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Published by Coet Kms, 2019-11-29 03:19:34

Coperative Learning

COPERATIVE_LEARNING_MATH_

DELIVER: Developing Independent Learning in

Vibrant Environment

: : LECTURER’S GUIDE : :

COOPERATIVE LEARNING: LECTURER’S
GUIDE

Centre of Excellence in

Copyright CoET KMS 2015

Teaching



KOLEJ MATRIKULASI SELANGOR
KementerianPendidikan Malaysia,
MukimJugra,
42700 Banting,
Selangor DarulEhsan.

All rights reserved. No part of this publication may be reproduced or distributed in
any form or by any means, or stored in a database or retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying or otherwise,
without the prior written permission of the publisher.

Copyright © 2015 by KolejMatrikulasi Selangor
Published 2015

ISBN (______________)
Introduction to Case Based Learning

Printed in Malaysia
(printing company)

"Education in Malaysia is an on-going effort
towards further developing the potential of
individuals in a holistic and integrated manner, so
as to produce individuals who are intellectually,
spiritually, emotionally and physically balanced
and harmonic, based on a firm belief in and
devotion to God. Such an effort is designed to
produce Malaysian citizens who are knowledgeable
and competent, who possess high moral standards
and who are responsible and capable of achieving
high level of personal well-being as well as being
able to contribute to the harmony and betterment
of the family, the society and the nation at large."

“ KMS
sebagai Penjana Unggul pelajar

Bumiputera berkualiti ke
Institusi Pengajian Tinggi dalam

bidang sains, teknologi dan
professional menjelang tahun

2020 ”

“ Membangunkan potensi
pelajar bumiputera dalam
bidang sains, teknologi dan
professional melalui pendidikan
pra-universiti yang berkualiti
untuk melahirkan modal insan

yang cemerlang ”

Index Page
Contributors iv
Preface v
Foreword vi
1.0 Introduction of Teaching Module 1

2.0 Module Objectives 2
2.1 For the Lecturers
2.2 For the Students 3
4
3.0 Teaching Module with Cooperative Learning : 8
3.1 Cooperative Learning and Independent Learners
3.2 To Get Started with the Teaching Module 10
3.3 Guidelines for Preparing a Cooperative Learning Lesson 12
13
4.0 Types of Cooperative Learning : 15
4.1 Team-Games-Tournament (TGT)
17
4.2 Student Teams-Achievement Divisions (STAD) 30
35
4.3 Jigsaw 41
4.4 Learning Together
51
5.0 Lesson plans
5.1 Team-Games-Tournament (TGT) I–V

5.2 Student Teams-Achievement Divisions (STAD)

5.3 Jigsaw
5.4 Learning Together

6.0 References

Appendix

iii

CONTRIBUTORS

Advisor : Dr Hjh Rosnah Selamat
Editorial Adviser (1) : Tuan Haji Mustaffar Musa, K.M.N (until October 2015)
Editorial Adviser (2) : Encik Mohamed Salleh Ahmad
and Proof Reader : Encik Hussain Hitam (until 16 July 2014)
Editorial Boards : Cik Turasima Marjuki
Co-ordinator : En Mohd Rizam Ahmad

Chief Editor : Coordinators of Modules
Editors Raja Suzita binti Raja Suleiman
Writers Tan Kim Leng
: Coordinator of Teams-Games-Tournament (TGT)
Tan Kim Leng
: Coordinator of Student Teams-Achievement Divisions (STAD)
Norazam Samsuddin
: Coordinator of Jigsaw
Suriati binti Abu Bakar
: Coordinator of Learning Together (LT)
Aznidar binti Abdul Aziz

: Puan Rosmawarni Sutrisno

: Pn Rosmawarni Sutrisno
: Cik Loke Lay Beng
: Puan Norazam Samsuddin

: Abidah Nor Baiti Mahmood : Noorul Emma Mohd Zohari

: Ahmad Khairi Paimin : Norazam Samsudin

: Ahmad Shuib Abdul Fatah : Noriah Jusoh

: Aishah Abd Samad : Norshahida Idris

: Anita Mohamed Adnan : Nur Ashikin Ari

: Aniza Mustap : Nur Fatin Nabihah binti Ismail

: Azlinda Maizan : Raja Suzita Raja Suleiman

: Aznidar Abdul Aziz : Rohani Ishak

: Farihah Ahmad : Rosmawarni Sutrisno

: Hamimah Ibrahim : Rosna Nordin

: Kean Kim Leong : Rushidah Ibrahim

: Khalijah Sulaiman : Shamihah Ahmad

: Lizawati Nayan : Suriati Abu Bakar

: Loke Lay Beng : Syed Azrinizal Syed Md

: Mashitah Masharuddin Damhuri

: Muhammad Anwar Hj Abd Karim : Tan Chiew Chi

: Muha Muhd Fazdhly Abd Muttalib : Tan Kim Leng

: Noorul Emma Mohd Zohari : Umar Zakir bin Khairuddin
: Norazam Samsudin : Widad binti Ahmad Ridzuan
: Muhammad Azzizuddin Abdullah
: Muhd Fazdhly Abd Muttalib : Zainun binti Fadzil @ Abd
Hadi

iv

v

PREFACE

Kolej Matrikulasi Selangor (KMS) has been entrusted by the Matriculation Division,
Ministry of Education Malaysia (BMKPM) as a Centre of Excellence in Teaching (CoET)
since its official opening in 2010. In relation to this, a few official committees have been
appointed to be responsible for making KMS a centre of excellence in teaching that develop
independent learning among students. As the Centre of Excellence in Teaching (CoET),
KMS further strides to produce many excellent lecturers in teaching and learning and
developing autonomous learners.

To realise this, several initiatives have been designed and implemented to strengthen
the competence of lecturers on an on-going basis. Among the initiatives is to provide a
reference source package "DELIVER: Lecturer’s Guide" that includes a teaching standard, a
perspective on self-study, guide to the implementation of professional learning community
(PLC) as well as the implementation of teaching and learning strategy that aim to develop
self-directed attitude among learners.

The name DELIVER, acronym for Developing Independent Learning in Vibrant
Environment, was chosen to reflect the way lecturers should implement the teaching and
learning processes thorough various strategies and among those strategies are active
teaching and active learning, cooperative learning, case based study, mobile learning,
integration of higher order thinking skills (HOTs) and science process skills. It is hope that
lecturers will get better insights about various approaches to teaching and learning so as to
promote independent learning in classrooms.

Publishing "DELIVER: Lecturer’s Guide" is also expected to help implement
workplace training and further foster a culture of PLC in accordance with the wishes of KMS
Education Development Plan, MECC (2013-2025). Hopefully this initiative can be utilized by
all citizens and residents, particularly at KMS, as well as lecturers form other matriculation
colleges.

