 7 - 1 
3 3 
 
 2 - 1 - 1 
3 3 
 3

b (i) x  Profit, in RM, obtained from the sale of 1kg of grade A rice.

y  Profit, in RM, obtained from the sale of 1kg of grade B rice.

z  Profit, in RM, obtained from the sale of 1kg of grade C rice.

2x  y  3z  24
x  2z  11
3x  2 y  z  31

2 1 3  x  24
0 2   11 
ii 1 2  y   

3 1  z  31

A X B

AX  B

X  A1B

543 5 2
3 3 
3  24 

X  - 7 - 1  11 
3 - 3  31 
  
 2 - 1 1 
3 3 
 3

32  55  62 
 3 3 

 77 31 
  40  3  3 

 16  11  31 
 3 3 
 

7 
 4

2 
 x  RM 7

y  RM 4

z  RM 2

3(a)

Let x - the number of wins
y - the number of draws
z - the number of losses

58

5000x  3000y 1000z  40000
5x  3y  z  40      (i)
x  y  z  12      (ii)
x  y  z  0      (iii)

AX  B

5 3 1  x   40
1 1 1 y   12 
1 1 1 z   0 

5 3 1 40 1 1 1 0   1 1 1 0 
1 1 12 R1  R3  1 1 12 *
1 1 R 2  (1) R1R 2 0 2 2 12

1 1 1 0  5 3 1 40 5 3 1 40

R*3  (5) R1  R 3  1 1 1 0  (1) R 2  1 1 1 0  R*1  (1) R 2  R1 
0 2 2 2 0 1 1 6 
12 R*2 
0 8 6 40
0 8 6 40

1 0 0 6  R*3  (8) R2  R3  1 0 0 6 R*3  ( 1) R 1 0 0 6
0 1 1 6  0 1 1  2 1 1 6 R*2  (1) R 3  R2
0 8 6  6  3  0 4

40 0 0  2  8 0 0 1

 1 0 0 6
0 1 0 2
4
0 0 1

x  6 , y  2 , z  4 ( 6 wins , 2 draws , 4 losses )

3(b) Participation fee = RM2000 x 12 = RM 24 000
Refund ( 1 win – RM2000 ) = RM2000 x 6 wins = RM12 000

After refund need to pay RM12 000 for participation fee.
Net income of the team = (RM5000 x 6)+(RM3000 x 2)+(RM1000 x 4) – RM12 000

= RM 28 000

59

Developing Independent Learning in Vibrant Environment

TOPIC : 4.0 MATRICES AND SYSTEMS OF LINEAR EQUATIONS

SUBTOPIC : 4.4 System of Linear Equations with Three Variables

LESSON : WORKSHEET

LEARNING OUTCOME : Students are able to:
(a) write a system of linear equations in the form of AX =
B.
(b) find the unique solution to AX = B using
(i) Inverse Matrix
(ii) Elimination Method

MATERIAL : Question Sheets, Answer Sheets, Cooperative Group Role
Cards, Mind Map (prepared by the student)

DURATION : 1 HOUR

INSTRUCTION TO THE STUDENT
(a) Read the question. Highlight the important key words.
(b) Plan the working by asking suggestion from each teammate.
(c) Start writing the answer.
(d) Double check the answer by referring to the lecturer.
(e) After the lecturer check the answer, proceed with the next question

COOPERATIVE GROUP ROLE CARDS

60

TIME KEEPER PRESENTER
 Presents the group’s finished work to
 Encourages the group to stay on task
. the class.
 Answer question that are ask from the
 Announces or alert the teammates
when time is halfway through and audience.
when time is nearly up. Examples :
 “How would you like this to sound?”
Examples :  “Do I need to explain _______ in
 "We only have five minutes left. Let’s
details?
see if we can wrap up by then.”
 “Five minutes before times up, we RECORDER
 Compiles group members’ ideas on
need to wrap up everything.”
collaborative A4 papers or writing
LEADER pad.
 Makes sure that every voice is heard  Writes on the board for the whole
class to see during the presentation (if
(all participate). ask by the lecturer).
 Focuses work around the learning Examples :

task or activities.  “I think I heard you say________; is that
Examples : right?”

 “Let’s hear from ____ next.”  “How would you like me to write this?”
 “That’s interesting, but let’s get back to

our task.”

ERRAND MONITOR

 Briefly leaves the group to get
supplies or to request help from the
teacher when group members agree
that they do not have the resources to
solve the problem.

Examples :
 “Do you think it’s time to ask the

teacher for help?
 “I’ll get an extra paper or writing pad

from the shelf.”

Role 1 : LEADER

(NAME) ______________________________________________

Role 2 : RECORDER

(NAME) ______________________________________________

Role 3 : TIME KEEPER

(NAME) ______________________________________________

Role 4 : PRESENTER

(NAME) ______________________________________________

Role 5 : ERRAND MONITOR

(NAME) ______________________________________________

61

Developing Independent Learning in Vibrant Environment

WORKSHEET (QUESTIONS)

1. Solve the following system of linear equations by using inverse matrix .

+ 2 + 3 = 5

7 + + 6 = 3

− + 2 = 7

(20 MINUTES)

2. (a) Matrices A and B are given as follows:

2 1 3 4 5 2 
A  1 0 2 ,  -1
2 1  B   5 -7
3
 2 -1 -1 

Find AB and deduce A1 .

(b) A rice mill produces three grades of rice, namely A, B and C. The total
profits obtained from the sales of 2 kg of grade A rice, 1 kg of grade B
rice and 3 kg of grade C rice are RM24. The total profits obtained from
the sales of 1kg of grade A rice and 2 kg of grade C rice are RM11.
The total profits obtained from the sales of 3 kg of grade A rice, 2 kg of
grade B rice and 1 kg of grade C rice are RM31.

