Unit-7- Understanding Shapes 2D and 3D

UNDERSTANDING UNDERSTANDING

UNIT - 7UNIT - 7

CLASS

VICBSE-i

Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India

UNDERSTANDING UNDERSTANDING

UNIT - 7

Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India

CLASS

VICBSE-i

The CBSE-International is grateful for permission to reproduce and/or

translate copyright material used in this publication. The

acknowledgements have been included wherever appropriate and

sources from where the material has been taken duly mentioned. In

case anything has been missed out, the Board will be pleased to rectify

the error at the earliest possible opportunity.

All Rights of these documents are reserved. No part of this publication

may be reproduced, printed or transmitted in any form without the

prior permission of the CBSE-i. This material is meant for the use of

schools who are a part of the CBSE-International only.

PrefacePrefaceThe Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos.

The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been conscious of the varying needs of the learners in countries abroad and has been working towards contextualizing certain elements of the learning process to the physical, geographical, social and cultural environment in which they are engaged. The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in view.

The nucleus of the entire process of constructing the curricular structure is the learner. The objective of the curriculum is to nurture the independence of the learner, given the fact that every learner is unique. The learner has to understand, appreciate, protect and build on values, beliefs and traditional wisdom, make the necessary modifications, improvisations and additions wherever and whenever necessary.

The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The speed and methods of assimilating knowledge have put forth many challenges to the educators, forcing them to rethink their approaches for knowledge processing by their learners. In this context, it has become imperative for them to incorporate those skills which will enable the young learners to become 'life long learners'. The ability to stay current, to upgrade skills with emerging technologies, to understand the nuances involved in change management and the relevant life skills have to be a part of the learning domains of the global learners. The CBSE-i curriculum has taken cognizance of these requirements.

The CBSE-i aims to carry forward the basic strength of the Indian system of education while promoting critical and creative thinking skills, effective communication skills, interpersonal and collaborative skills along with information and media skills. There is an inbuilt flexibility in the curriculum, as it provides a foundation and an extension curriculum, in all subject areas to cater to the different pace of learners.

The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now introducing it to other affiliated schools who meet the requirements for introducing this curriculum. The focus of CBSE-i is to ensure that the learner is stress-free and committed to active learning. The learner would be evaluated on a continuous and comprehensive basis consequent to the mutual interactions between the teacher and the learner. There are some non-evaluative components in the curriculum which would be commented upon by the teachers and the school. The objective of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives, SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'. The Core skills are the most significant aspects of a learner's holistic growth and learning curve.

The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework (NCF 2005) NCERT and the experience gathered by the Board over the last seven decades in imparting effective learning to millions of learners, many of whom are now global citizens.

The Board does not interpret this development as an alternative to other curricula existing at the international level, but as an exercise in providing the much needed Indian leadership for global education at the school level. The International Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The Board while addressing the issues of empowerment with the help of the schools' administering this system strongly recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to their peers through the interactive platforms provided by the Board.

I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr. Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the development and implementation of this material.

The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion forums provided on the portal. Any further suggestions are welcome.

Vineet JoshiChairman

AcknowledgementsAcknowledgementsAdvisory Conceptual Framework

Ideators

Shri Vineet Joshi, Chairman, CBSE Shri G. Balasubramanian, Former Director (Acad), CBSE

Sh. N. Nagaraju, Director(Academic), CBSE Ms. Abha Adams, Consultant, Step-by-Step School, Noida

Dr. Sadhana Parashar, Director (Training),CBSE

Ms. Aditi Misra Ms. Anuradha Sen Ms. Jaishree Srivastava Dr. Rajesh Hassija

Ms. Amita Mishra Ms. Archana Sagar Dr. Kamla Menon Ms. Rupa Chakravarty

Ms. Anita Sharma Ms. Geeta Varshney Dr. Meena Dhami Ms. Sarita Manuja

Ms. Anita Makkar Ms. Guneet Ohri Ms. Neelima Sharma Ms. Himani Asija

Dr. Anju Srivastava Dr. Indu Khetrapal Dr. N. K. Sehgal Dr. Uma Chaudhry

Material Production Group: Classes I-V

Dr. Indu Khetarpal Ms. Rupa Chakravarty Ms. Anita Makkar Ms. Nandita Mathur

Ms. Vandana Kumar Ms. Anuradha Mathur Ms. Kalpana Mattoo Ms. Seema Chowdhary

Ms. Anju Chauhan Ms. Savinder Kaur Rooprai Ms. Monika Thakur Ms. Ruba Chakarvarty

Ms. Deepti Verma Ms. Seema Choudhary Mr. Bijo Thomas Ms. Mahua Bhattacharya

Ms. Ritu Batra Ms. Kalyani Voleti

English :

Ms. Rachna Pandit

Ms. Neha Sharma

Ms. Sonia Jain

Ms. Dipinder Kaur

Ms. Sarita Ahuja

Science :

Dr. Meena Dhami

Mr. Saroj Kumar

Ms. Rashmi Ramsinghaney

Ms. Seema kapoor

Ms. Priyanka Sen

Dr. Kavita Khanna

Ms. Keya Gupta

Mathematics :

Political Science:

Ms. Seema Rawat

Ms. N. Vidya

Ms. Mamta Goyal

Ms. Chhavi Raheja

Ms. Kanu Chopra

Ms. Shilpi Anand

Geography:

History :

Ms. Suparna Sharma

Ms. Leela Grewal

Ms. Leeza Dutta

Ms. Kalpana Pant

Material Production Groups: Classes VI-VIII

English :

Geography:

Ms. Sarita Manuja

Ms. Renu Anand

Ms. Gayatri Khanna

Ms. P. Rajeshwary

Ms. Neha Sharma

Ms. Sarabjit Kaur

Ms. Ruchika Sachdev

Ms. Deepa Kapoor

Ms. Bharti Dave Ms. Bhagirathi

Ms. Archana Sagar

Ms. Manjari Rattan

Mathematics :

Political Science:

Dr. K.P. Chinda

Mr. J.C. Nijhawan

Ms. Rashmi Kathuria

Ms. Reemu Verma

Ms. Sharmila Bakshi

Ms. Srelekha Mukherjee

Science :

Economics:

Ms. Charu Maini

Ms. S. Anjum

Ms. Meenambika Menon

Ms. Novita Chopra

Ms. Neeta Rastogi

Ms. Pooja Sareen

Ms. Mridula Pant

Mr. Pankaj Bhanwani

Ms. Ambica Gulati

History :

Ms. Jayshree Srivastava

Ms. M. Bose

Ms. A. Venkatachalam

Ms. Smita Bhattacharya

Material Production Groups: Classes IX-X

Coordinators:

Dr. Sadhana Parashar, Ms. Sugandh Sharma, Dr. Srijata Das, Dr. Rashmi Sethi, Head (I and R) E O (Com) E O (Maths) E O (Science)

Shri R. P. Sharma, Consultant Ms. Ritu Narang, RO (Innovation) Ms. Sindhu Saxena, R O (Tech) Shri Al Hilal Ahmed, AEO

Ms. Seema Lakra, S O Ms. Preeti Hans, Proof Reader

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Preface

Acknowledgment

1. Syllabus 1

2. Scope Document 2

3. Teacher’s Support Material 4

Teacher's Note 5

Activity Skill Matrix 9

Warm up Activity W1 11

Geometry on the Floor

Warm Up Activity W2 11

Geometry Crossword

Warm Up Activity W3 12

Lines and Angles

Pre Content Worksheet P1 12

Tangrams

Pre Content Worksheet P2 13

Class Mosaic

Content Worksheet CW1 13

Open and Closed Shapes


Understanding Polygons 1


Regular and Irregular Polygons


2D Shapes




Classification of Triangles 1

2

2

2

2

2

2

2

2

2

2

2

2

CONTENTS

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2




Types of Triangles




Types of Quadrilaterals 1








Interior Angles of a Polygon




Polygon Capture


Visualizing Solid Shapes


Nets of 2D and 3D Objects


Nets of Curved Objects


Solid Shapes 1


Solid Shapes 2

CO

NT

EN

T

CO

NT

EN

T2

2

2

2

2

2


Symmetry 1


Symmetry 2


Symmetry 3


Symmetry 4


Symmetry 5

Post Content Worksheet PCW1 34

4. Assessment of the Chapter 35

Sample Assessment Rubric 40

5. Study Material 44

6. Student's Support Material 75

SW 1 : Warm up Activity W1 76

Geometry on the floor

SW 2 : Warm up W2 77

Geometry Crossword

SW 3 : Warm up W3 79

Lines and Angles

SW 4 : Pre Content Worksheet P1 83

Tangrams

SW 5 : Pre Content Worksheet P2 85

Class Mosaic

SW 6 : Content Worksheet CW1 86


CO

NT

EN

T SW 7 : Content Worksheet CW2 88



Regular and Irregular polygons


2D shapes








Types of Triangles












Interior Angles of a Polygon



CO

NT

EN

T SW 21 : Content Worksheet CW16 132

Polygon Capture




Nets of 2D and 3D objects




Solid Shapes 1


Solid Shapes 2


Symmetry 1


Symmetry 2


Symmetry 3


Symmetry 4


Symmetry 5

SW 32 : Post Content Worksheet PCW1 158

Acknowledgments 163

Suggested videos/ links/ PPT's 165

1

SYLLABUS

UNDERSTANDING SHAPES - 2D AND 3D

SHAPES

2D AND 3D

Observing and naming shapes around us. Talking about

them with reference to their sides.

Defining a polygon made of straight lines with reference to a

closed figure in a plane.

Classifying polygons based on the number of sides, special

mention of the root words.

Defining a Triangle as a polygon with three sides, types of

triangles based on the measure of the sides and angles,

Classifying quadrilaterals based on their sides

Identifying and differentiating between 2D and 3D shapes.

Creating solids from their nets.

Identifying faces, edges and vertices of a solid and naming

them.

SYMMETRY

Observing symmetry around us,

Exploring reflection symmetry.

Drawing and identifying lines of symmetry

2

SCOPE DOCUMENT

REVIEW AND RECALL: Basic geometrical concepts of lines and angles,

Parallel and perpendicular lines

Measuring sides using ruler and angles using protractor

Concepts:

1. Recognizing simple polygons (Up to octagons, regulars as well as non regular).

2. Classifying triangles (on the basis of sides, and of angles)

3. Classifying quadrilaterals – Trapezium, parallelogram, rectangle, square,

rhombus.

4. Identifying 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism

(triangular), pyramid (triangular and square)

5. Define and identify elements of 3-D figures in the surroundings

6. Observe and recognize nets for cube, cuboids, cylinders, cones and tetrahedrons.

7. List out the Faces, Edges and vertices of the different 3d solids by looking at the

solids.

8. Observe and identify 2-D symmetrical objects for reflection symmetry

9. Learn the operation of reflection (taking mirror images) of simple 2-D objects.

10. Recognizing reflection symmetry and identifying axes of reflection.

Learning objectives

At the end of this lesson student will be able to

Differentiate between open and closed figures, simple and complex polygons

Understand and appreciate the properties of regular polygons.

Understand and recognize types of triangles and quadrilaterals.

Understand and apply the properties of quadrilaterals to classify the

quadrilaterals .

3

Identify the various 3D objects and know how to obtain them from 2D flat

figures.

Identify and define edges, faces and vertices of all types of 3D objects.

Identify and appreciate symmetrical objects in nature.

Recognize reflection and reflect on the given axis.

Extension activities:

The concept of and the process of making tessellations

Create tessellations using rotation and translation

Understand and write about the works of M.C. Escher

Cross curricular links

English: Students would write about the works of M.C. Escher. Throughout the topic

students get a lot of chances to look up root words / etymology of the topics

done.

ART: Students understand the meshing of Geometry and topics taught to different

art works.