Hj Mustafar Musa
Director

Kolej Matrikulasi Selangor
Kementerian Pendidikan Malaysia

vi

FOREWORD
As the centre of excellence in teaching (CoET) for matriculation program, Kolej Matrikualsi
Selangor has developed several learning modules to be used as a guide for lecturers in
matriculation college in hopes to help lecturers to implement various teaching techniques. In
conjunction with the effort, the computer science unit of Kolej Matrikulasi Selangor was given
the responsibility to develop and explore a method of learning through case studies. Hence,
the development in preparing the module is driven through strategic planning which was
designed systematically. As a result, a proper case based learning module is produced as a
guide in implementing learning techniques through case studies. This module consists of an
introduction up to the post-implementation of the method of learning using case studies. The
module is designed so that it can be adapted to a variety of different topics. Through the use
of this module, the lecturers are expected to understand the purpose of the case study.
Thus, lecturers are expected to adapt and use the case study method by the relevance of
the respective topics. Our hope is that this module can be the beginning of a broader
exploration in learning through case studies in matriculation program.

Chief Editor

vii



Developing Independent Learning in Vibrant Environment

1.0 INTRODUCTION OF THE TEACHING MODULE
An Effort Towards The Centre of Excellence In Teaching (CoET)”

Jon Strickler(2008) defined CoE as “Center of Excellence (CoE)” and, at the
most basic level should ‘consist of a team of people that promotes
collaboration using best practices around a specific focus area to drive
business results’. CoEs should serve five basic needs:
 Support: For their area of focus, CoE’s should offer support to the

business lines. This may be through services needed, or providing
subject matter experts.

 Guidance: Standards, methodologies, tools and knowledge
repositories are typical approaches to filling this need.

 Shared Learning: Training and certifications, skill assessments, team
building and formalized roles are all ways to encourage shared
learning.

 Measurements: CoEs should be able to demonstrate they are
delivering the valued results that justified their creation through the use
of output metrics.

 Governance: Allocating limited resources (money, people, etc.) across
all their possible use is an important function of CoEs. They should
ensure organizations invest in the most valuable projects and create
economies of scale for their service offering. In addition, coordination
across other corporate interests is needed to enable the CoE to deliver
values.

The lecturers in KMS are expected to teach in creative and innovative ways
that enable students to learn science and mathematics concepts while
acquiring process skills, positive attitudes and values, and problem solving
skills.

The Teaching Module with Cooperative Learning is a guide as the
individual lecturer’s manual, with a compilation of cooperative learning
activities suitable for use in teaching all courses in Matriculation level and may

8

be used to supplement a more traditional tutorial class . For each type of
cooperative learning activity, several lesson plans for different subtopics to
carry out the suitable cooperative learning activities are included.

2.0 MODULE OBJECTIVES

2.1 For the Lecturers
After using this module, the lecturers would be able to :
i. define Cooperative Learning and the essential components that turn a
group activity into a Cooperative Learning experience.
ii. define steps for developing a Cooperative Learning activity.
iii. know how to effectively monitor group work.
iv. develop ways to cope with issues that may arise during Cooperative
Learning activities in the classrooms.
v. use this module as a teaching aid during the teaching and learning
process.
vi. enhance student motivation for learning.
vii. promote ongoing formative assessment of student learning.

2.2 For the Students
After using this module, the students would be able to :
i. learn from each other.
ii. apply basic skills in learning.
iii. improve their preparation in summative assessment.
iv. involve themselves in self-directed learning.
v. reinforce their understanding through systematical practice.
vi. be more confident in learning.
vii. promote deeper understanding and ownership of content.

9

Developing Independent Learning in Vibrant Environment

3.0 TEACHING MODULE WITH COOPERATIVE LEARNING

3.1 Cooperative Learning and Independent Learners
Cooperative Learning is especially beneficial in Mathematics courses
(Davidson 1990). Many of the activities, discussions, and activities in the
Teaching Module with Cooperative Learning involve pedagogical
approaches that use the basics of cooperative learning. Cooperative learning
incorporates respect for students of all backgrounds, and it stresses that all
students can be successful academically.
Cooperative Learning involves building activities into the class that allow
students to examine, analyze, evaluate, and apply course-related concepts in
small groups. Then, Students construct knowledge by thinking and giving
explanations about what they are learning independently with tutors or without
tutors as the facilitators.

3.1.1 Five basic elements that make cooperative learning work.
Research has shown that in order for cooperative learning to be effective and
promote independent learners, certain components must be promoted and
structured into the learning activity. The two most important components are
positive group interdependence and individual accountability. Furthermore, In
order to help students work successfully in groups, the instructor should also
find ways to enable students to develop interpersonal and small group skills
and allow time for group processing or reflection.
Cooperative learning is not simply a synonym for students working in groups.
A learning exercise only qualifies as cooperative learning to the extent that the
five listed elements below are present.

a. With positive interdependence
Students feel that they truly need and depend on one another to complete the
task at hand. The students feel they are linked together and are concerned
with one another’s success. All of the students must see that by helping the
other members of the group to achieve goals, they help themselves.

10

b. Individual accountability
It means that students are ultimately held responsible for their own learning
and for their contributions to the group process. This equality encourages a
socially stable and emotionally safe working environment. To mandate this
independent accountability, instructors must build some individual
participation and objectives into the activity (Johnson, Johnson, & Holubec,
1994).

c. Face-to-face promotive interaction.
Although some of the group work may be parceled out and done individually,
some must be done interactively, with group members providing one another
with feedback, challenging reasoning and conclusions, and perhaps most
importantly, teaching and encouraging one another.

d. Appropriate use of collaborative skills.
Students are encouraged and helped to develop and practice trust-building,
leadership, decision-making, communication, and conflict management skills.

e. Group processing/Reflection.
Team members set group goals, periodically assess what they are doing well
as a team, and identify changes they will make to function more effectively in
the future.

3.2 To Get Started with the Teaching Module

The information in this section is intended to help instructors get started with
this teaching module. For any of the activities described here, the tutor should
keep in mind some general “good practices.” Each activity in the lesson plan
should have a beginning (Introduction), a middle (Development), and an
end (Closure). To begin, the tutor may set the stage perhaps telling the
students what material is to be covered during the class period or doing a
demonstration. The students then continue with the activity planned for the
day. At the end of class, the instructor facilitates a closure activity. This
closure activity should review the goals accomplished during the class. This
structure of setting the stage, doing the activity, and coming to closure should
be applied to every class period.

11

Developing Independent Learning in Vibrant Environment

The instructor should also vary the types of teaching activities that are used.
Learning effectiveness is lost if the students are doing only worksheets or only
small group discussions in solely Cooperative learning activities.
3.2.1 Forming Groups
Groups are the core of cooperative learning. Group members depend on
each other to achieve objectives and improve their interpersonal skills. The
group is the framework that allows easy transition into teaching and learning
techniques such as think-pair-share, jigsaw, laboratory work, and group
discussions.
Instructors should form teams rather than permitting students to choose their
own teammates. When students self-select into teams, the best students tend
to cluster, leaving the weak ones to shift for themselves, and friends cluster,
leaving some students out of groups and excluding others from cliques within
groups.

The instructors should try to make the teams heterogeneous in ability level
[See Appendix I (a & b): ‘An Example: How to form heterogeneous study
groups’]. The unfairness of forming a group with only weak students is
obvious, but groups with only strong students are equally undesirable. The
members of such teams are likely to divide up the homework and
communicate only cursorily with one another, avoiding the interactions that
lead to most of the proven benefits of cooperative learning.

