GRADE 9 Topic MATHEMATICS - FODE
Topic
DEPARTMENT OF EDUCATION
GRADE 9
Topic
MATHEMATICS
UNIT 5
DESIGN IN 2D AND 3D GEOMETRY (1)
Published by:
FLEXIBLE OPEN AND DISTANCE EDUCATION
PRIVATE MAIL BAG, P.O. WAIGANI, NCD
FOR DEPARTMENT OF EDUCATION
PAPUA NEW GUINEA
2013
GR 9 MATHEMATICS U5
1
GRADE 9
MATHEMATICS
UNIT 5
DESIGN IN 2D AND 3D GEOMETRY (1)
TOPIC 1:
POINTS, LINES, PLANES
AND ANGLES
TOPIC 2:
POLYGONS
TOPIC 3:
AREA
TOPIC 4:
SURFACE AREA AND
VOLUME
TITLE
GR 9 MATHEMATICS U5
2
ACKNOWLEDGEMENT
Acknowledgements
We acknowledge the contributions of all Secondary teachers and
people who in one way or another helped to develop this Course.
Special thanks is given to the Staff of Mathematics Department of
FODE who played active role in coordinating writing workshops,
outsourcing lesson writing and editing processes, involving selected
teachers from NCD.
We also acknowledge the professional guidance provided by the
Curriculum Development and Assessment Division throughout the
processes of writing and, the services given by the members of the
Mathematics Subject Review and Academic Committees.
MR. DEMAS TONGOGO
Principal-FODE
Flexible Open and Distance Education
Papua New Guinea
Published in 2016
@ Copyright 2016, Department of Education
Papua New Guinea
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted in
any form or by any means electronic, mechanical,
photocopying, recording or any other form of reproduction by
any process is allowed without the prior permission of the
publisher.
ISBN: 978-9980-87-738-3
National Library Services of Papua New Guinea
Written by:
Luzviminda B. Fernandez
Printed by the Flexible, Open and Distance Education
GR 9 MATHEMATICS U5
3
CONTENTS
CONTENTS
Page
Secretary¡®s Message¡¡..¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.¡..
4
Unit Introduction¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
5
Study Guide¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
6
TOPIC 1:
POINTS, LINES, PLANES AND ANGLES¡¡¡¡¡¡¡¡¡¡¡¡..
Lesson 1:
Points, Lines, Angles and Planes¡¡¡¡¡¡..¡¡¡¡¡¡¡..
Lesson 2:
Types of Angles¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.......
Lesson 3:
Complementary and Supplementary Angles¡¡¡¡¡¡¡¡.¡..
Lesson 4:
Intersecting. Lines¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..
Lesson 5:
Parallel Lines¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡...
Lesson 6:
Reasoning with Parallel Lines.¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
Summary¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
Answers to Practice Exercises 1-6¡¡¡¡¡¡¡¡¡¡¡¡..........
.
TOPIC 2:
POLYGONS¡¡¡¡¡¡¡¡¡.¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
Lesson 7:
Types of Polygons¡¡¡¡¡..¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
Lesson 8:
Triangles¡¡¡¡¡¡¡¡¡¡¡..¡¡¡¡¡¡¡¡¡¡¡¡¡.
Lesson 9:
Quadrilaterals¡¡¡¡.¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
Lesson 10: Mixed Problems¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡......
Summary¡¡¡¡¡....¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..
Answers to Practice Exercises 7-10¡¡¡¡¡¡¡¡¡¡¡¡¡¡.
7
9
17
25
31
39
44
51
52
TOPIC 3:
AREA¡¡¡¡¡¡¡¡¡¡..¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡...
Lesson 11:
Area of Triangles and Rectangles¡¡¡¡¡¡¡¡¡¡¡¡......
Lesson 12:
Area of Parallelograms, Rhombuses and Trapeziums¡...¡¡¡.
Lesson 13:
Compound Shapes¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
Lesson 14:
Applied Problems¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..
Summary¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡......
Answers to Practice Exercises 114...¡¡¡..¡¡¡¡¡¡¡¡¡....
97
99
107
117
125
131
132
TOPIC 4:
Surface Area of Prisms..¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..
Volume of Prisms¡...¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡.¡¡..
Surface Area and Volume of Pyramids¡¡¡¡¡¡¡¡¡¡¡..
Surface Area and Volume of Cylinders¡¡¡¡¡¡¡¡¡¡¡..
Surface Area and Volume of Cones¡¡¡¡¡¡..¡¡¡¡¡¡.
Surface Area and Volume of Spheres¡¡¡¡¡¡¡¡¡¡¡¡
Summary¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..¡
Answers to Practice Exercises 15-20¡¡¡¡¡¡¡¡¡¡¡¡¡..
133
135
143
152
159
167
174
181
182
REFERENCES¡¡...¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
184
SURFACE AREA AND VOLUME¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡..
Lesson 15:
Lesson 16:
Lesson 17:
Lesson 18:
Lesson 19:
Lesson 20:
55
57
67
76
86
93
94
GR 9 MATHEMATICS U5
4
MESSAGE
SECRETARY¡¯S MESSAGE
Achieving a better future by individual students and their families, communities or the
nation as a whole, depends on the kind of curriculum and the way it is delivered.
This course is part and parcel of the new reformed curriculum. The learning
outcomes are student-centered with demonstrations and activities that can be
assessed.
It maintains the rationale, goals, aims and principles of the national curriculum and
identifies the knowledge, skills, attitudes and values that students should achieve.
This is a provision by Flexible, Open and Distance Education as an alternative
pathway of formal education.
The course promotes Papua New Guinea values and beliefs which are found in our
Constitution and Government Policies. It is developed in line with the National
Education Plans and addresses an increase in the number of school leavers as a
result of lack of access to secondary and higher educational institutions.
Flexible, Open and Distance Education curriculum is guided by the Department of
Education¡®s Mission which is fivefold:
? to facilitate and promote the integral development of every individual
? to develop and encourage an education system that satisfies the
requirements of Papua New Guinea and its people
? to establish, preserve and improve standards of education throughout Papua
New Guinea
? to make the benefits of such education available as widely as possible to all
of the people
? to make the education accessible to the poor and physically, mentally and
socially handicapped as well as to those who are educationally
disadvantaged.
The college is enhanced through this course to provide alternative and comparable
pathways for students and adults to complete their education through a one system,
two pathways and same outcomes.
It is our vision that Papua New Guineans¡® harness all appropriate and affordable
technologies to pursue this program.
I commend all the teachers, curriculum writers and instructional designers who have
contributed towards the development of this course.
................
................
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