Sports: Students work on their perceptions and lateral thinking thus enhancing their

meta cognition.

Technology help : Web links for reference, research and remedial

You tube to deliver content

5

TEACHER’S NOTE

The teaching of Mathematics should enhance the child’s resources to think and reason,

to visualise and handle abstractions, to formulate and solve problems. As per NCF

2005, the vision for school Mathematics include :

1. Children learn to enjoy mathematics rather than fear it.

2. Children see mathematics as something to talk about, to communicate through,

to discuss among themselves, to work together on.

3. Children pose and solve meaningful problems.

4. Children use abstractions to perceive relation-ships, to see structures, to reason

out things, to argue the truth or falsity of statements.

5. Children understand the basic structure of Mathematics: Arithmetic, algebra,

geometry and trigonometry, the basic content areas of school Mathematics, all

offer a methodology for abstraction, structuration and generalisation.

6. Teachers engage every child in class with the conviction that everyone can learn

mathematics.

Students should be encouraged to solve problems through different methods like abstraction, quantification, analogy, case analysis, reduction to simpler situations, even guess-and-verify exercises during different stages of school. This will enrich the students and help them to understand that a problem can be approached by a variety of methods for solving it. School mathematics should also play an important role in developing the useful skill of estimation of quantities and approximating solutions. Development of visualisation and representations skills should be integral to Mathematics teaching. There is also a need to make connections between Mathematics and other subjects of study. When children learn to draw a graph, they should be encouraged to perceive the importance of graph in the teaching of Science, Social Science and other areas of study. Mathematics should help in developing the reasoning skills of students. Proof is a process which encourages systematic way of argumentation. The aim should be to develop arguments, to evaluate arguments, to make conjunctures and understand that there are various methods of reasoning. Students should be made to understand that mathematical communication is precise,

6

employs unambiguous use of language and rigour in formulation. Children should be encouraged to appreciate its significance. At the upper primary stage, students get the first taste of power of Mathematics through the application of powerful abstract concepts like Algebra, Number System, Geometry etc. Revisiting of the previous knowledge and consolidating basic concepts and skills learnt at the Primary Stage helps the child to appreciate the abstract nature of Mathematics. Whether it is Number system or algebra or Geometry, these topics should be introduced by relating it to the child’s every day experience and taking it forward to abstraction so that the child can appreciate the importance of study of these topics.

The students in the middle grades have an informal knowledge about a point, line and plane. By this stage they are aware of various 2 dimensional and 3 dimensional shapes. They recognize these shapes early, even before they know the technical terms for the different shapes they see. They have an intuitive idea about different polygons, angles and triangles. They are now expected to define and draw all these terms and their components mathematically.

According to the National Council of Teachers of Mathematics, grades 6-8 students should be able to:

Precisely describe, classify, and understand relationships among types of two-

and three-dimensional objects using their defining properties;

Use two-dimensional representations of three-dimensional objects to visualize

and solve problems such as those involving surface area and volume; and,

Use geometric models to represent and explain numerical and algebraic

relationships (NCTM, 2000).

The students at this level should be able to learn the geometric vocabulary of the three

dimensional shapes such as faces, edges and vertices. They should be able to create and

use two dimensional representations of three dimensional shapes by forming nets of the

three dimensional figures. The teacher may encourage the students to discover,

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through investigation of various structures the Euler’s Formula, the algebraic relation

between the edges, vertices and faces of the polyhedrons.

Common Errors

Type of error Error made Correction

Diagonals of a Pentagon

Counting the number of

diagonals

Its best to ask the students

to pick up one vertex of the

pentagon and start making

diagonals.

Prism and Pyramid

Difference between a prism

and pyramid

A prism has two identical

bases and all the faces are

rectangles. A pyramid has

a single base and a top

vertex and all the faces are

triangles.

Cuboid and prism Is a cuboid a prism? Yes a cuboid is a

rectangular prism with two

rectangular bases

Overview of the students’ worksheets

The first Warm up activity (W1) is an artistic geometrical design where the students are

using their previous knowledge of informal geometry and appreciate the use of

geometry.

In Warm Up activity (W2), the students use their previous knowledge of geometrical

terms in a crossword game.

In Warm up activity (W3), the students recollect the known terms in Lines and Angles.

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Through Pre content 1, (P1), the students are informally introduced to Quadrilaterals

and its types through Tangrams.

In Pre content 2 (P2), the students try to find out how and where geometry exists

around us.

The focus on the warm up and pre content activities shall be to refresh the previous

knowledge of the students so that they can comfortably build up the new topic. The pre

content activities act as a bridge between the previously learnt concepts and the new

concepts to be studied.

The content worksheets from C1 through C26 aim at achieving the above stated

learning objectives. Not only shall the students learn the basic concepts of geometry,

they shall be encouraged to find how closely and beautifully mathematics is related to

their daily lives. The teacher may encourage them to make projects where they can

appreciate the applicability of geometry in real life.

Further the post content activity (PC1)is designed to assess the students’ understanding

of the concepts learnt in the chapter. The post content worksheet 2 is an assessment test

to test the concepts learnt in totality. It is not included in the students’ Worksheets. The

teacher may use it as a timed test by giving print outs to students.

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Activity – Skill Matrix

Activity Name of the activity Skills learnt

Warm up (W1)


Application of geometry in

art

Warm up (W2) Geometry crossword Knowledge and

understanding

Warm up (W3) Lines and angles Knowledge and

understanding

Pre content (P1) Tangrams Understanding by doing

Pre content (P2) Class Mosaic Understanding by doing

Content worksheet (C1) Open and closed

shapes Learning by doing

Content worksheet (C2) Understanding polygons Knowledge and

understanding

Content Worksheet (C3)

Regular and irregular

polygons

Knowledge and

understanding

Content Worksheet (C4) 2 D shapes Observation skills

Content worksheet (C5)


Knowledge and

Geometrical skills

Content Worksheet (C6) Classification of triangles1 Knowledge and

Understanding

Content Worksheet (C7) Classification of triangles 2 Representation skills

Content Worksheet (C8) Types of Triangles Diagrammatical and

geometrical understanding.

Content Worksheet (C9) Classification of triangles 3 Knowledge and

understanding

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Content Worksheet (C10) Types of Quadrilaterals 1 Knowledge and

understanding

Content Worksheet (C11) Types of Quadrilaterals 2 Understanding and

geometrical skills

Content Worksheet (C12) Types of Quadrilaterals 3 Analytical skills

Content Worksheet (C13) Types of Quadrilaterals 4 Exploration skills

Content Worksheet (C14) Interior angles of polygons Activity based learning

Content Worksheet (C15) Types of Quadrilaterals 5 Knowledge and geometrical

skills

Content Worksheet (C16) Polygon capture Reasoning skills

Content Worksheet (C17) Visualizing solid shapes geometrical skills

Content Worksheet (C18) Nets of 2D and 3D objects geometrical skills

Content Worksheet (C19) Nets of curved objects geometrical skills

Content Worksheet (C20) Solid Shapes 1 Observational skills

Content Worksheet (C21) Solid shapes 2 Knowledge and application

skills

Content Worksheet (C22) Symmetry 1 Analytical skills

Content Worksheet (C23) Symmetry 2 Analytical skills

Content Worksheet (C24) Symmetry 3 Learning by doing

Content Worksheet (C25) Symmetry 4 Application and drawing

skills

Content Worksheet (C26) Symmetry 5 Application and drawing

skills

Post Content Worksheet

(PC1) Extended Practice

Knowledge and self

learning

11

WARM UP ACTIVITY W1

Geometry on the Floor

Objective– Teacher gives and solicits a brief description about Rangoli a famous art

form of India.

Pre preparation – Teacher will give an isometric dot paper to each student to practice.

Description- Teacher models by joining a set of 6 dots and create a star shape on it.

Students practice along with the teacher and then try some on their own.

.

Follow up – Students complete the design on their own and display the same in the

class.

WARM UP ACTIVITY W2

Geometry Crossword

Objective– Recall of the basic geometrical words and concepts done till class V.

Description- Students solve the crossword puzzle by using the clues given below. This

can be done in pairs.

Follow up-Teacher cross checks the answers and reinforces important words once again

and reinforces the importance of using the correct words for effective communication in

mathematics.

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WARM UP ACTIVITY W3

Lines and Angles

Objective– Recall of the basic geometrical words and concepts they have done

till class V.

Description- Students do the worksheet which is a recap of all terms and concepts done

in class V like definitions of angles, lines etc. This also checks their understanding of

formation of angles

PRE CONTENT WORKSHEET P1

Tangrams

Specific Objectives – To recall shapes learnt on the basis of the number of sides.

Material Required –Cartridge sheets, ruler, scissor.

Pre preparation – Teacher will ensure that the material is available and each student

knows the safety precautions working with scissors.

Description – Teacher in a play way method acquaints students of the different shapes

which they see around them. The teacher induces students to think about the number of

sides based on which the shapes will be classified.

Follow up: As a fun activity teacher asks students to rearrange the shapes cut out to

form a square again. The teacher may extend the activity to the other shapes.

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PRE CONTENT WORKSHEET P2

Class Mosaic

Objective – Identify different shapes and create a mosaic which is aesthetic to look at.

Material needed- Colored papers, cartridge sheets, crayons, scissors, glue.

Description – Teacher allows students to recall, identify and collect objects of different

shapes and sizes, classify them based on their sides and then create mosaics of various

shapes and patterns.

Follow up-Teacher goes around the group’s work and facilitates mathematical thinking

putting up probing questions related to shapes , symmetry and color coordination.

CONTENT WORKSHEET CW 1


Material required: Computers in computer lab

Specific objective - Identify and differentiate between closed and open shapes using

microsoft paint .

Description - Through this activity, teacher helps students to derive the meaning of

open and closed curves while the students work on the MS paint. This allows the

students to actually test, verify and later visualize why a particular shape is closed or

otherwise.

Execution -Students follow instructions given by the teacher and try to justify how and

why the shapes are known as closed or open curves.

Follow Up-Teacher intervenes where required while students are working with

Microsoft paint and ensures that all students have understood the difference between

open and closed and are able to communicate the same .

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Material required: Online dictionary

Specific objective-Define a polygon with special emphasis on the root word.

Description-To acquaint students with mathematical words, and their origin. Through

this activity, teacher directs the students to refer to the online mathematics dictionary

and define the term Polygon with special focus on the root words and their origin. This

shall also act as a precursor to understand the meanings of different types of polygons.

Follow up-The students will then tabulate their meanings and complete the

corresponding worksheet


Regular and Irregular Polygons

Objective – Observe and define regular and irregular polygon, simple and complex

polygons.

Description – This is an induction activity where teacher derives the meaning of the

words irregular and regular polygons complex and simple polygons. Teacher will

familiarize the students with these terms by asking them to draw and think of shapes

which they see around them.

15

Execution - Teacher notes down all observations put up by the students and then

develops the definitions of regular, irregular, simple and complex polygons.

Follow Up- Students complete the activity and teacher checks for errors in

communicating the meanings of simple, complex, regular, irregular polygons by the

students. Teacher should ensure that students use proper mathematical terms while

defining the terms.


2D Shapes

Objective – Students consolidate their understanding of polygons by doing this quiz.

Description: The quiz in an unconventional manner ensures that the students have

learned and visualized the different types of polygons. The students are required to

answer on the basis of clues given. This is followed by another puzzle with different

polygons for the students and students to classify them based on the number of sides

each has. Some words are given and using some clues students are required to complete

the puzzle.

16

Execution- This could be a group activity and the group which gives the correct answer

scores points.

Follow up- Students watch video clip 2 as a closure which talks about different types of

quadrilaterals based on their sides. .



Specific Objective –Students consolidate their learnings of the content learnt so far

Description – Students work on the worksheet which checks understanding about

different types of polygons in the class and complete the same at home.