In heterogeneous groups, the weaker students gain from seeing how better
students approach problems, and the stronger students gain a deeper
understanding of the subject by teaching it to others.
3.2.2 Group Size
There are many factors that affect the optimal size of the groups. One factor is
the level of interpersonal skills used effectively by the students. A small group,
2-3 students, has few interpersonal interactions and is better for students who
are beginning to build their skills. Large groups, those of 7-8 students, have
many interactions and therefore do not work well until the students have built

12

their skill to this level. Another factor is the time available; the less time
available the smaller the group should be.
Groups of four seem to be optimal for work that needs a variety of personal
resources without overburdening students who have trouble with interpersonal
skills. The ideal size for cooperative learning groups according to most
experts in the field is four learners per group.

3.2.3 Assigning Students to Groups

The compositions of groups can be determined in any number of ways. A
random assignment is most common for short-term groups. There are three
basic types of Cooperative learning groups can be assigned by the intention
of the shared learning goal or the duration of the learning process. For an
instant, the length of time that a group stays together depends on the activity
at hand. The group should stay together to finish a project.

(i) Base or Home Groups

Base or Home groups are long-term cooperative learning groups with
stable membership. Learners are chosen for home groups in a manner that
will guarantee a good mix of academic levels in the group. These groups are
set up so that members provide upport to each other and hence all can
succeed academically. For example, they may pick up handouts for each
other if one of the group members is absent, and they will coach each other to
prepare for individual tests. The use of home groups tends to personalize the
classroom, improve attendance and also improve the quality and quantity of
learning. If you have large numbers of learners in your classes, you should
consider using home groups.

Home groups should be set up so that they can remain together for at least a
term and longer if possible. The more learners you have in a class and the
more complex the subject matter, the more important it is to have home
groups organized. The members should be compatible and supportive.

(ii) Formal Cooperative Learning Groups

These groups may last from several minutes to several class sessions to
complete a specific task or assignment (such as doing a set of problems,
completing a unit of work, writing a report, conducting an experiment, or

13

Developing Independent Learning in Vibrant Environment

reading and comprehending a story, play, chapter or book). The members are
carefully chosen for heterogeneity to maximize learning and minimize ‘group
think’.

(iii) Informal Cooperative Learning Groups
These groups are temporary, ad hoc groups that last for a few minutes,
one discussion or class period. The members are often chosen randomly
and will rotate on a regular basis. Their purposes are to focus learner
attention on the material to be learned, create an expectation set and mood
conducive to learning, as well as help organize in advance the material to be
covered in a class session. They may be used at any time but they are
especially useful during a lecture or direct reading. The length of time that
most college learners can attend to a lecture before they begin to drift away is
around 20 to 25 minutes. These groups help break up the lecture and allow
learners to process the content as they take part in class.

Bookend Process: By breaking up the tutorial session into several mini-
sessions and having learners process the material in cooperative learning
groups, you do decrease the amount of tutorial time, but you will enhance
what is learned and build relationships among the learners in your class.
When we are instructing we need to remember all the different learning styles
and not going to either extreme and completely eliminate lecture or to give up
on group work.

3.2.4 Assign Roles: Small Group Skills

The heart of the guide is on how to develop Small Group Skills among
students and Implement Student Learning. By using many examples in the
Cooperative Learning Teaching Module, the active learning approach is made
accessible for beginning lecturers, and the experienced lecturers find new
teaching ideas and learn more about module.

In order for cooperative groups to work well, it is important for group members
to develop the skills necessary for working together successfully. It is
problematic for lecturers to assume that “This is a college so I don’t have to
worry about student behavior.” Students still need assistance in learning how

14

to be good group citizens. They need to be aware of the importance of being
good listeners and efficient team members.

One way to teach students about appropriate group behavior is through
assigning roles. Roles may be rotated for different activities and can be
dropped all together if you choose as the semester proceeds. Some important
group job assignments include:
 Task leader :
a task leader starts the group discussion and keeps the discussion moving
toward the group objectives.
 Time-keeper :
a student who makes sure that small tasks are not taking too long and
reminds other group members of the time remaining.
 Recorder :
a student who keeps minutes of the group meeting or produces a written
version of the outcomes of the group discussion.
 Reader :
a student who verbalizes any written information given to the group.
 Materials manager :
a student who makes sure each group member has any materials necessary,
and that the group receives any materials from the instructor.
 Praiser :
a student who gives positive feedback to group members sharing good ideas.
This student should exclaim periodically, “That’s a great idea!”
 Participation encourager :
a student who makes sure all group members is taking part actively.
It is important that each student in the group have a role. In this way,
students will learn the content and learn social skills that will benefit them in a
variety of settings.

3.2.5 Grading
Instructors and students often have questions and concerns about: “How to
grade cooperative efforts?”

15

Developing Independent Learning in Vibrant Environment

Instructors should realize that groups that work together can be much like
teams in the workforce and like these teams can be evaluated on the out-
comes of the group. This means that all members of a team can earn the
same grade. This does not mean that every grade should be given to the
team as a whole. Many of the exercises in the modules are meant to be done
individually and should be graded likewise.
Students may be apprehensive about grading if they have had previous bad
experiences with group work, where positive interdependence and individual
accountability were not built into the activity. If an explicit method of telling
students how grades will be awarded is used, these difficulties can easily be
overcome. When students are confident about how they will be graded, they
will work toward achieving a high standard.
In exercises that stress positive group interdependence, the students are
given the same grade as all of the other students in the group, so each
student’s work can raise or lower the grade of the entire group. This increases
the likelihood that students will encourage each other to achieve a high
standard in order to keep a high group grade.
3.3 Guidelines for Preparing a Cooperative Learning Lesson.
Very often most lecturers mistakenly equate cooperative learning with group
work. In actual fact, cooperative learning is much more than simply putting
students in groups. For examples, all the following situations are NOT
considered as cooperative learning:
• A group assignment is given to students, but only one student does all the

work.
• Students just sit in groups, but do their own work.
• Students share materials to complete their own work.
• The teacher only asks the smarter students to help the slow ones.

16

Table below gives a set of basic guidelines for planning a cooperative learning
lesson.

1. Students need to be concerned about the performance of all group
members as well as their own.

2. Each student’s mastery of the assigned material is assessed, each
student is given feedback on his/her progress, and the group is
given feedback on how each member is progressing so that the
other group members know whom to help and encourage.

3. In cooperative learning groups the membership is typically
heterogeneous in ability and personal characteristics.

4. All members share responsibility for performing leadership
actions and there is no formal leader.

5. In cooperative learning groups responsibility for each other’s
achievement is shared. Group members are expected to provide
help and encouragement to each other in order to ensure that all
members do the assigned work.

6. Students’ goals focus on both maximizing each member’s
learning and maintaining good working relationships among
members.

7. In cooperative learning groups, the social skills students need to
work collaboratively are directly taught.

8. When cooperative learning groups are used the teacher observes
the groups, analyses the problems they have working together, and
gives feedback to each group on how well they are working
together.