(i) If x, y and z represent the profits, in RM, per kg obtained from the sales of
grade A, grade B and grade C rice respectively, determine a system of
linear equations based on the information given.

(ii) Write down the system of linear equations in the form of a matrix equation
AX  B . Hence, find the values of x, y and z.
(20 MINUTES)

3. In a local football league, the prize money for a win is RM5000, a draw RM3000
and a loss RM1000. A team has played 12 matches and the total amount of
prize money won is RM40 000. The number of wins is equal to the sum of the
draws and losses.
If x represents the number of wins, y the number of draws and z the number of

losses, write the system of linear equations for the above information in the
matrix form AX  B.

(a) Use the Gauss-Jordon Elimination Method to solve the system of linear
equations.

(b) Hence, if the participation fee is RM2000 for each match, and for each win,
the fee is refunded. What is the net income of the team?
(20 MINUTES)

62

REFERENCES
1. Akta Pendidikan 1996. Pendidikan (Peraturan Kurikulum Kebangsaan) 1997.

Kementerian Pendidikan Malaysia.
2. Peter F. Oliva, 1982. Developing the Curriculum. Boston: Little, Brown &

Company. p. 5
3. Pelan Operasi Kolej Matrikulasi Selangor (draf), 2010.
4. Jon Strickler (2008). What is a Center of Excellence

http://agileelements.wordpress.com/2008/10/29/what-is-a-center-of-
excellence/
5. Robert E. Slavin, (1990). Cooperative Learning: Theory Research and
Practice. :Allyn and Bacon.
6. Alice Macpherson, (2008). Cooperative Learning Group Activities for College
Courses. Kwantlen:Polytechnic university.
7. Ted Panitz’s web based book on cooperative learning
http://home.capecod.net/~tpanitz/ebook/contents.html
8. Program Matrikulasi
http://www.moe.gov.my/bmkpm/index.php/program-matrikulasi/45-maklumat-
umum/66-latar-belakang-bmkpm

63

Developing Independent Learning in Vibrant Environment

Appendix I (a)
An Example: How To set up academically Heterogeneous Home Teams

a) Based on the grades on Test 1, prepare a ranked student list as below. Form groups of

5.
(or alternate size is 4, or use 3’s if the students are good);
b) Four heterogeneous teams of about equal ability is formed (20/5=4). Each student is
allocated to Team A, Team B, Team C or Team D as shown in the last column.

Subject: Mathematics Science QS 015 Class: SM1K2T5

NO. NAME MATRIC TOV TEST 1
NO. GRADE HOME TEAM

GRADE

1 Student 1 BA A

2 Student 2 BA B

3 Student 3 B- A C

4 Student 4 B+ A D

5 Student 5 BA D

6 Student 6 A A- C

7 Student 7 B A- B

8 Student 8 B- A- A

9 Student 9 B- A- A

10 Student 10 B B+ B

11 Student 11 B- B+ C

12 Student 12 C+ B D

13 Student 13 C+ B D

14 Student 14 B- B- C

15 Student 15 C+ B- B

16 Student 16 D+ B- A

17 Student 17 D+ C+ A

18 Student 18 B C+ B

19 Student 19 C+ C C

20 Student 20 B C- D

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Appendix I (b)

a) Every team member is given a number identity as A1, A2 and so on. (Last column)

The teams are mixed ability learning groups. (A1 has higher learning achievement if

compares to A2, A3, A4 and A5).

Subject: Mathematics Science QS 015 Class: SM1K2T5

NO. NAME MATRIC TOV TEST 1 HOME TEAM
TEAM MEMBERS
NO. GRADE GRADE

1 Student 1 BA A A1

2 Student 8 B A- A A2

3 Student 13 B- A- A A3

4 Student 16 B B- A A4

5 Student 10 B C+ A A5

6 Student 3 B- A B B1

7 Student 18 C+ A- B B2

8 Student 15 C+ B- B B3

9 Student 11 B- B+ B B4

10 Student 19 B- C+ B B5

11 Student 4 C+ A C C1

12 Student 6 B A- C C2

13 Student 20 B+ B- C C3

14 Student 12 B B+ C C4

15 Student 7 B- C C C5

16 Student 5 D+ A D D1

17 Student 2 BA D D2

18 Student 9 AB D D3

19 Student 14 C+ B D D4

20 Student 17 D+ C- D A5

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Developing Independent Learning in Vibrant Environment
Appendix II

HOME TEAM GAME

COOPERATIVE LEARNING /INDEPENDENT LEARNING

A2 A3 B2 B3
A1 B1

Home Team A Home Team B

A4 A5 B4 B5

C2 C3 D2 D3
C1 D1

Home Team C Home Team D

C4 C5 D4 D5

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Appendix III:
Heterogeneous Home Teams break into Homogeneous Tournament Teams

TOURNAMENT BEGINS:

A1 A2

TABLE TABLE
D1 1 B1 D2 2 B2

A3 C2
C1

TABLE
D3 3 B3

A4 C3 A5

D4 TABLE B4 TABLE
4 D5 5 B5

C4
C5

See Lesson plan

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Developing Independent Learning in Vibrant Environment

NUMBER Appendix IV 4
CARDS 8
23 12
1 16

567

9 10 11

13 14 15

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Appendix V

SCORE

SHEET
TUTORIAL GROUP:…………………….. TOPIC:…………………

TOTAL SCORE SHEET (TGT)

TABLE Player A Player B Player C Player D Day’s Total Tournament
(TEAM) Points

1

2

3

4

5

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Developing Independent Learning in Vibrant Environment

DELIVER: Developing Independent
Learning in Vibrant Environment
Centre of Excellent in
Teaching

www.kms.matrik.edu.my

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