Follow Up: Teacher discusses the worksheet by asking students to communicate what

they have done and intervene where required.



Objective - To acquaint students with the types of triangles based on their sides.

Activity – 1 : Understanding triangles.

Material Required – Cut outs of different types of triangles, tracing paper

Description –

17

Through this inductive activity, teacher creates knowledge about the different types of

triangles based on the measurement of their sides. Based on what they have researched,

students answer the corresponding worksheet wherein some clues are given based on

which students write the names of triangles in question number 1.

In question 2, students create different types of triangles using drinking straws and then

measure the sides and identify the triangle created. They then answer some questions

based on perimeter and the triangles which can be created by the same perimeter and

their corresponding names.

Execution –Students follow the instructions given by the teacher and answer the

questions put up by her. They also record what they observe in their notebooks.

Follow up – Teacher allows students to communicate their deductions about the

triangles in the class. She/he may want to give alternate ways of doing the activity to

students finding it difficult to overlap/superimpose. Some students find difficulty in

folding sides from vertex they can cut out and separate the three sides of triangle, place

those over each other one by one to verify as shown below.

Use a ruler and measure the three sides to verify the same

Repeat the above step(s) for all three triangles.

Record the observations.

She then asks all to verify their findings by measuring the sides of the triangle cutouts.

The students are allowed to solve the questions that follow for more clarity.

18



Activity 2 – Understanding triangles

Objective - To acquaint students with the types of triangles based on their Angles

Material Required – Cut outs of different types of triangles, tracing paper.

Description:

After a warm up session where teacher recalls various types of angles through hand

gestures and movements, the students then try to guess the measures of the angles of

the triangle given and then verify their answers by measuring. They are then

encouraged to find out the names of these triangles using a dictionary thus using

different techniques to reinforce the meaning of different types of triangles.

Execution-Students follow the directions of the teacher and show evidence of their

understanding by responding to the questions posed by the teacher. They show the

correct measurements and record the same in their notebooks.

Follow up: Teacher discusses students’ responses and guides them to use the correct

terminology and logic. She wraps up the class followed by a video clip as closure.

Students watch Video clip 3 to reinforce the concepts learnt which talks about the

different types of triangles based on their sides and measures of the angles.

19


Types of Triangles

Activity 3 :

Specific Objective - Reinforce the types of triangles and looking for a connection in the

two.

Material Required Geo dot paper, scissors, protractor .

Description –

Through this activity students re-acquaint themselves with different type of triangles

using the geo-board as a manipulative. This acts as an aid for visual and kinesthetic

learners. The students then answer some questions based on their observations and

tabulate the same in the corresponding activity worksheet.

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Execution-Students follow the instructions of the teacher and try to complete the table

given.

Follow Up-Teacher to give them as many as different types of triangles to draw

conclusions as well as encourage the students to draw as many logical conclusions from

this activity. Students note down their observations and teacher wraps up the activity

by rephrasing the conclusions.



Objective - Recapitulation of the work done in content C2.1.

Description - This is a recapitulation worksheet to make students recall all the concepts

learnt in content C2.1. Teacher will ask students to do the work as directed.



Objective – Acquaint students to geometrical terminology.

Description- Through this activity, Teacher acquaints students of names of different

shapes and helps them define them using a dictionary.

Execution - Students will complete the

maze and then write the definitions

using the online dictionary.

Follow up- Teacher discusses the

solutions and students showcase their

ability to write the definitions.

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Objective – Acquaint students to geometrical names and shapes of different types of

quadrilaterals

Description- This is a share and pair activity in which teacher defines different types of

polygons. Special attention is paid to the root words for the names of the polynomials,

by referring to the dictionary. The quadrilaterals are then displayed on the board and

Students are allowed to identify and name the various quadrilaterals that observed

which is again followed by a cryptic clue puzzle which is further extended by

completing a puzzle on quadrilaterals.

Execution - Students follow directions of the teacher and then display their work for all

to see. They also talk about the name of their quadrilateral

Follow Up - Students look for the words in this word maze and then write down the

definitions of each of them in their notebook



Activity 3– Classifying quadrilaterals

Specific Objective – Students classify quadrilaterals using a flow chart teaching them

an important tool of decision making.

Material required: A cut out of a quadrilateral and a flow chart to refer to.

Description- In this activity teacher uses cut outs of different quadrilaterals and a flow

chart as a graphic organizer to classify the quadrilaterals.

22

FLOW CHART

Execution- Students follow instructions and try to identify the quadrilateral which they

have. Students then exchange their quadrilateral with their partner and repeat the

procedure again.

Follow up-Students list characteristics about the shape of the quadrilateral, based on

the observations.



Activity 4– Classifying quadrilaterals

Specific Objective –Students classify quadrilaterals using a venn diagram teaching

them an important tool of decision making.

23

Description- Students Watch video clip 4 on special types of quadrilaterals followed

by the discussion using the venn diagram. They then observe the following figure

carefully and make correct geometrical statements:

Execution- Students watch video clip 4 and then answer questions looking at the venn

diagram. They then complete the table and check for geometrical logic.

Follow Up-Teacher checks for understanding and students’ skill of communicating

their arguments logically


Interior Angles of Triangles and Quadrilaterals

Specific Objective-Students investigate the angle sum property of a triangle and a

quadrilateral.

Description-In this very physical activity teacher allows students to investigate the sum

of the three angles of any triangle. Once students are able to identify the sum of the

three angles of a triangle, they are allowed to explore the sum of the interior angles of a

quadrilateral.

24

Execution- Students follow the directions of the teacher and try to complete the activity.

Teacher keeps the group focused by asking probing questions. They then solve some

problems based on the activity done.

Follow Up-Based on the activity done students try to conclude the outcome for the

interior angles of a quadrilateral.



Specific Objective- Students test their understanding and consolidate the skills

acquired by doing this worksheet.

Execution- Students complete the task allotted to them independently.

Follow Up- Teacher checks for understanding and skill of communication by asking

students to explain the task done. Teacher checks for accuracy and intervenes where

required.

25


Polygon Capture

Specific Objective- Students test their understanding and consolidate the skills

acquired by playing this game.

Preparation- Before playing the game, cards are cut out on the Polygon Captultre

Game Cards sheet. They have to be arranged in such a way that the adjacent sides

have the solution it the question. The teacher may draw the resultant figure to be

obtained on the board. Following is the answer figure.

26



Specific Objective - Students observe and then visualize different solids around them

Material required: Isometric dot paper.

Description-Through this activity teacher models and instructs students to join the

appropriate dots to make the given figures.

For example:

Shape 1 Shape 2

Execution - Each student works independently, explore and try to, get the shapes right.

27


Nets of 2D and 3D Objects

Specific Objective-Students explore, observe and then create nets of some regular

solids.

Material required: Isometric dot paper, a closed box made of cardboard, some solids to

display for the students to visualize.

Description - This is a deductive activity. Through this activity students explore solids

by opening up a cubical box to visualize the net of a cube. This enables them to see the

2d cardboard being changed into a sol.id shape. They will then be encouraged to create

nets of different simple solids which they have seen before.

Execution - Each student works independently, explores and tries to, get the shapes

right.

28

Follow up- Teacher checks for understanding of the task by going around and

intervene where required. Teacher then asks students to mention the 2D shapes used to

make 3D objects in each of the shapes given above.


Nets of Curved 3D Objects

Specific Objective-Students explore, observe and then create nets of some curved 3D

objects as well. Use online dictionary to name the solids so formed.

Material required: Nets of some solids. .

Description- This is an explorative hands on activity. Teacher instructs students to cut

out and use the following nets and try to convert them into 3D objects without any

further modifications. They are then encouraged by the teacher to use the math online

dictionary to name these solids and complete the corresponding worksheet on 3d

solids.

Execution- Students watch video clip 5 and follow the teacher’s directions and create

solids by folding the nets. They then refer to the online dictionary and name their

solids.

29


Solid Shapes 1

Specific Objective-Students explore, observe and then answer some questions based on

the shape of the solids under consideration.

Material: Some solids on display for students of different learning styles to analyze

the solids.

Description- In This exploration activity, teacher keeps a solid before the students

and guides them to be able to identify the face, edge and the vertices of a solid by

asking questions and leading students to the correct answers by hand gestures and

actions. The students are then encouraged to look for the edges, vertices and the

faces of different solids which are given in the corresponding worksheet.

Execution-Teacher models the term under considerations and students follow

instructions to answer the questions put up by the teacher. They then try to work

independently and complete the table.

30


Solid Shapes 2

Activity1 – Independent practice

Description - Students test their understanding and consolidate the skills acquired by

doing this worksheet.



Symmetry 1

Specific objective- Warming up with this riddle for out of box thinking. Solve this

riddle

Description- Students are asked to give the answer to an open ended riddle. The

answer to the riddle will encourage students to think of out of the box answers and

would be acceptable if the students is able to provide a plausible justification. This also

allows students to visualize mirror images (halves)

31

Execution- Teacher allows students to give their responses without giving any

affirmation. Students counter each other and discuss the logic of their answer with the

group.

Follow up- Students explore similar, various things and numbers when they are

divided in half but in an unusual manner.


Symmetry 2

Specific objective- Warming up with this riddle for out of box thinking and initiate the

concept of mirror images and symmetry .

Description- In this pattern finding activity, teacher asks students to solve the riddle by

looking for a pattern.

The teacher introduces the word mirror image and models the same to the student to

see her view point. This is followed by video clip 7 to introduce Symmetry and use the

online dictionary to complete the corresponding worksheet wherein they have to write

the etymology of the word symmetry and give some examples.

Execution- Students answer the questions that follow, after listening to the teachers

instructions followed by watching the video.

32

Follow Up- Teacher encourages all of them to answer and monitor their thinking. This

is followed by playing this game wherein you hand in the correct shape to Pablo to

complete his Robot.

http://www.bbc.co.uk/schools/ks1bitesize/numeracy/shapes/fs.shtml


Symmetry 3

Specific objective- Find symmetry and the lines of symmetry by cutting and folding.

Description- In this activity teacher encourages students to cut out each of the shapes

given in the corresponding worksheet and then fold to look for the lines of symmetry

and then write the lines of symmetry for each shape.

Execution- Students follow the teacher’s directions and then write their answers.

Follow up- Teacher monitors and checks for understanding about symmetry and lines

of symmetry.

http://www.bbc.co.uk/schools/ks1bitesize/numeracy/shapes/fs.shtml

33


Symmetry 4

Specific objective- Find the lines of symmetry using a mirror and then completing the

shape using the properties of symmetry.

Material Used: Blank sheet of paper and a mirror.

Description-Through this hands on activity, the teacher demonstrates the use of the

mirror to “see” the reflection of one’s name and reflect the same.

Execution- Students follow the teacher’s directions and complete the set task. Now

based on what they have learnt, students reflect half of the raccoon face to make a

complete raccoon face using a mirror. The teacher, if required, provides support to the

students as needed while the students work on this task.


Symmetry 5

Specific objective- Students consolidates their learnings about symmetry through this

independent work.


34

Follow Up- Teacher checks for understanding and skill of communication and by

asking students to explain the task done. Teacher checks for accuracy and intervenes

where required.

POST CONTENT WORKSHEET PCW 1

Objective: To Practice the concepts learnt in the chapter in totality.

Pre Preparation: Teacher will prepare the comprehensive worksheets of the chapter.

Description: Teacher will hand out the worksheets to the students

Follow up: Teacher will assess level of her students on the basis of the post content

worksheets PCW1 and give remedial wherever required.

Note for the teacher:

1. Students weak at the concepts must be given the enough practice through the basic

worksheets and then post content worksheets may be given to them.

2. Students who have grasped the concepts very well and are able to solve regular

problems quite easily may be advised to move to extension activities.