9. In cooperative learning the teacher structures procedures for groups
to “process” how effectively they are working.

4.0 TYPES OF COOPERATIVE LEARNING

4.1 Teams-Games-Tournament (TGT)
Teams-Games-Tournament is one of the team learning strategies designed
by Robert Slavin for material review and to promote mastery learning. It is
also one of the effective evaluating procedures of Cooperative Learning. TGT

17

Developing Independent Learning in Vibrant Environment

requires home groups or base groups that consistently function in the class
for a period of time. The main idea behind TGT is to motivate students, and to
help each other to master the skills presented by the lecturer. The lecturer
then organizes the games/practices.

Procedures in Teams-Games-Tournaments : A Cooperative Learning Strategy

1. Select an instructional topic and present it to the students. Students learn the
topic in a formal class presentation. This can be taught traditionally, in small groups,
individually, using activities and etc.

2. Set-up or generate academically heterogeneous Study Teams/home teams of
about equal ability. Balance the teams for performance level, gender, ethnicity, etc.
The purpose of the home teams is to make sure that students reinforce, review and
study the worksheets or other materials prepared by the teacher cooperatively as a
team, and the intention is to raise the overall team performance. (Appendix I[a])

3. Develop ‘Game’ - the core of TGT in Cooperative Learning.
‘Game’ consists of the numbered questions. Develop a list of questions on the topic.
Number them. Prepare sets of numbered cards (Appendix IV) so that the total cards
match the number of questions that you have developed for the topic. Give a game
sheet (the set of numbered questions) to every group.

4. Home Team Game (Chapter Review Session) – arrange students in heterogeneous
groups of 4-5 by ability. Groups must be equal in size. Give each group a “Letter
Identity” (e.g. Team A) and each student a Number Identity (e.g. Student 1, student 2
and so on).
Students reinforce, review and study the worksheet or material that prepared by the
teacher cooperatively during this “Home Team” phase.
In each game, a student picks a card and finds the corresponding numbered
question. The student reads the question loudly and all the team members must try
to answer the question that matches the number on the card. If this reader cannot
come up with an answer, a teammate can “steal” the question. All teams share
knowledge during this phase of the lesson by teaching their teammates. (See
appendix I[b] & appendix II)

5. Tournament Team– place students in new groups made up of individuals from each
of the “Home Team” tables. All “Students 1s” go to Table 1 (these might be lower
achieving students) while all “Student 2s” (higher achieving) go to Table 2. In the
“Game” phase, students are placed in homogeneous groups with students of
similar ability and compete against one another. For every question that a student

18

answers correctly, he or she earns a point. One person at each “tournament table”
must keep scores for every individual at the “Game” table. (See appendix III)

* Tips : allow students to place any numbered cards for which they were unable to
come up with the correct answers in a small bag. Collect those cards and use them
to guide what you will teach again.

Rules of TGT
a. Each player chooses a card from the stack. The one with the highest

card number begins. Return cards to the stack and shuffle.
b. The first person should draw a numbered card from the top of the stack

and show it on the table. Read the question out loud. (This original
“reader” gives an answer with no penalty!) .
c. Play goes in clockwise direction. Each successive person in order may
only say either “PASS” (and give no answer) or “CHALLENGE.” A
challenge is made if incorrect answers have been given so far.
d. After the last person passes or challenges, check the answer on the
answer sheet.
e. To score: first correct player gets the card; each incorrect person who is
challenged returns a card to the bottom of the stack. (An incorrect
reader does not lose point!) .
f. The next play continues with question sheet moving clockwise.
g. When the card stack is empty, record the number of cards each player
earned under the “Game” column of score sheet. Shuffle the stack and
play until time is called or the question sheet is changed. (Appendix V).
h. At the end of tournament, add the total of cards earned for all games
and find the Tournament Points. (Appendix VI)

6. Students return to their Home Team tables and report their scores. Team scores are
compared and the winning team earns a reward.

7. Students take an assessment. The scores for each Team (e.g. A, B, C…) are
compiled and averaged. Offer “bonus points” for the team that earns the highest
average and/or “improvement points” to the team that improves its average the most
over previous assessment.

8. Advantages and Disadvantages Learning Model TGT
8.1 Advantages of Team Group Tournament.

a. Students are more active during the learning process.

19

Developing Independent Learning in Vibrant Environment

b. Students will acquire better mastery in the material provided.
c. Students will Improve their communication skill.
d. Learning process will be more attractive.
e. Improving the teachers’ teaching quality.
8.2 Disadvantages of Team Group Tournament.
a. It is difficult to know whether students can solve problems in

intellectual or team work.
b. It takes a long time during the process.

9. TGT materials
Number cards, score sheets, question sheets and answer sheets. All the
materials need to be prepared for each team.

4.2 Student Teams-Achievement Divisions (STAD)

Student Teams-Achievement Divisions (STAD) is a cooperative learning method for
mixed-ability groupings involving team recognition and group responsibility for
individual learning. STAD and TGT have been used in a wide variety of subjects,
from Mathematics to language arts to social studies, and have been used from
second grade through college.

The STAD method is most appropriate for teaching well-defined objectives with
single right answers, such as mathematical computations and applications, language
usage and mechanics, geography and map skills, and science facts and concepts.
However, it can easily be adapted for use with less well-defined objectives by
incorporating more open-ended assessments, such as essays or performances.

In Student Teams-Achievement Divisions (STAD) (Slavin, 1994a), students are
assigned to four-member heterogeneous learning teams that are mixed in
performance level, gender, and ethnicity. The teacher presents a lesson, and then
students work within their teams to make sure that all team members have mastered
the lesson. Finally, all students take individual quizzes on the material, at which time
they may not help one another.

20

Students’ quiz scores are compared to their own past averages, and points
are awarded on the basis of the degree to which students meet or exceed
their own earlier performance. These points are then summed to form team
scores, and teams that meet certain criteria may earn certificates or other
rewards. In a related method called Teams-Games-Tournaments (TGT),
students play games with members of other teams to add points to their team
scores.

A Four-Step Cycle
a. Teach

The teaching phase begins with the presentation of material, usually in a
lecture-discussion format. Students should be told what it is they are going
to learn and why it is important.
b. Team Study
During team study, group members work cooperatively with teacher-
provided worksheets and answer sheets.
c. Test
Next, each student individually takes a quiz. Using a scoring system that
ranges from 0 to 30 points and reflects degree of individual improvement
over previous quiz scores, the teacher gives scores to the papers.
d. Recognition
Each team receives one of three recognition awards, depending on the
average number of points earned by the team. For example, teams that
average 15 to 19 improvement points receive a GOOD TEAM certificate,
teams that average 20 to 24 improvement points receive a GREAT TEAM
certificate, and teams that average 25 to 30 improvement points receive a
SUPER TEAM certificate.

