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.

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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.

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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?”

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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

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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.

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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 x2 y5

a=-4 , b= -4 , c = 0,

CD.

d 1

9. 13 7 4 0 x 2 2

11 1 y 73 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 3c 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 73 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 3c 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.

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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,

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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