35

ASSESSMENT OF THE CHAPTER

Name of the student ______________________ Date ___________

1. State whether the adjacent figure is a polygon. If it is, identify the polygon and state

whether it is convex or not. If it is not, explain why.

2. State whether the following figure is a polygon. If it is, identify the polygon and

state whether it is convex or not. If it is not, explain why.

3. A polygon can be either convex or concave. Draw an example of each Show how

the diagonals test or the line test is used to illustrate the convexity or concavity of

your polygons.

4. Can a slice of pizza be considered a polygon? Explain.

5. Tell whether the dotted line on each shape is a line of symmetry. Write yes or no.

Explain why do you think so?

36

6. Describe this shape.

7. What shape am I? I am three-dimensional. I have 6 faces and 8 vertices. All my faces

are rectangles. I can be stacked.

I am a

8. Draw 2 two-dimensional shapes that are exactly the same (congruent).

9. The diagram shows an eight sided figure.

a) What special name is given to this shape?

b) Write the name of line segments which are parallel to each other.

c) Into how many triangles can this shape be triangulated?

d) What is the sum of the interior angles of this shape.

37

e) Measure accurately angle F. What type of

angle is angle F?

10. The grid shows a triangle. Measure the angles

of the triangle. What special name do you

give to this triangle?

11. Are these statements true or false?

a) A parallelogram is never a square.

b) A square is always a rectangle.

c) A rhombus is never a square.

d) A trapezoid is a parallelogram.

e) A parallelogram has one set of opposite sides.

f) A rectangle has four right angles.

g) A rhombus always has four equal sides.

12. Measure the angles in each case and add up the

three angles so obtained. Write what do you

observe.

13. What Shape Am I?

38

14. Polygon G has k sides. How many diagonals can be drawn inside of polygon G?

15. Briefly and in your own words describe the properties of a polygon.

16. A square is a special kind of rhombus. What makes it special?

17. Identify each of the following polygons. You may want to try describing them with

more than one term.

In the blank box draw a polygon of your choice.

18. Draw reflections of the images along the reflection lines shown.

39

19.

20. Three angles of a Quadrilateral are 100o, 50o, 60o. Find the measure of the fourth

angle of the quadrilateral.

40

Sample Assessment Rubric -

Parameter 0 1 2 3 4

Ability to define and identify different types of polygons.

Ability to define a regular polygon and apply properties of polygon to solve simple problems

Can make no sense of what a polygon is. Is unable to recognize and define it.

Can recognize a closed figure but cannot recognize a polygon from a curve.

Can recognize and define a polygon but finds it difficult to communicate his ideas. Can tell the property of a polygon.

Can identify and define a polygon. Can understand and recall the various polygons from its root words and properties of polygons and apply it to problems.

Can define a polygon using appropriate words and justify his explanations Can understand and apply the properties of polygons in different problems, with proper sketches and plan of action with accuracy and helps his peers to understand too.

Ability to define and identify triangles as a polygon with 3 sides, Ability to classify triangles based on the sides and angles. Ability to Extend this

Can recognize a triangle but cognition does not go beyond this. Cannot measure sides and angles and can no make no sense of

Can define a triangle but is unable to name its elements accurately. Can measure but not accurately and gets mixed up with the types of triangles. Is

Can define a triangle and types of triangles. Can classify triangles with some guidance. Cannot extend and integrate two concepts to solve simple but higher level

Can define the triangle and types of triangles. Can classify triangles by sketching and labeling information, analyze the information and solve problems with a proper plan

Can define a triangle and its types. Can extend properties to problems and come up with a suitable alternate plan of action independently with appropriate justifications for all the

41

to know more properties of triangles

different types of triangles.

unable to associate the word to its root word for clarity.

problems. of action after some guidance.

solutions. Presents a well organized work and helps his peers in understanding too.

Ability to define and identify different types of quadrilaterals and classify them. Ability to Use properties of quadrilaterals to simple problems.

Can Recognize a Quadril-ateral but cognition does not go beyond this. Cannot measure sides and angles and can not make sense of different types of Quadril-aterals.

Can define a Quadrilateral but cannot name its elements accurately. Can measure but not accurately and gets mixed up with the types of Quadril-aterals.

Can define a quadrilateral and types of quadrila-terals. Can classify quadrila-terals with some guidance. Cannot extend and integrate two concepts to solve simple but higher level problems.

Can define the quadrilateral and types of quadrila-terals and show the same with the help of a flow chart or a venn diagram. Can justify the statements related to quadrila-terals with a little guidance and use of manipul-ative, use information, analyze the information and is able to solve problems with a proper plan of action

Can define a Quadrilateral and its types using a flow chart independently.. Can extend properties to problems and come up with a suitable alternate plan of action independently with appropriate justifications for all the solutions. Presents a well organized work and helps his peers in understanding too.

42

after some guidance.

Ability to define 2D and 3D objects. Ability to Identify the different types of solids.

Ability to find its vertices, faces and edges

Can locate 2D and 3D shapes but cannot explain why they are referred to as such. Cannot create models and has no cognition about the faces, vertices and edges of a solid.

Can identify, and understand 2D and 3D shapes and classifies them easily. Can Make models of the solids but needs a lot of assistance. Due to Poor eye –hand coordination, cannot differentiate between face, vertex and edge

Can define, classify 2D and 3D shapes and can relate to them. Can create straw and paper models using templates and answer questions by using them physically. Can use the net, but cannot recognize the solid by just looking at the net.

Can define, classify 2D and 3D shapes and can relate to them. Can

create straw and paper models using templates and answer questions by drawing them, Can identify a net of a solid by drawing the solid.

Can define, classify 2D and 3D shapes and can relate to them. Can

create straw and paper models using templates and answer questions by drawing as well as visualizing them. Can identify and draw a net of a solid by visualizing the solid with appropriate justifications

Abilty to define and identify symmetry and lines of symmetryAbility to understand Reflection symmetry and its property.

Can identify symmetry but cannot draw the same. Cannot locate the lines of symmetry easily. Under-stands reflective symmetry and draws

Can identify symmetry but is unable to draw the same. Can locate the lines of symmetry easily. Understands reflective symmetry and draws the shapes with a reasonable

Can identify the symmetry easily by drawing the shape. Is able to identify the different lines of symmetry and can explain the rule of reflection on a geo dot

Can identify the symmetry easily by drawing the shape. Is able to identify the different lines of symmetry and can explain the rule of reflection using a geo

Can visualize and identify symmetry and the lines of symmetry accurately. Is able to explain the reflection symmetry without the aid of geo dot paper and mirror.

43

the shapes with a very immature under-standing.

level of logic.

paper with a lot of guidance.

dot paper accurately with a high level of maturity.

44

STUDY

MATERIAL

45

Understanding Shapes - 2D and 3D

1. Introduction

In the previous chapter, you were introduced to some basic concepts of geometry

including open and closed curves as well as curves which are simple and not

simple. We also discussed polygons as simple closed curves made up of line

segments only.

In this chapter, we shall first review these concepts and then discuss more of

polygons with special reference to quadrilaterals and triangles. We shall also

extend this study of 2D figures to some familiar 3D figures (shapes) such as

prisms, pyramids including cuboids, cubes, cylinders, cones, etc.

Finally, we shall study symmetry of plane figures with respect to a line.

2 Open and closed curves – a Review

Closed curves: If we place a tip of a pencil on any point on a curve, starting

from this point and going along the curve, we can reach the same point

without retracing the path, then the curve is known as a closed curve, For

example, curves (i), (ii) and (iv) (Fig. 1) are closed curves, while (iii) and (v)

are not closed curves (why?).

Fig. 1

Open curves: A curve which is not closed is known as an open curve. Thus,

curves (iii) and (v) in Fig. 1 are open curves.

46

Simple curves: A curve that does not intersect itself is known as a simple

curve. For example, curves (i), (ii) and (v) in Fig. 1 are simple curves,

whereas curves (iii) and (iv) are not simple curves.

Simple closed curve: A curve which is simple as well as closed is known as a

simple closed curve.

For example, in Fig. 1, (i) and (ii) are simple closed curves, whereas curve (iv)

is a closed curve but not simple.

Example 1: Classify the following curves as (a) closed curves (b) open curves (c) simple

curves (d) simple closed curves:

Fig. 2

Solution:

(a) Closed curves : (ii), (iii), (iv), (vi), (viii), (ix) and (x)

(b) Open curves : (i), (v) and (vii)

(c) Simple curves : (i), (ii) (iii), (iv), (v), (vi), (viii), (ix) and (x)

(d) Simple closed curves : (ii), (iii), (iv), (vi), (viii), (ix) and (x)

47

3 Polygons

Recall that a simple closed curve made up of line segments only is called a

polygon.

For example, curves in (i) , (ii) and (vii), in Fig. 3 are polygons, whereas curves in (iii),

(iv), (v), (vi) and (viii) are not polygons (why?).

Fig. 3

Convex and Non-convex Polygons

Recall that polygon like as in (i) is called a convex polygon, whereas polygons

like as in (ii) and (vii) (Fig. 3) are not convex polygons.

In case of a convex polygon, if you take any two points P and Q in the interior of

the polygon, then the entire line segment PQ lies in its interior. But in case of a

non-convex polygon, it is not so. (See Fig. 4 below).

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Fig. 4

A non-convex polygon is also called a concave polygon. From now onwards, we

shall use the word ‘polygon’ to mean a convex polygon, unless stated otherwise.

Types of Polygons

Polygons may be classified based on the number of sides.

A polygon of 3 sides is called a triangle,

a polygon of 4 sides is called a quadrilateral,

a polygon of 5 sides is called a pentagon, and so an. (See the table below)

Number of sides Name of polygon Illustration

3 Triangle

4 Quadrilateral

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5 Pentagon

6 Hexagon

7 Septagon or

Heptagon

8 Octagon

9 Nonagon

10 Decagon

50

Regular Polygons:

A polygon whose all angles and all sides are equal is called a regular polygon.

For example, following are regular polygon (Fig. 5):

Fig. 5

Following polygons are not regular (Fig.6), why?.

Fig. 6

51

Example 2: Write the name of the polygon for each figure :

Fig. 7

Solution: (i) Septagon (ii) Triangle (iii) Quadrilateral

(iv) Quadrilateral (v) Triangle (vi) Hexagon (vii) Pentagon (viii) Octagon.

4 Triangles and their types

Recall that a triangle is a polygon of 3 sides, i.e. a polygon of least number of

sides, Triangles can be classified in two ways:

(a) According to Sides

A triangle having all three unequal sides is

called a scalene triangle [Fig. 7(i)]

A triangle having two equal sides is called an

isosceles triangle (Fig. 7(ii)).

52

A triangle having all three equal sides is called an

equilateral triangle [(Fig. 7(iii)]

F

i

g

.

Fig. 7

(b) According to Angles

A triangle whose each angle is less than 90°, i.e.,

each angle is an acute angle, is called an acute

angled triangle or acute triangle (Fig. 8(i)).

A triangle whose any one angle is of 90°, then the

triangle is called a right angled triangle or right

triangle. (Fig. 8(ii)).

A triangle whose any one angle is greater than

90°, then the triangle is called an obtuse

angled triangle or obtuse triangle (Fig.

8(iii)).

Fig. 8

53

Example 3: The lengths of the sides of triangles are given below. Classify them as

scalene, equilateral or isosceles.

(i) 4 cm, 5 cm,, 8 cm

(ii) 11 cm, 11 cm, 11 cm

(iii) 8.7 cm, 7.2 cm, 11 cm

(iv) 9 cm, 12 cm, 9 cm

(v) 2.3 cm, 3.1 cm, 2.3 cm

(vi) 3.4 cm, 5 cm, 6 cm

Solution:

Scalene: (i), (iii), (vi)

Isosceles: (iv) , (v)

Equilateral: (ii)

An important Note!