21

Developing Independent Learning in Vibrant Environment

4.3 Jigsaw
4.3.1 History of Jigsaw

In Jigsaw (Aronson, Blaney, Stephen, Sikes, & Snapp, 1978), students are assigned
to six member teams to work on academic material that has been broken down into
sections. For example, a biography might be divided into early life, first
accomplishments, major setbacks, later life, and impact on history. Each team
member reads his or her section. Next, members of different teams who have studied
the same sections meet in expert groups to discuss their sections. Then the students
return to their teams and take turns teaching their teammates about their sections.
Since the only way students can learn sections other than their own is to listen
carefully to their teammates, they are motivated to support and show interest in one
another’s work.

In a modification of this approach called Jigsaw II (Slavin, 1994a), students work in
four- or five-member teams, as in STAD. Instead of each student being assigned a
unique section, all students read a common text, such as a book chapter, a short
story, or a biography. However, each student receives a topic on which to become an
expert. Students with the same topics meet in expert groups to discuss them, after
which they return to their teams to teach what they have learned to their teammates.
The students take individual quizzes, which result in team scores, as in STAD.

4.3.2 Benefit of the Jigsaw
What is the benefit of the ‘jigsaw classroom’? First and foremost, it is a
remarkably efficient way to learn the material. But even more important, the
jigsaw process encourages listening, engagement, and empathy by giving
each member of the group an essential part to play in the academic activity.
Group members must work together as a team to accomplish a common goal;
each person depends on all the others. No student can succeed completely
unless everyone works well together as a team. This "cooperation by design"
facilitates interaction among all students in the class, leading them to value
each other as contributors to their common task.

22

4.3.3 Jigsaw in 10 Easy Steps
The jigsaw classroom is very simple to use. If you're a teacher, just follow
these steps:

1. Divide students into 5- or 6-person jigsaw groups. The groups should be
diverse in terms of gender, ethnicity, race, and ability.

2. Appoint one student from each group as the leader. Initially, this person
should be the most mature student in the group.

3. Divide the day's lesson into 5-6 segments. For example, if you want history
students to learn about Eleanor Roosevelt, you might divide a short biography
of her into stand-alone segments on: (1) Her childhood, (2) Her family life with
Franklin and their children, (3) Her life after Franklin contracted polio, (4) Her
work in the White House as First Lady, and (5) Her life and work after
Franklin's death.

4. Assign each student to learn one segment, making sure students have direct
access only to their own segment.

5. Give students time to read over their segment at least twice and become
familiar with it. There is no need for them to memorize it.

6. Form temporary "expert groups" by having one student from each jigsaw
group join other students assigned to the same segment. Give students in
these expert groups time to discuss the main points of their segment and to
rehearse the presentations they will make to their jigsaw group.

7. Bring the students back into their jigsaw groups.
8. Ask each student to present her or his segment to the group. Encourage

others in the group to ask questions for clarification.
9. Float from group to group, observing the process. If any group is having

trouble (e.g., a member is dominating or disruptive), make an appropriate
intervention. Eventually, it's best for the group leader to handle this task.
Leaders can be trained by whispering an instruction on how to intervene, until
the leader gets the hang of it.
10. At the end of the session, give a quiz on the material so that students quickly
come to realize that these sessions are not just fun and games but really
count.

23

Developing Independent Learning in Vibrant Environment

4.4 Learning Together

Learning Together, a model of cooperative learning developed by David Johnson
and Roger Johnson (1999), involves students working in four- or five-member
heterogeneous groups on assignments. The groups hand in a single completed
assignment and receive praises and rewards based on the group ‘product’. This
method emphasizes team-building activities before students begin working together
and regular discussions within groups about how well they are working together.
Students work on a worksheet together and turn it in as a group. The group can be
graded on correct number of answers, improvement, collaboration, etc.

Implementation
 Lecturers need to make short term goals as well as long term.
 Make each student accountable for their work, but at the same time they should

still rely on the group to finish the task.
 Group and individual reflection.

Implications
 Allow sufficient time.
 Social skills should be taught in the classroom

THE DO’S AND DON’TS
The do’s
 Make sure to arrange the student in their group.
 Make sure that they have group discussion before they come in to class.
 State the role of each student clearly.
 Make sure that they summit their work before presentation.
The don’ts
 Do not let them exceed the time limit.
 Do not let them change role.
 Do not let them ask other group for answer.

24

Summary
Some teachers may feel that they have been applying cooperative learning
approach because they have occasionally placed their students in small
groups, instructing them to cooperate. Yet cooperative learning requires more
than seating youngsters around a table and telling them to share, to work
together, and to be nice to one another. Such loose, unstructured situations of
the students do not have crucial elements of the structured cooperative
strategies.
Past Researches suggested strongly that team-building structured
cooperative learning could increase academic achievements and develop
students’ social skills. Educational reform is now on the verge of taking a giant
step towards this incredible teaching strategy. Our children yearn for an
effective way of learning and understanding of concepts and they need
cooperative learning.
Thus, we have to start with this Teaching Module, promote and incorporate
cooperative learning skills into Mathematics problem-solving situations
consistently. With sufficient practice and support, we believe that our students
will be able to accomplish Mathematical problem-solving tasks successfully,
and working cooperatively in their teams.

25

Developing Independent Learning in Vibrant Environment

5.0 LESSON PLANS LECTURERS’
INSTRUCTION

Subject : Mathematics

Code : QS015 / DM015 / QA016

5.1 THE LESSON PLAN USING COOPERATIVE LEARNING APPROACH :

TGT

TOPIC : CHAPTER 4 MATRICES AND SYSTEM OF LINEAR
EQUATIONS

SUBTOPIC : 4.1 MATRICES WORKSHEET

LESSON : WORKSHEET 1 & 2(a) & 2(b)

LEARNING OUTCOME : Students are able to
a) identify the different types of matrices.
b) perform operations on matrices
c) transpose a matrix and solve related problems

MATERIAL : Question Sheets, Tournament Sheets, Answer Sheets, Score
Sheets,
sets of cards numbered from 1- 16

DURATION : 1 HOUR (TOURNAMENT)

PHASES SUGGESTED SUGGESTED
INSTRUCTION/ACTIVITY COMMUNICATIO
PREPARATIO
N Call for a discussion among members N
by each individual home team. (Team (By facilitator/
(A day before A, Team B, …). Have a chapter
tournament) review using worksheet 1. students)

For each question in the worksheet, Elect a group
make sure everyone in the team can leader in each
perform the solutions. team.

Cooperative
learning done by
students in their
own teams without
lecturer.

TOURNAMENT DAY

INTRODUCTIO STEP 1 : SET UP TOURNAMENT Group leaders
N TEAMS help to set up
the game.
(5 minutes) a) Arrange the tables according to the
number of tournament teams involved. “A1,B1, C1
and D1 go to
b) According to the list prepared, allocate
students into their individual tournament

26

teams. Students will be placed in groups table 1, A2,
of three/four and seated around a table.
B2, C2 and C2
In each team, everyone is given 1
Tournament Question Sheet. go to table 2
and so on;”

c) To play the game : 1 Answer Sheet, 1
Score Sheet and 1 set of numbered
cards from 1 to 16 are placed on every
table. Follow the instruction given by
lecturer / instruction sheet and start
playing the game.0

STEP2 a) Students draw cards at each table. For example:
The highest number goes first. “The question
DEVELOPMEN
T The first player (Reader) picks a number
numbered card and reads out the is 9”
(45 minutes) number as the question number.
Everyone refers to the corresponding
question on the game sheet 1 and tries
to answer.

b) The reader gives/reads out his answer He or she says
once completed the solution. ”challenge” if
Other players are Challengers. This
happens if either one of them wants to one does not
give a different answer OR he or she
passes the answer (agrees with the agree with the
answer).
answer.
c) The last Challenger checks all
answers using the answer sheet He or she can
provided. Whoever answers correctly say ”pass” if
keeps the card.
he or she

agrees with the

answer.