An equilateral triangle is also considered as an isosceles triangle because of its definition

but not conversely. In this sense, triangle in (ii) is also an isosceles triangle.

Example 4: Classify the triangles whose angles are given below :

(i) 40°, 50°, 90°

(ii) 60°, 60°, 60°

(iii) 35°, 45°, 100°

(iv) 45°, 45°, 90°

(v) 45°, 40°, 95°

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Solution:

Acute angled – (ii)

Right angled – (i), (iv)

Obtuse angled – (iii), (v)

You can verify that in an isosceles triangle, angles opposite equal sides are equal and if in

a triangle, two angles are equal, then sides opposite equal angles are also equal.

Also, in an equilateral triangle, all angles are equal as all sides are equal.

Classify each of the following triangles in two different ways. One is done for you.

5. Quadrilaterals and Their Types

Recall that a quadrilateral is a polygon of four sides

(Fig.9). There are many types of quadrilaterals.

Trapezium: A quadrilateral in which a pair of

55

opposite sides is parallel is called a trapezium.

In Fig. 10, ABCD is a trapezium in which

AB||CD.

You can verify by measurement that

A + D = 180° and B + C = 180°.

Parallelogram: A quadrilateral in which both

the pairs of opposite sides are parallel is called

a parallelogram. In Fig. 11, PQRS is a

parallelogram in which PQ||SR and PS||QR.

You can verify by actual measurement that

PQ = SR and PS = QR.

Also, P = R and Q = S.

Rectangle: A rectangle is a special type of a parallelogram in which one angle

is a right angle. In Fig. 12, ABCD is a rectangle in which AB||DC, AD||BC

and A = 90°.

You can check by actual measurement that

A = B = C = D = 90°. Also, AB = DC and AD = BC.

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Rhombus: A rhombus is a special type of a

parallelogram in which a pair of adjacent sides is

equal. In Fig. 13, MNPQ is a rhombus in which

QM = QP, MN||QP and MQ||NP.

You can verify by actual measurement that

MN = NP = PQ = QM.

Also, M= P and N = Q.

Square: A square is a quadrilateral which is a rectangle

as well as a rhombus.

In Fig. 14, ABCD is a square, because it is a rectangle as well as a rhombus.

That is, AB||DC, AD||BC, A = B = C = D = 90°

and AB = BC = CD = DA.

Example 5: State whether the following statements are true or false:

(i) The opposite sides of a trapezium are parallel.

(ii) All the sides of a rhombus are equal.

(iii) A square is a parallelogram.

(iv) A parallelogram is a rhombus.

(v) Each angle of a rectangle is of 90°.

(vi) A square is a special type of a rectangle.

(vii) All angles of a rhombus are equal.

(viii) In a parallelogram, each pair of opposites sides are equal.

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Solution:

(i) False, as in general only one pair of opposite sides is parallel.

(ii) True

(iii) True

(iv) False, a rhombus is a parallelogram but not conversely.

(v) True

(vi) True

(vii) False, only in some cases, opposite angles are equal but not in general.

(viii) True

Example 6: State whether the following statements are true or false:

(i) A rectangle is a regular polygon.

(ii) A square is a regular polygon.

(iii) A rhombus is a regular polygon.

(iv) A polygon is regular if its all sides are equal

Solution:

(i) False. All angles of a rectangle are equal but all sides are not equal.

(ii) True. All angles and all sides are equal.

(iii) False. All sides are equal but all angles are not equal.

(iv) False. For a polygon to be regular, all sides as well as all angles have to be

equal.

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6 Three Dimensional Shapes (3D Shapes)

You have studied so far about polygons such as triangles, quadrilaterals,

pentagons etc. All these shapes wholly lie in a plane.

Such shapes are called two dimensional shapes. (2D shapes or plane figures).

Thus, a triangle, rectangle, rhombus, square, pentagon etc. and even a circle are

2D shapes.

Look at the following shapes which you see in day to day life.

(Fig. 15)

You can see that each of them does not wholly lie in a plane.

Such shapes are called 3D shapes (or solid shapes or solid figures).

They are given special names like cuboid, cube, cylinder, cone, sphere, prism, pyramid

etc.

59

Cuboid

Look at the shape in Fig. 16.

It is called a cuboid.

It is made up of 6 rectangular regions called its faces.

So, it has 6 faces. Opposite faces of a cuboid are

equal in size.

Two faces meet in a line segment called edge of the cuboid.

See that there are 12 edges.

Three edges meet in a point called a corner or vertex.

See that there are 8 vertices (plural of vetex).

Thus,

a cuboid has : 6 faces, 12 edges and 8 vertices.

Cube


It is called a cube.

A cube is a special type of a cuboid in which all the edges are

equal. Clearly, all its faces are squares of the same size.

Thus,

60

A cube has 6 faces, 12 edges and 8 vertices.

Prism


It is a prism.

It is made up of two triangular faces of equal size and three rectangular faces. It is a

special type of prism called triangular prism. See that a triangular prism has 5 faces, 9

edges and 6 vertices.

In general, in place of two triangular faces of equal size, a prism can have any two

polygonal faces of equal size.

If these faces are pentagonal, then prism is called a pentagonal prism. If these faces are

hexagonal, then it is called a hexagonal prism etc.

Note that cuboid is also a prism, a cube is also a prism.

Cylinder


It is called a cylinder.

It is made up of two circular faces and one curved surface.

A cylinder has two circular faces, one curved surface and

two circular edges and no vertex.

A cylinder may be thought of as a prism whose base and top are circular (i.e.

polygon of infinitely many number of sides of equal size).

61

Pyramid

Look at the shapes in Fig. 20.

Each of them is a pyramid.

Shape (i) is made up of a triangular base, three more

triangles meeting at one vertex. It is called a triangular

pyramid or a tetrahedron.

It has 4 faces, 6 edges and 4 vertices.

Shape (ii) is again made up of 4 triangular faces meeting at

one vertex and a square base.

It is called a square pyramid.

It has 5 faces, 8 edges and 5 vertices.

A pyramid can have any polygonal face as its base. The other faces will be triangular

meeting at one vertex. Thus, if the base is pentagonal, then it is called a pentagonal

pyramid. If the base is hexagonal, then it is called a hexagonal pyramid.

62

Cone


It is called a cone.

It is made up of a circular face (called base) and a

curved surface. Thus, a cone has one circular face, one

curved surface, one circular edge and one vertex.

A cone may be thought of a pyramid whose base is circular (i.e. polygon of infinite

number of sides)

Sphere


It is called a sphere.

It has only curved surface, no edge and no vertex.

63

Example 7: Match the following:

(a) Cone

(b) Sphere

(c) Cylinder

(d) Cuboid

(e) Pyramid

64

Solution:

(a) (ii)

(b) (iv)

(c) (v)

(d) (iii)

(e) (i)

Example 8: Complete the table :

S.No. Shape Faces Edges Vertices Curved

Surface(s)

1. Cube 6 12 8 0

2. Cuboid - - - -

3. Cylinder - - - -

4. Triangular Pyramid - - - -

5. Triangular Prism - - - -

6. Square pyramid - - - -

7. Cone - - - -

8. Sphere - - - -

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Solution:

(2) 6, 12, 8, 0

(3) 2, 2, 0, 1

(4) 4, 6, 4, 0

(5) 5, 9, 6, 0

(6) 5, 8, 5, 0

(7) 1, 1, 1, 1

(8) 0, 0, 0, 1

7 Nets of 3D Shapes

Cuboid :

Look at the shape in Fig. 22. It is a 2D shape. Cut it out and fold it along the dotted

lines.

You will get a cuboid (3D shape).

The shape in Fig. 22 is called a net of a cuboid.

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Cube :


It is a 2D shape.

Cut it out and fold it along the dotted lines.

You will get a cube (3D shape).

The shape in Fig. 23 is called a net of a cube.

Triangular Prism


It is a 2D shape.

Cut it out and fold it along the

dotted lines.

You will get a triangular prism (3D

shape).

The shape in Fig. 24 is called a net of a triangular prism.

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Pyramid

Look at the shapes in Fig. 25(i) and (ii).

These are 2D shapes.

Cut them out and fold each along the dotted lines.

You will get a triangular pyramid (tetrahedron)

from (i) and a square pyramid from (ii).

The shapes in Fig. 25(i) and (ii) are called nets of

a tetrahedron and a square pyramid

respectively.

Cylinder

The shape in Fig. 26 is a 2D shape.

Cut it out and fold it along length so that two ends

coincide.

You will get a cylinder.

The shape in Fig. 26 is called a net of a cylinder.

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Cone

The shape in Fig. 27 is a 2D shape.

Cut it out and fold it (sector) so that two radii

coincide with each other.

You will get a cone.

The shape in Fig. 27 is called a net of a cone.

Suggested Activities

Make nets of the following 3D shapes:

(i) cuboid (ii) cone (iii) cylinder (iv) tetrahedron (v) cube (vi) triangular prism

(vii) square pyramid

(8) Symmetry

Symmetry Around Us

Look at the following pictures (Fig. 28) :

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These pictures look beautiful because of their ‘symmetry’. If you could fold a picture

along a line such that one part of the picture covers exactly the other part of the picture,

then we say that the picture is symmetrical with respect to line of folding. The line of

folding is called the line of symmetry (or the axis of symmetry) for the picture

(Fig. 29).

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This type of symmetry is usually referred to as line symmetry or linear symmetry.

Reflection and Symmetry

Let us place a plane mirror along the line of symmetry in each of the above

pictures. You will find that one part of the picture will appear to be the image of

the other part.

Because of this reason, the line symmetry is also called

the reflection symmetry.

Now look at the picture showing the reflection of the

English letter P in a plane mirror.

Clearly, the object (P) and its image ( ) are symmetrical

with reference to the mirror line. If the paper is folded, the

mirror line becomes the line of symmetry.

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Drawing and Identifying Lines of

Symmetry

(i) Look at the adjoining Fig.31.

(ii) If the figure is folded along the line m, then

one part covers the other part exactly. So, m

is a line of symmetry for this figure.

(iii) Look at the adjoining Fig.32.

In this case, by folding the figure in two different ways,

you will find that there are two lines of symmetry (i.e. l

and m) for the figure.

Thus, a rectangle has two lines of symmetry.

(iii) Look at the adjoining Fig.33 (square).

By folding the paper, you can find that there are four lines

of symmetry in this case. Thus, a square has four lines of

symmetry.

l

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(iv) Look at the adjoining equilateral triangle (Fig. 34)

By folding the figure in three different ways, you can find

that there are three lines of symmetry of an equilateral

triangle.

(v) Look at the circle given below: (Fig. 35)

By folding the circle along one of its diameters, you can

find that a diameter is a line of symmetry for the circle.

Since there are infinitely many diameters of a circle, so

there are infinitely many lines of symmetry for a

circle.

(vi) Look at the adjoining parallelogram (Fig. 36).

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Try to fold it in such a way that one part of the parallelogram covers the other part of the

parallelogram. Can you find any line of symmetry? No.

Thus, a parallelogram has no line of symmetry.

A plane figure which has no line of symmetry is called an asymmetric figure.

Example 9: Find the number of lines of symmetry in each of the following figures:

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Solution:

Example 10: Write the number of lines of symmetry for the following :

(i) Isosceles triangle (ii) Equilateral triangle (iii) A (iv) H (v) N (vi) E

(vii) Rhombus (viii) T

Solution: (i) One (ii) Three (iii) One (iv) Two (v) Zero (vii) One (vii) Two (viii) One

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STUDENT’S WORKSHEET – 1


WARM UP ACTIVITY W1

Name of the student ______________________ Date ____________

Activity 1- Geometry on the floor

Step 1 - Select a set of six dots as shown.

Draw three concurrent line segments passing through the six dots as shown.

Step 2 - Now join the three lines to dots as shown to see a star as shown.

This is a Chukkala (dot) Muggu( Rangoli) .To draw

this kolam, first draw 13 dots in the centre and then

go in the descending order on both sides then add

those chukkalu as per the final design, add colors to

it.

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STUDENT’S WORKSHEET – 2

Geometry cross word

WARM UP ACTIVITY W2

Activity 2- Cross word time

Instructions: Read the clues given below and then complete the crossword.

Across down

2. extends in one dimension, usually

represented by arrowheads

1. two lines that intersect to form a right

angle

4. extends in two dimensions,

represented by a shape that looks like

a table top

3. Consists of two different rays. They

have the same initial point

5. the point that divides or bisects a

segment into two congruent segment

6. lines that do not touch each other but

run right beside each other

7. angle measure 8. an angle with a measure equal to 90

degrees

9. where two rays come together to form

an angle 10. represented by a small dot

11. part between two points on a line 12. part of a line that consists of a point

12. device used to measure length of a

straight line

13. device used to measure angles

14. an angle with a measure equal to 180

degrees

15. one or more sets of lines that cross

each other

79

STUDENT’S WORKSHEET -3

Lines and angles

Warm Up WORKSHEET -3


1. Choose the most appropriate answer from the box to fill in the blanks:

a) Two lines that intersect and form a right angle are called _________.

b) In geometry, a ______________ extends endlessly in both directions.

c) A ____________________ is part of a line with two end points.

d) The symbol for a _________________ is a dot.

e) When you write and angle with three letters (angle ABC), the ___________ is

always the middle letter.

f) An ____________________ is greater than 900.

g) A __________________ measures 1800.

h) An __________________ is less than 900.

2. Are the pair of the angles shown below complementary or supplementary? Justify.

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(i) (ii)

Working space

3. Find the missing angle in the following figures:

d = _______________

Working space

81

4. Here is a list of words connected with angles:

Choose the correct word to describe each of these angles

5. Write down the pairs of parallel lines and perpendicular lines in the shape given

below:

Working space

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6. Find the angle measure between the hands of the clock in each figure:

9.00 a.m. 1.00 p.m. 6.00 p.m.

Working space

7. Where will the large hand of a clock stop if it

(a) starts at 12 and makes 2

1 of a revolution, clockwise?

(b) starts at 2 and makes 2


(c) starts at 5 and makes 4


Working space

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Student’s WORKSHEET 4

Tangrams

PRE-CONTENT WORKSHEET (P1)


Activity 1- Tangrams

1. Take a regular piece of paper (8.5 x 11) and fold the paper down to make a

triangle.

2. Now cut the rectangle at the bottom of the paper off.

3. Unfold the paper, and write what shape you see.

_____________________________________________________________________

4. Cut on the folded line, and write what shape you have now?

_____________________________________________________________________

5. Take one triangle; Bring one corner to opposite

corner to make 2 triangles. Unfold and cut on the

folded line.

6. These two triangles are a part of your puzzle.

Place them to the side.

7. Now take the other large triangle, and lay it

down, to look like a mountain, with a flat base

and a point.

8. Take the point and fold it to the bottom part of the mountain. Write what shape

you see.

_____________________________________________________________________.

9. Now cut the small triangle you created and write what shape you are left with.

Is there a special name to the shape which is left over? Observe the shape carefully.

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_____________________________________________________________________

10. Fold this shape (trapezium) in half. Cut on the folded line.

11. Now take one half of this shape, fold the long point to the other side.

What shapes do you see?

_____________________________________________________________________

12. Now cut on the folded line and Write the names of the two shapes.

13. Take the other half of the trapezoid and fold the corner on the same plane with the

long point. Write what shapes do you see?

_____________________________________________________________________

14. Unfold and cut on the folded line. Write what shapes did you get?

_____________________________________________________________________

15. Write the answer to the following question; The finished set now has

_________________________________________________________________________

_____________________________________________________________________

16. All of the seven pieces are needed for any tangram puzzle. Now try these in pairs:

a) In how many ways can you make a square with tangram pieces? Draw figure

to explain.

b) In how many ways can a rectangle be made with tangram pieces?

c) Make a square with all 7 tangrams pieces.

d) Make a square without using triangular pieces of tangram.

Paste all your material here

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Student WORKSHEET 5

Class Mosaic

PRECONTENT WORKSHEET P2


Activity 2- Make a class mosaic

Answer the following ;

1. What do you mean by a mosaic.

___________________________________________________________________

___________________________________________________________________

2. Observe around you and write the different shapes you see.

______________________________________________________________

3. Draw them in this workbook here .

4. Decide on a design of a mosaic which you want to create.

Remember your mosaic would be judged on:

Complexity of Shape

Neatness,

Number of different shapes used,

Colour coordination

Design/paste your mosaic here

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Student WORKSHEET 6

Open and closed shapes



Activity 1: Using Microsoft paint (open and closed shapes)

Instructions;

Copy the following shapes on paint.

Choose ‗fill with colour‘ tool and try to fill the above objects with any colour of your

choice.

What do you observe?

______________________________________________________________________ Can you

fill in the figure without changing the background color?

_______________________________________________________________________

Give reasons to justify your answer.

Record the observation and explain:

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Figure 1 and 4

______________________________________________________________________________

______________________________________________________________________________

_________________________________________________________________________

Figure 2, 3 and 5

______________________________________________________________________________

______________________________________________________________________________

_____________________________________________________________________________

Conclusion:

Figure 1 and 4 are _____________________.

Figure 2, 3 and 5 are ___________________.

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Student WORKSHEET 7

Understanding polygons 1

Content worksheet CW 2

Name of the student ______________________ Date _____________

Activity 2: Understanding polygons

Refer to the online math dictionary and define the term Polygon

What does the word ‗poly‘ mean?

______________________________________________________________________________

_________________________________________________________________________

What does the word ‗gon (gonia)‘ mean?

______________________________________________________________________________

_________________________________________________________________________

Define polygon:

______________________________________________________________________________

__________________________________________________________________________

What are the important things to observe for a polygon:

______________________________________________________________________________

__________________________________________________________________________

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Based on the definition justify if the following are polygons

Read this definition of polygon carefully and answer the following:

The examples of polygons are _______________________ because ___________________

_________________________________________________________________________

The figures ____________________ are not polygons because ______________________

_________________________________________________________________________

The figure below is not a polygon, since_________________________________________

Polygon is a Greek word. Different types of polygons must also get their names from

Greek.

Let us discover:

Find the meaning of the following words in Greek/Latin.

Tri, tetra, pent, hex, hept (sept), oct, Nona (or Ennea) and Deca

90

Working space

Now, Count the numbers of sides for each of the polygons given below and then name

them based on the word power:

Name the polygon.

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Student WORKSHEET 8

Regular and irregular polygons



Activity 3: Regular and irregular Polygons

Name the following polygons:

Give one point of similarity and one point of

difference between each of the following pairs

of polygons :

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Working space

On the basis of your observations define the following terms

Regular polygons

______________________________________________________________________________

______________________________________________________________________________

_________________________________________________________________________

Irregular polygons

______________________________________________________________________________

______________________________________________________________________________

__________________________________________________________________________

Simple and complex polygons

State one point of similarity and one point of difference between the following pairs of

quadrilaterals.

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Working space

Based on your observations define

Simple polygon

______________________________________________________________________________

______________________________________________________________________________

_________________________________________________________________________

Complex polygon

______________________________________________________________________________

______________________________________________________________________________

__________________________________________________________________________

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Student WORKSHEET 9

2 D Shapes



Activity 4: Shape quiz

1) Which shape has 3 sides?

2) Name the shape with 5 sides

3) Name a shape that has 4 straight equal sides

4) Which of the shapes has 7 sides?

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5) The shape with 4 unequal sides is called a …

6) An octopus has 8 arms, so an ________ has 8 sides

7) The shape with 6 sides is called a …

8) A tricycle has 3 wheels and a ________ has 3 sides

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Student WORKSHEET 10

Understanding polygons 2



Task 1: Test your understanding;

1. Given the following items, identify the polygon shape:

An exterior door ______________________________________________________

An eight-sided window _________________________________________________

A 12'' × 12'' floor tile ____________________________________________________

A six-sided deck _______________________________________________________

2. Name the following polygons:

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3. Decide which figures are polygons. If they are not, explain why??

Working space

4. A carpenter is preparing to install a window with five equal sides. This shape is

Heptagon Hexagon Pentagon Octagon

5. The sum of all of the sides of a stop sign is 96 inches. A stop sign is an octagon

with all sides equal. How many inches does each side measure?

6. If you multiply the number of sides I have by the number of sides in an octagon,

you will get 48. What polygon am I?

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7. If you add the number of sides that I have into the number of sides in a triangle,

you get 8 sides. What polygon am I?

8. The sum of my sides is 21 inches. Each of my sides measures 7 inches. Who am I?

9. Can you find a triangle in the picture below? A quadrilateral? A hexagon? Can

you find any other polygons in the picture?

Pompeii, Italy

99

10. Use the grid below to draw the following:

i) a 5-sided shape ii) a 6-sided shapes iii) a 7-sided shape

iv) an 8-sided shape v) a 9-sided shape vi) a 10-sided shape

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Classification of triangles 1



Activity 1:Understanding Triangles

Instructions:

Copy the above triangles (using tracing paper) on a separate sheet of paper.

And cut out the three triangles.

Now Fold triangle 1 at one of the vertex to see if the sides over lap.

Now try this with all the three vertices and answer the following questions:

What do you observe?

______________________________________________________________________________

__________________________________________________________________________

What can you say about the sides of triangles touching each other from vertex to vertex?

______________________________________________________________________________

___________________________________________________________________________

If the sides overlap what does it mean to you? If they do not overlap what do you

understand?

______________________________________________________________________________

__________________________________________________________________________

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What can you deduce from this activity?

______________________________________________________________________________

__________________________________________________________________________

What do you conclude from this activity?

Triangle 1 – None of the sides of triangle are equal.

Triangle2 - _____________________________________________________________

Triangle3 - ______________________________________________________________

(Refer to online math dictionary to name the triangles)

On the basis of sides there are three types of triangle:

Triangle 1 is known as ______________.



Look for the root word of each of the names and explain why the triangle is named so

______________________________________________________________________________

______________________________________________________________________________

__________________________________________________________________________

Paste all your findings here

102

Based on what you have researched, answer the following;

1. Tell whether each triangle is isosceles, scalene or equilateral. Give reason for your

answer (for example write ―because two sides are equal‖

• My sides measure 3cm, 4cm and 5cm. What triangle am I?

________________________________________________________________________

My sides measure 4cm, 8cm, and 7cm .What triangle am I?

________________________________________________________________________

My sides measure 5cm, 5cm, 5cm .What type of triangle am I?

________________________________________________________________________

My sides measure 15cm, 15cm and 12cm. What type of triangle am I?

________________________________________________________________________

Two of my sides measure 14cm, 18cm. The sum of the three sides is 50cm.What

type of triangle am I?

________________________________________________________________________

2. a) Create triangles with a single drinking straw. Measure the sides and Compare

your triangle with your peers. Did you all get the same triangle?

Draw diagrams to explain your findings

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b) Classify your triangle based on the measure of the sides. Do you always need to

measure to check that out?

c) What is the sum of the three sides of a triangle known?

d) Given the perimeter of a triangle, how many triangles can you create? Write 2

sets of measures of triangles. Classify the triangle based on their side length.

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Classification of triangles 2



Activity 2 – Understanding triangles

Draw the different types of angles discussed in the class.

1. Look at the angles of the triangles and write the difference(s) between the three

triangles shown above.