If the reader is wrong, there is no
penalty, but if the challenger is wrong,
he or she must put a previously won
card if any, back in the deck..

d) For the next round, everyone moves Instruction:
one position to the left or
anticlockwise.(OR inversely) “The player on
the left of the
Student takes turn with different roles. former reader
can draw a
When the game is over/times-up, card to start
players record the number of cards they the next
won on the Game Score Sheet. question,”

The game can be continued with the
tournament worksheet 2(b) if the time is
sufficient or during the next lesson.

27

Developing Independent Learning in Vibrant Environment

STEP 3 Ask students to try to complete
worksheet 2(a) and send back the
EVALUATION/ answers as evaluation.
FEEDBACK

Role 1 : READER

The first person in each round of tournament to draw the card.

Role 2 : CHALLENGER
Other players are Challengers. He or she can give a different answer or passes the
answer (If he or she agrees with the answer).

Role 3: CHECKER
The last Challenger in each round of tournament.

Role 4 : TIME KEEPER
The Checker will be the Time Keeper as well. He will check all answers once the
Reader has completed his answer or the answering time taken by the Reader is
more than 3 minutes.

28

WORKSHEET 1 LECTURERS’
(Question Sheet: Topic Review) WORKSHEET

NO. QUESTIONS ANSWERS
2 rows
1. Determine the number of rows of P  0 6  1
 7 2  8

2. State the order of A  1 3 0
2 4 1
2x3

3. Write down the 2 × 2 matrix B such that = 3 − 1 W 5O RKSHEET
4 .   2
 2

4.

Let A 1 2 A=[ aij ], identify a12 and a22 . a12  2
6 3 . If a22  3

5. State the types of matrices of A  0 0 0 ,

B   1 10  and C   1 2 0  . A is a row matrix
0 3 0 3  B is a identity matrix
 2 1 C is a square matrix
2 

6. Given that A 1  3 and B  2 3 [141 −63]
2 0  7 6 , find 2A +

B.

7. C  2 1 D  1 0
0  1 5 , find
Given that and  2

0 5
( )  2  5

8. Given that [23 −−22 ++2 + − ] = [48 00]. Find
0

, and . x=2 , y=4 and z=6

9. Given that = [14 −32] and = [−23 6 51] find
0
−7 14
( ) . [ 6 24]
16 −6

29

Developing Independent Learning in Vibrant Environment

10 identity matrix
. Given a square matrix, [ ] identify the types



of matrix if = = = = = = 0 and = =

= 1.

11.

Given that = [−41 0 62] and = [−15 −1 35] [−01 −1 11]
7 7 0

find A+B.

12. 13 23 03
[10 9 ]
Given that = [5 4] and = [0 −1] find 2F-E.
6 10
78 36

13. 130 100

Given that = [ 4 1 −2] and = [ 1 0] find

−1 2 1 1 x=-2 , = 9 and z=-2

the values of x, y and z such that AB is an upper 5

triangular matrix of order 3x3

14. Determine the values of x, y and z such that x=6 , = 3 and = 9
[24 7 ] = [ 1+2 2 1]
4
15. −1 0
Given that = [ 8 −4] find 2. undefined
71

30

ROUND 1 : WORKSHEET 2(a) (50 MINS)
(Game Sheet 1 / Tournament Sheet 1)

NO. QUESTIONS ANSWERS

1. Determine the order of each matrix.

 3 a) 1x3 b) 3x1
 
a) 1 5 8 b)  y 

 5 

2. Find the order of AB in each case if the matrices a) 3x5
can be multiplied b) 3x3

a) A has order 3x2, B has order 2x5

b) A has order 3x1, B has order 1x3

3. 3 2 0  4 0 0

Given A  0 0 8  , B  0 5 0 , C  0 1
0  0 7 1 0
0  4 0

 3 0 0
and D  1 2 0 .

 0 4 5

Determine which of the above matrices are : a) A, B, C, D f) A
a) square b) B
b) diagonal matrix c) D
c) lower triangular matrix

4. 7 2 1 3 Undefined because
Find the sum of 2 5 0  2 the matrix are in
5 6 4 1 different order.

5. Find the sum of 0 1  3 5 3 6
1 0 4 2 5 2

6. 4 1  8 6 4
Given P  3  2 find (2P)T = 2PT .  2  4 10
2 5 
4 6 8 
7. 2   6  9 12
 2 3 4 
Let A   3  and B  2 3 4 , find AB.

 1 

31

Developing Independent Learning in Vibrant Environment

8. 2 3 
2  and D  4 
Given that C  1 5 5  , find 20 21

1 0  x2 y5
a=-4 , b= -4 , c = 0,
CD.
d 1
9.  13 7 4 0 x 2 2
11  1 y 73 1 .
Given 2 12  3  2 0 1
 0 3 8
7 9 0
Find the values of x and y.

10. Find the values of a, b, c, and d if

2  a 3 4   6 3c 4 .
 4 2b 2 2  4d 8 2

11.

2 0 7
Given matrix Q  0 3 9 . Find QT

1 8 0

12. Find the product of the matrix

1  1 2 1 2 0 6 4  4
3 0 2  1  7 8  2
 2 0 2  .
1
 1

13. 5 2 4 2 0 4

If matrix M  1  2 3 and N  6 3 2 . 13 6 8
1 3 0 1 5 0  3  9 7
 2 4 0
Find 3M – N.

14. If D is a diagonal matrix given by D   3 0 ,
 2
 0 D2   9 0
 4
find D2.  0

15. Given C  3 3 , find the values of x and y if
 y
 x

C2  0 0 x  3 y  3
0 0 .

The game may be continued at round 2 if there is a sufficient time left
after completing Game One. Or it can be done as second tournament on
day 2

32

ROUND 2 : WORKSHEET 2(b) (40 MINS)
(Game Sheet 2 / Tournament Sheet 2)

NO. QUESTIONS ANSWERS

1. Determine the order of each matrix.

a) 7 w Z a) 1x1 b) 2x2

b)  x y 
 

2. Find the order of AB in each case if the matrices

can be multiplied a) 4x5

a) A has order 4x2 , B has order 2x5 b) undefined

b) A has order 4x2, B has order 3x4

3. If A is a diagonal matrix given by D3  8 0
0  1
D  2 0
0  1 .

Find D3

4. A   4 1 , B   1  2  5  1
0 10 4 
Let  3  7 4  , find A+B.
  

5. 1 6  7 ET. 1 1 2 
Given matrix   ,find
E   1 2 8  6 2 1
 
 2 1 0 
 7 8 0 

.

6. x x   y 2  y2 when x  0 and y  0
Given that  y y   x  , find the when x  1 and y  1
 
x

values of x and y.

7. If C  1  1 , find 3C-C. 2  2
0  0  4
2  41
15
8. 7 1  6  2 
2  3  1 a=2 , b= 3 , c = -1,
Let A  1 4  , B  , find AB. d=13

9. Determine the values of a, b, c and d such that 17  23 40 
13 2  26
a 1 1  3 1 1  3 5 1  0  9 26 
b 3  c b  12  3 
0   a b 

1 4 a 1 a 0  9 1 d 

10. 2 7`  2 1 6
 5  3 3 
 3 1  .

Find the product of 2   4

33

Developing Independent Learning in Vibrant Environment

STUDENTS’
INSTRUCTION

TOPIC : CHAPTER 4 MATRICES AND SYSTEM OF LINEAR
EQUATIONS

SUBTOPIC : 4.1 MATRICES

LESSON : WORKSHEET 1 & 2(a) &2(b)

LEARNING OUTCOME : Students are able to
a) identify the different types of matrices.
b) perform operations on matrices
c) transpose a matrix and solve related problems

MATERIAL : Question sheets, Tournament Sheets, Answer Sheets, Score
Sheets, sets of cards numbered from 1- 16

DURATION : 1 HOUR (TOURNAMENT)
INSTRUCTION TO STUDENTS

PREPARATION Call a discussion among members in individual home team.
( A day before
tournament) Have a chapter review using worksheet 1.

For each question in the worksheet, make sure everyone in
the team can perform the solutions.

TOURNAMENT DAY SET UP TOURNAMENT TEAMS
STEP 1
Go to the allocated tournament team according to the list
(5 minutes) prepared by lecturer.

In each team, take 1 Tournament Question Sheet, 1
Answer Sheet, 1 Score Sheet and 1 set of numbered cards
from 1 to 16.

STEP 2 Follow the instruction given by the lecturer/instruction
(50 minutes or end of sheet, OR activities in Team-Games-Tournament and start
playing the game.
lesson)
Record 1 point for each correct answer in Score Sheet.

Role 1 : READER

The first person in each round of tournament to draw the card.

Role 2 : CHALLENGER

Other players are Challengers. He or she can give a different answer or passes the

answer (If he or she agrees with the answer).

Role 3: CHECKER

The last Challenger in each round of tournament.

Role 4 : TIME KEEPER

The Checker will be the Time Keeper as well. He will check all answers once the

Reader has completed his answer or the answering time taken by the Reader is

more than 3 minutes.

34

WORKSHEET 1 STUDENTS’
(Question Sheet: Topic Review) WORKSHEET

NO. QUESTIONS ANSWERS

1. P  0 6  1
 7 2  8
Determine the number of rows of

2. A  1 3 0
2 4 1
State the order of

3. Write down the 2 × 2 matrix B such that = 3 −
4 .

4. 1 2
6 3 . If
Let A  A=[ aij ], identify a12 and a22 .

5. State the types of matrices of A  0 0 0 ,

B   1 0  and C   1 2 0  .
0 1  3 0 3 
 2 1
2 

6. Given that A  1  3 and B  2 3
2  7 6 , find 2A
0 

+ B.

7. Given that C  2 1 and D  1 0
0  1  5 , find
 2

( ) .

8. Given that [23 −−22 ++2 + − ] = [48 00].
0

Find , and .

9. Given that = [14 −32] and = [−23 6 15] find
0
( ) .

10.
Given a square matrix, [ ] identify the



types of matrix if = = = = = = 0 and

= = = 1.

11. Given that = [−41 0 62] and = [−15 −1 35]
7 7
find A+B.

35

Developing Independent Learning in Vibrant Environment

12. 13 23

Given that = [5 4] and = [0 −1] find 2F-E.

78 36

13. 130 100

Given that = [ 4 1 −2] and = [ 1 0]

−1 2 1 1

find the values of x, y and z such that AB is an

upper triangular matrix of order 3x3

14. Determine the values of x, y and z such that
12 2 1]
[24 7 ] = [ +

−1 0
15. Given that = [ 8 −4] find 2.

71

36

ROUND 1 : WORKSHEET 2(a) (50 MINS) ANSWERS
(Game Sheet 1 / Tournament Sheet 1)

NO. QUESTIONS

1. Determine the order of each matrix.
 3
 
a) 1 5 8 b)  y 

 5 

2. Find the order of AB in each case if the matrices
can be multiplied

a) A has order 3x2, B has order 2x5

b) A has order 3x1, B has order 1x3

3. 3 2 0  4 0 0
B  0 0 ,
Given A  0 0 8  , 5

0 0  4 0 0 7

0 1  3 0 0
1 0 and D  1 0 .
C   0 2 5
4

Determine which of the above matrices are :
a) square b) diagonal matrix c) lower
triangular matrix

4. 7 2 1 3
Find the sum of 2 5 0  2
5 6 4 1

5. Find the sum of 0 1  3 5
1 0 4 2

6. 4 1
Given P  3  2 find (2P)T = 2PT .
2 5 

7.  2 
 3 
Let A  and B  2 3 4 , find AB.

 1 

37

Developing Independent Learning in Vibrant Environment

8. 2 3 
2  and D  4 
Given that C  1 5 5  , find

1 0 

CD.

9.  13 7  4 0  x 2
11  1 y 73 1 .
Given 2 12 3


Find the values of x and y.

10. Find the values of a, b, c, and d if

2  a 3 4   6 3c 4 .
 4 2b 2 2  4d 8 2

11.  3 0 4 1 3 

Given T   5 1 6 and R  0 0  .
 
1 2 7 3  4

Find (TR)T .

12. 2 0 7
Given matrix Q  0 3 9 . Find QT
1 8 0

13. Find the product of the matrix
1 2 0
1  1 2  1 
3 0 2  2 0 2  .
1
 1

14. 5 2 4 2 0 4
If matrix M  1  2 3 and N  6 3 2 .
1 3 0 1 5 0

Find 3M – N.

15. If D is a diagonal matrix given by D   3 0 ,
 0 2

find D2.

16. Given C  3 3 , find the values of x and y if
x y

C2  0 0
0 0 .

The game may be continued t round 2 if there is a sufficient time left after
completing Game One. Or it can be done as second tournament on day 2.

38

ROUND 2 : WORKSHEET 2(b) (40 MINS) ANSWERS
(Game Sheet 2 / Tournament Sheet 2)

NO. QUESTIONS

1. Determine the order of each matrix.
w Z
a) 7 b)  
 x y 

2. Find the order of AB in each case if the matrices
can be multiplied
a) A has order 4x2 , B has order 2x5
b) A has order 4x2, B has order 3x4

3. If A is a diagonal matrix given by
2 0
D  0 1 .

Find D3

4. A   4 1 , B   1  2
Let 0  , find A+B.
 3  7 4 
 

5. 1 6  7 ET.
Given matrix   ,find
E   1 2 8

 2 1 0 

6. x x  y 2  y2
y  x  , find the
Given that  y  
 x

values of x and y.