2. Identify the different types of angles in each of the triangle.

3. Now complete the following statements: ( one has been done for you)

Triangle 1 has one right angle and two acute angles. Depict it by drawing a figure

as shown below.

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Triangle 2 has

_________________________________________________________________________

Triangle 3 has

4. Verify your answers by measuring each angle with the help of a protractor.

5. Refer to online dictionary and name the above triangles.

Triangle 1 has a right angle so will be named after that angle. It is a right angled

triangle.

Triangle 2 has

______________________________________________________________________________

_________________________________________________________________________

Triangle 3 has

______________________________________________________________________________

__________________________________________________________________________

6. Watch Video clip 3 to reinforce the concepts learnt and write what you have learnt.

106


Types of Triangles



Activity 3 – Extension (Types of triangles)

Instructions:

On a geo board (paper) draw a scalene triangle, an isosceles triangle and an equilateral

triangle.

Now use paper folding or paper cutting or simply use protractor to compare the three

angles of each if the triangles.

Now record what you observe.

107

Complete the following based on YOUR observations:

In a scalene triangle no two angles are equal.

In an isosceles triangle _______________________________________________________

In an equilateral triangle_____________________________________________________

Students now use tracing paper and copy the triangles given in the table below on a

separate sheet of paper.

They use paper folding, paper cutting or protractor to make conclusions and complete

the following table.

Shape Name

of the

triangle

Is

A=

B?

Is

A =

C?

Is

B =

C?

Concl-

usion

Write what you conclude from this activity.

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CONTENT WORKSHEET CW9


Activity 4: Check your understanding

Check your understanding:

1. In the triangles below, how many of the sides are of equal length?

2. For the triangles below, place each in one or more of the categories by writing the

lead letter below each triangle:

Equilateral, Isosceles, Scalene, Obtuse, Right or Acute

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3. Draw the triangles listed below. If triangle is not possible, explain why.

a) Equilateral Obtuse Triangle b) Equilateral Right Triangle

c) Equilateral Acute Triangle d) Isosceles Obtuse Triangle

e) Isosceles Right Triangle f) Isosceles Acute Triangle

g) Scalene Obtuse Triangle h) Scalene Right Triangle

i) Scalene Acute Triangle

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4. Complete the following ‗If and then‘ statements

a. If it is a triangle then it has __________sides.

b. If it is a triangle then it has __________angles.

c. If the three sides of a triangle are equal then ___________________________

d. If the three angles of a triangle are acute then __________________________

e. If all the angles of a triangle are acute then it is a ______________triangle.

f. If any one angle is right, then it is _________________triangle.

g. If all sides are unequal then it is ________________triangle.

h. If any two sides are equal then it is a ______________triangle

5. If the three angles are used to group the triangles, classify the triangles on the basis

of their angles.

6. Jitendra has a pool in the shape of a triangle. The sum of the sides of the pool is

100ft. One of the sides of the pool measures 30 ft and other measures 40ft. What type

of triangle is it? Draw a figure (not to scale) to answer.

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7. a) If the sum of the sides if an equilateral triangle is 45ft, what is the measure

of each side?

b) What is the ratio of all sides of an equilateral triangle?

8. The sides of a triangle are in the ratio 2: 3: 4. What type of triangle is this? Justify

your answer.

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9. On the triangle grid paper below, locate and draw the following:

a) Equilateral triangle b) Isosceles triangle

c) Scalene triangle d) Right triangle

e) Obtuse triangle f) Acute angled triangle

10. Measure, if required, and sort and classify the triangles given below;

a) On the basis of its angles b) On the basis of its sides

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11. Extension: AB is drawn in a plane as shown.

Locate all points C such that Triangle ABC is

a) Right b) Acute c) Obtuse

d) Isosceles e) Scalene f) Equilateral

Note : Use a different colour to represent the points for each of the six

classifications. For instance, use green to indicate all points that create right

triangles, use red for all points that create isosceles triangle.

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12. Match the following:

Measures of Triangle Type of Triangle

(i) 3 sides of equal length (a) Scalene

(ii) 2 sides of equal length (b) Isosceles right angled

(iii) All sides are of different length (c) Obtuse angled

(iv) 3 acute angles (d) Right angled

(v) 1 right angle (e) Equilateral

(vi) 1 obtuse angle (f) Acute angled

(vii) 1 right angle with two sides of equal length (g) Isosceles

13. Try to construct triangles using match sticks. Some are shown here.

(i) Make a triangle with

(a) 3 matchsticks? (b) 4 matchsticks?

(c) 5 matchsticks? (d) 6 matchsticks?

(Remember you have to use all the available matchsticks in each case)

(ii) Name the type of triangle in each case. If you cannot make a triangle, write

what could be the possible reason for the same.

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Draw/Paste your Triangles here

116





Activity 1: Word perfect:

Instructions:

Look for the words in this word maze. Then write down the definitions of each of the

following in your notebook

117





Activity 2 - Flexible I am……

Instructions:

Using flexi straws create a four sided closed polygon.

Refer to the dictionary and write the special name given to this polygon?

_________________________________________________________________________

Now display the quadrilaterals on the board, then check with the classmates and see if

they have the same shape as your polygon.

Identify and name the various quadrilaterals that you observed. (Feel free to refer to the

math dictionary for help)

______________________________________________________________________________

______________________________________________________________________________

_________________________________________________________________________

Instructions:

Solve this puzzle to see if there are more quadrilaterals than what you could think of!!!!

Work out the answers to the multiplication sums below. Each chain of answers will

form a quadrilateral when you join the dots up above. Use a different colour for each

chain and then write the name of the quadrilateral in the space provided

118

Choose from:

21

119





Activity 3 – Classifying quadrilaterals

Instructions;

Cut out the quadrilaterals and

Follow the steps shown in the flow chart.

• Identify the type of quadrilateral you have.

• Discuss with your friends and your teacher.

• Classify the quadrilaterals.

Different shapes of a quadrilateral

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FLOW CHART

• Refer to the table below and identify the quadrilateral you have now.

• If you get ‗YES‘ for all the findings, you get your quadrilateral too.

List characteristics about the shape of the quadrilateral, based on the observations and

the video clip observed.

Now Exchange your quadrilateral with your partner and repeat till you have explored

each cut out and filled up the table.

121





Activity 4 – Classifying quadrilaterals

Watch video clip 4 on special types of quadrilaterals.

Observe the following figure carefully and make correct geometrical statements:

For example:

1. All squares are rectangles but all rectangles are not squares.

________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

______________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

______________________________________________________________________

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Interior Angles of Polygons



Activity 5 – Interior angles of triangle and quadrilateral

Instructions:

Test the sum of the angles of a triangle with your feet.

Draw a large chalk triangle on the pavement. Make the lengths of the sides between

1 and 2 meters long.

Choose one person to be the Walker. The others will be Observers who stand

outside (exterior) the triangle and watch the motion of the Walker.

When you are moving FORWARD, you pivot on your TOES at the vertex,

When you are moving BACKWARD, you pivot on your HEELS at the vertex,

Stand inside the triangle with your right foot along the midpoint of one side.

One observer to mark the location of feet of walker with chalk, as this will be both

the starting and ending location.

Walk until you reach the VERTEX in front of you—the point where two of the lines

come together—so that your toes go into the corner.

To ―walk‖ the interior angle, pivot clockwise on your toes just enough so that your

heels point toward the next vertex and your left foot is lined up with the second

side. (See illustrations.)

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Walk backward along this second side until your heels reach the vertex.

Pivot clockwise on your heels so that your toes point toward the third vertex and

your right foot is lined up with the third side.

Walk along the third side, pivot clockwise in the last vertex, and then finish by

walking backward to the starting/ending chalk line.

Now answer the following questions:

In which direction did the walker face before starting? __________________

What is direction the walker is facing after end of walk? _________________

By what angle did the walker rotate? __________________.

Complete the statement, and write what you conclude about a special property of a

triangle?

Sum of the three interior angles of a triangle is ___________________

In other words, A triangle is possible only if the sum of the three angles is ________.

Now try the same activity but with a quadrilateral and answer the following

questions.

How many times did you rotate? ________________________.

Sum of all angles of a quadrilateral is ___________________.

Also a quadrilateral is made up of ______________ triangles.

Sum of angles of two triangles _________________________.

Did you get the same answer?

125

Based on what you have learnt , test your findings by measuring the angles in each

case.

b)

In triangle 1

A = ___________, B = ___________ and C = _______

A + B + C = _____________

In triangle 2

A = ___________, B = ___________ and C = _______

A + B + C = _____________

In triangle 3

A = ___________, B = ___________ and C = _______

A + B + C = _____________

c) Draw any quadrilateral and verify that the sum of all angles of any quadrilateral is

3600.

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Activity 6 - Test your understanding:

1. Write the letter of the figure from the list below that is best described by each

definition given below;

_____________ 1. A parallelogram with at least one right angle

_____________ 2. A quadrilateral with exactly one pair of opposite sides parallel

_____________ 3. A four sided polygon

_____________ 4. A quadrilateral in which two disjoint pairs of consecutive sides

are equal

_____________ 5. A quadrilateral with both pairs of opposite sides parallel.

_____________ 6. A parallelogram with at least one pair of consecutive sides equal

_____________ 7 A trapezoid whose non parallel sides are equal

_____________ 8 A parallelogram that is both a rectangle and a rhombus

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2. Make a Geo board shape that fits the conditions given below. You may use a ruler to

measure and make the required shapes. Also identify their name

3. True or False? Explain with the help of a reason/diagram:

a) Every square is a rhombus.

b) Every rhombus is a square.

128

c) Every square is a kite.

d) Every kite is a rhombus.

e) If a quadrilateral is a trapezoid, then it is a parallelogram.

f) A property of a square is a property of a kite.

g) A property of a trapezoid is a property of a parallelogram.

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4. Use the information given below and name the shapes.

5. Choose the appropriate answer

a) A quadrilateral with 2 pairs of parallel sides is called ____________

Trapezoid Parallelogram Square

b) Quadrilaterals are polygons with ____________

Four sides Three sides Five sides

c) A quadrilateral with only 1 pair of parallel sides is called ____________

Square Trapezoid Parallelogram

d) What is a parallelogram with 4 right angles and 4 sides equal ___________

Trapezoid Rectangle Square

6. Extension:

Given the three sides of a triangle as 6 cm, 5cm, and 12cm.

Create a triangle using drinking straws. What do you observe?

Change the straws with bigger or smaller straws and try to make triangle.

What do you conclude? Discuss your answer with your class and your teacher.

…………………………………

…

…………………………………

…

…………………………………

…

…………………………………

…

130

7. Find the missing angle in the following figures:

Working space

8. In a right angled triangle, one acute angle is 39o. Find the other angle.

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9. Two angles of a triangle are 60o and 85o. What can you say about this type of

triangle? (Scalene, isosceles, equilateral)

10. Three angles of a Quadrilateral are 1000, 500, 600. Find the measure of the fourth

angle of the quadrilateral

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Polygon Capture


Name of the student ______________________ Date ______

Activity 7 –Polygon Capture Game

Instructions:

Play this game to enhance your learning.

Cut out the cards to get different shapes. Arrange them so that the answer of the

question on the card is adjacent to the arrangement.

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STUDENT WORKSHEET 22

Visualizing solid shapes



Activity 1 – Visualizing solid shapes:

Follow the instructions given below and complete the task.

Instructions:

Join the appropriate dots in the isometric paper and make the given figures.

For example:

Shape 1 Shape 2

On the given isometric paper sketch the shapes given below:

135


Nets of of 2 D and 3 D objects



Activity 2 - Getting 3D objects from 2D (NETS)

Instructions:

1. Bring a closed box made of cardboard.

Unfold the box ,one face at a time.

Simultaneously draw the shape you observe at each step on the isometric dot paper.

The net of the 3D cube is obtained. Now cut out the flat net from isometric paper.