7. If C  1  1 , find 3C-C.
0 2 

8. 7 1  6
2  3  1
Let A  1 4  , B  , find AB.

9. Determine the values of a, b, c and d such that

a 1 1  3 1 1  3 5 1
b 3  c b  12  3 
0   a b 

1 4 a 1 a 0  9 1 d 

10. 2 7`  2 1 6
 5  3 3 
 3 1   .

Find the product of 2   4

39

Developing Independent Learning in Vibrant Environment

5.2 THE LESSON PLAN USING COOPERATIVE LEARNING APPROACH : STAD

TOPIC : 1.0 NUMBER SYSTEMS

SUBTOPIC : 1.1 Real numbers

LESSON : WORKSHEET

LEARNING OUTCOME : Students are able to
(a) define natural numbers, whole numbers,
integers, prime numbers, rational numbers and
irrational numbers.
(b) represent rational and irrational numbers in
decimal form.
(c) represent the relationship of number sets in a
real number system diagrammatically showing
N  W  Z  Q and Q  Q  R where N, W, Z, Q,

Q and R represent the set of natural, whole,

integer, rational, irrational, and real numbers
respectively.
(d) represent open, closed and half-open intervals
and their representations on the number line.
(e) simplify union,  , and intersection,  , of two
or more intervals with the aid of number line.

MATERIAL : Question Sheets and Answer Sheets

DURATION : 1 HOUR (To complete the worksheet)

PHASES SUGGESTED INSTRUCTION/ACTIVITY SUGGESTED
COMMUNICATIO
INTRODUCTIO
N N
(By facilitator /
(10 minutes)
students)

STEP 1: SET UP TEAMS-PAIRS- Partner A is the
CHECK problem solver
(a) Students are assigned into teams of and partner B is
the coach.
four. Then break the team into two
pairs of two partners, A and B.
Partners will work on a worksheet.
(b) Partner A works the first problem
while partner B tries to help if
necessary and checks his partner’s
work for agreement.
(c) If partner B (coach partner) cannot
agree on the answer, they may ask
the other pair on the team.
(d) If the team as a whole cannot agree

40

on the answer, each teammate raises
a hand, 4 hands up is a team
question. They can ask lecturer
assistance.
(e) If the partners agree on the answer,
the coach gives his partner positive
feedback, praises him for a job well
done.

STEP 2 (a) The partners switch roles for the next After 15 minutes
DEVELOPMEN problem. The student who had been switch the role
the coach now becomes the problem between partner
T solver while the other student A and B to
(30 minutes) becomes the coach and praiser. answer worksheet
2.
STEP 3 (b) Repeat the steps and work in pairs to
CLOSURE/ complete the worksheet.
CONCLUSION
(20 minutes) The team reunites and the pairs compare Discuss question
answers. If the team disagrees and is which the student
unable to figure out why, four hands go up feel confuse or
for teacher assistance. complicated.

41

Developing Independent Learning in Vibrant Environment

WORKSHEET (Question and answer )
1. Put a tick (√) in the appropriate box if it is true.

Number N W Z Prime Q Q
Number √
-3.14 √ √

81 √ √
5 √ √
 √

25 √ √ √ √ √

1.2121...

7

85.31476....
3e

473.456 √

 15
5

2. Graph the following intervals and write the resulting intervals.

Question : Answer :

(a) (4,0)   2,2 (a) (4,2)
(b) (,5)  3,  (b) 
© [3,5)  4,6 (c) [4,5)
(d) (,3)  3,  (d) 
(e) [4,6)  0,6 (e) [4,6]
(f) (1,2]  2,8 (f) {2}
(g) (,6]  3,10 (g) (3,6]
(h) (2,5]  4,  (h) [4,5]

42

TOPIC : 1.0 NUMBER SYSTEMS STUDENTS’
INSTRUCTION

SUBTOPIC : 1.1 Real numbers

LESSON : WORKSHEET

LEARNING OUTCOME : Students are able to
(a) define natural numbers, whole numbers,
integers, prime numbers, rational numbers and
irrational numbers.
(b) represent rational and irrational numbers in
decimal form.
(c) represent the relationship of number sets in a
real number system diagrammatically showing
N  W  Z  Q and Q  Q  R where N, W, Z, Q,

Q and R represent the set of natural, whole,

integer, rational, irrational, and real numbers
respectively.
(d) represent open, closed and half-open intervals
and their representations on the number line.
(e) simplify union,  , and intersection,  , of two
or more intervals with the aid of number line.

MATERIAL : Question Sheets and Answer Sheets

DURATION : 1 HOUR (To complete the worksheet)

INSTRUCTION TO STUDENTS

STEP 1 a) Get class organized into four member-learning teams.
SET UP Then, a team of four breaks into two pairs of 2
TEAMS-PAIRS- partners, A and B. Partners work on a worksheet.
CHECK (Partner A is the problem solver and partner B is the
10 minutes coach)

b) Partner A works the first problem while partner B tries
to help if necessary and checks his partner’s work for
agreement.

c) If the coach partner cannot agree on the answer, they
may ask the other pair on the team. If the team as a
whole cannot agree on an answer, each teammate
raises a hand, four hands up is a team question. You
can ask lecturer assistance

d) If the partners agree on the answer, the coach gives
his partner positive feedback, praises him for a job
well done.

43

Developing Independent Learning in Vibrant Environment

STEP 2 a) The partners switch roles for the next problem. The
(30 minutes) student who had been the coach now becomes the

problem solver while the other student becomes the
coach and praiser.
b) Repeat the steps sand work in pairs to complete the
worksheet.

STEP 3 The team reunites and the pairs compare answers. If the
(20 minutes) team disagrees and is unable to figure out why, four
hands go up for teacher assistance.

44

WORKSHEET (Question) STUDENTS’
1. Put a tick (√) in the appropriate box if it is true. WORKSHEET

Number N W Z Prime Q Q
Number

-3.14

81
5


25

1.2121...

7

85.31476....
3e

473.456

 15
5

2. Graph the following intervals and write the resulting intervals.

(a) (4,0)   2,2
(b) (,5)  3, 
(c) [3,5)  4,6
(d) (,3)  3, 
(e) [4,6)  0,6
(f) (1,2]  2,8
(g) (,6]  3,10
(h) (2,5]  4, 

45

Developing Independent Learning in Vibrant Environment

5.3 THE LESSON PLAN USING COOPERATIVE LEARNING APPROACH :

JIGSAW

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

PHASES SUGGESTED INSTRUCTION/ACTIVITY SUGGESTED
COMMUNICATIO

N
(By facilitator/

students)

PREPARATION (i) Divide the class into smaller groups You can create
(2-3 days known as HOME GROUPS (HG). table to divide the
before) *The no. of concepts=The no. of class.
students in each HG
HOME GROUPSTable 1 : (5 concepts with 25 students)Appoint one of the
students to be the
EXPERT GROUPS discussion leader
EG EG EG EG EG for each HG and
12345 EG, on a rotating
HG basis.
1
HG
2
HG
3
HG
4
HG

46


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