Try to fold it and get the cube from it.

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2. Think of some other net which can give a cube. Cut out and make the cube from it.

3. Observe the net given below and describe the process involved.

a) What is the shape of the solid seen?

b) What are the various shapes you see when the solid is unfolded?

137

4. Now try to make the net for the following on the isometric dot paper.

5. Write what do you conclude from this, by completing the sentence given below:

All 3D hollow objects can be _____________________________________

138

6. In each of the above cases mention the 2D shapes used to make 3D objects in the

table given below:

Solid 2d shapes used

140

7. Compare the following pairs of shapes. State difference(s) between them.

a)

b)

c)

d)

e)

141

• What do you mean by Dimensions?

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

• State the number of dimension of each of the shape in above pairs? Explain.

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

• Explain the difference between 2D and 3D objects? Give two examples of each.

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

142





Activity 3 – Nets of curved 3D objects/Getting 3D objects from 2D (NETS)

Instructions:

1. Use the following nets and try to convert them into 3D objects without cutting them

any further

2. Copy the following flat objects on hard board and fold it to form a 3D object

143

1. Naming 3D objects:

Use online math dictionary to name the following 3D objects:

2. Write what did you observe and learn from the video clip 4.

144


SOLID SHAPES 1



Activity 4 – Analyzing Solids

Instructions:

Reconsider the following net of a cube:

How many corners do you see in the cube?_______

The corners of the cubes are known as __________.

The toy above is placed at the edge of the cube.

How many edges are there in a cube? _______

Why is this known as edge of the cube?

_______________________________________________________

How many flat surfaces it opens up into? ____________

The flat surfaces are known as ____________.

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• Think of as many as 3D objects you have studied and fill up the details of the table

same as the above table.

Shape number of faces number of edges number of vertices (points)

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Solid Shapes 2



Activity 1 –Independent Practice

Label the shapes with the names from the box below

2. a) Here are five different objects. Match them up to a 3D object.

cube cylinder diamond square triangle

cone pyramid rectangle sphere pentagon

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b) List certain things you can find around the classroom or playground that match

the following solid shapes? Place them in the correct column.

3. Match the flattened shapes given in one group with that of its 3D shape in the other

group.

4. Solve the following Riddles:

Riddle time!!!!! Read each of the following shape riddles and answer.

148

a) I have six faces. I have twelve edges. All of my faces are rectangles. Who am I?

b) I have one flat surface and one curved surface. I have one edge and no corners.

What am I?

c) I have six square faces. What am I?

I have five flat faces. Two of them are triangles. I look like a Toblerone package.

What am I?

d) I have no corners. I have one curved surface. I have no edges. What am I?

e) I have six faces and twelve edges. Two faces are squares and four are rectangles.

What am I?

f) I have one curved surface. If you cut me in half I look like a circle on top. What

am I?

149

5. For the given net make the 3D shape inside the circles

6. Make as many nets as you can, to make a cube.

7. Fill in the missing words:

a) Cylinders have two ends that are _______________ and ____________ curved

surface.

b) Prisms have _____________ that are of the same shape. Their sides are

_______________.

c) The sides of a pyramid are ____________. They meet to make a _______.

d) A (square based) pyramid has ___________ number of corners.

e) A cone has a total of _________ faces.

f) A sphere is a _____________ object.

g) A pentagon has _______________ angles.

h) A cylinder has ________________ edges

150


Symmetry 1



Activity 1- It is everything to do with perception

Instructions;

Solve this riddle.

Use the space here to think and draw your response. Give a reason why you think this

is the answer.

?

151


Symmetry 2



Activity 2 - It is all in the mind!!!!

Observe and draw the next shape in the pattern given below:

Use the space given here for your answer. Explain why you think your answer is

correct.

Now write the correct answer and explain how you get this answer.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

____________________________________________________________________________

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What is another name for mirror images ?

____________________________________________________________________________

Refer to a dictionary, and write the meaning of the word Symmetry.

______________________________________________________________________________

Also write down the etymology of the word symmetry.

______________________________________________________________________________

_____________________________________________________________________________

Based on the video viewed,

Give some examples of symmetry in nature. ___________________________________

Give two examples of symmetry from your body.

______________________________________________________________________________

____________________________________________________________________________

Discuss with your friend, why you think symmetry is important.

______________________________________________________________________________

____________________________________________________________________________

What is meant by the line of symmetry? Draw two shapes having one / two lines of

symmetry.

______________________________________________________________________________

____________________________________________________________________________

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Symmetry 3



Activity 3: Cut and fold

Cut out each of these shapes; fold it to show the lines of symmetry.

Write the lines of symmetry for each shape.

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Symmetry 4



Activity 4 – Mirror mirror on the wall !!!

Write your name on the piece of paper.

Now reflect your name on the sheet of paper using the mirror.

Place your mirrors on the dotted line in the following figure.

By looking into the mirror complete the picture behind the mirror.

Reflect half of the raccoon face to make a complete raccoon face using a mirror.

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Closing Activity :

Questions:

Refer to the above diagrams and state the properties of symmetry:

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

_________________________________________________________________________

Differences between the object and the image…

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

_________________________________________________________________________

156


Symmetry 5



Activity 5 - Test your understanding:

1. Draw the lines of symmetry for each shape. Some of them may have more than one

line of symmetry.

2. Tell whether the dotted line on each letter represents a line of symmetry .Write yes

or no.

a)

157

b)

3. Draw a line of symmetry on each letter.

4. Draw the second half of each symmetrical letter.

5. Reflect each of the shapes given below in the mirror line.

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POST CONTENT WORKSHEET PCW 1


1. Which of the following are regular polygons? Give reasons for your answer.

2. Draw in the line(s) of symmetry on each shape

3. Which pattern is symmetrical? Draw any lines of symmetry

159

4. Complete the pattern using the dotted line as the mirror line

5. Write the name of these shapes on the line under the shape:

________ ________ ________ ________ ________

6. What shape am I?

Draw me Draw me

I am 2 D.

I have 4 sides.

All my sides are the same

length.

I have right angles.

I am a ______________.

I am a flat shape.

I have 6 corners.

I have 6 edges.

I am a ______________.

I am 2D.

I have 5 sides.

I am 3 D.

All my faces are squares.

160

7. Which of the following triangles is scalene, isosceles, or equilateral triangle?

a) 15cm, 30 cm, 20 cm b) 13cm, 8cm, 6cm

c) 12cm, 12cm, 12cm e) 12cm, 8cm, 8cm

f) 7cm, 9 cm, 11cm.

8. The three angles of a triangle are 40o and 75 o and 650. What can you say about this

type of triangle? ( scalene, isosceles, equilateral)

9. One of the equal angles of an isosceles right angles triangle is 68o. Find the other

angles of the triangle.

10. Look at the following figure:

a) What type of quadrilateral is this?

b) What is the measure of side EH, HG?

I am a ______________. I have 6 faces.

I am a _____________.

I am 3D.

I have 2 faces.

I have 1 point.

One of my faces is a circle.

I am a ______________.

I am 3 D.

I have 5 faces.

I have 8 edges.

I have 5 corners.

4 of my faces are triangles.

One of my faces has two long

sides and two short sides.

I am a ____________.

I am 3D.

I have 1 face.

I have no edges.

I have no corners.

I am a ________________.

I am a flat shape.

I have 3 edges.

I have 3 corners.

I am an ______________.

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c) If EG = 9.5 cm, what is the length of HF?

d) Fill in the blanks to make each a correct statement:

i) When three angles of a triangle are equal then it is known as

_______________.

ii) When two angles of a triangle are equal, then the sides opposite these

angles are __________. The triangle is known as ______________

iii) A triangle having no sides equal is known as ________________.

iv) The measure of each angle of an equilateral triangle is _____.

v) A _______________ is a parallelogram in which all four sides are

_____________.

vi) In a trapezium, one pair of opposite sides is _______________.

vii) A ___________ possesses all the properties of a trapezium, parallelogram

and a rhombus also.

viii) A solid having many faces is called _______.

ix) A ___________is a solid with side edges meeting in a point.

x) The drawing of an unfolded shape is called _____________ of the solid.

e) During a local math Olympiad the team from Bigtown High School was presented

with the following problem to solve in no more than 2 minutes: "What is the

relationship between the number of vertices of a regular polygon and the number

of symmetry lines of the polygon?" They did it! What was their answer?

f) Each point of a polygon at which two sides intersect is called ___________.

162

g) Find the unknown angle in the following figures :

h) Do as directed:

Colour the pattern to make a symmetrical design

i) Find the unknown angle in the following figures: (hint: use straight angle and

then sum of a quadrilateral)

163

Acknowledgement:

Websites Referred to:

http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/Worksheets/Po

lygonWordRoot.pdf

http://www.education2000.com/teachers-guide/p6-polygons.pdf

http://www.racismnoway.com.au/classroom/lesson_ideas/20021211_53.html

http://www.mathrealm.com/PDFiles/Geometry/02_lines_angles.PDF

http://www.mymaths.co.uk/integrate/file.asp?section=shape&fileID=948&sectionID=

3&topic=polygons

http://www.suite101.com/content/basic-math-shapes-a18143

http://www.mathsisfun.com/puzzles/cubic-outlines.html

http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/Clas

sifying_Triangles.pdf

http://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Classifying%20T

riangles%20and%20Quadrilaterals.pdf

http://bemidji.ntcmn.edu/academics/departments/math_computer_science/smi/smi

_archive/projects/2004/Session_1/Geom/tammylesson%20TM%20JM.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr6_Course%201_PDFs/Expl

oring%20Triangles.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr5_PDFs/Triangle%20Sort.p

df

https://sites.google.com/site/8thgrademathhomepage/tessellation-project

http://homepage.mac.com/efithian/Geometry/Activity-12.html

http://www.learner.org/courses/learningmath/geometry/support/lmg2.pdf

http://ellerbruch.nmu.edu/classes/cs255f01/cs255students/rbudek/P10/quadworksh

eet.pdf

http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/Worksheets/PolygonWordRoot.pdf

http://www.swarthmore.edu/SocSci/Education/Portfolios/rwillem1/Worksheets/PolygonWordRoot.pdf

http://www.education2000.com/teachers-guide/p6-polygons.pdf

http://www.racismnoway.com.au/classroom/lesson_ideas/20021211_53.html

http://www.mathrealm.com/PDFiles/Geometry/02_lines_angles.PDF

http://www.mymaths.co.uk/integrate/file.asp?section=shape&fileID=948&sectionID=3&topic=polygons

http://www.mymaths.co.uk/integrate/file.asp?section=shape&fileID=948&sectionID=3&topic=polygons

http://www.suite101.com/content/basic-math-shapes-a18143

http://www.mathsisfun.com/puzzles/cubic-outlines.html

http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/Classifying_Triangles.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/Classifying_Triangles.pdf

http://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Classifying%20Triangles%20and%20Quadrilaterals.pdf

http://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Classifying%20Triangles%20and%20Quadrilaterals.pdf

http://bemidji.ntcmn.edu/academics/departments/math_computer_science/smi/smi_archive/projects/2004/Session_1/Geom/tammylesson%20TM%20JM.pdf

http://bemidji.ntcmn.edu/academics/departments/math_computer_science/smi/smi_archive/projects/2004/Session_1/Geom/tammylesson%20TM%20JM.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr6_Course%201_PDFs/Exploring%20Triangles.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr6_Course%201_PDFs/Exploring%20Triangles.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr5_PDFs/Triangle%20Sort.pdf

http://www.kgcs.k12.va.us/instruction/SS%20Math%20Gr5_PDFs/Triangle%20Sort.pdf

https://sites.google.com/site/8thgrademathhomepage/tessellation-project

http://homepage.mac.com/efithian/Geometry/Activity-12.html

http://www.learner.org/courses/learningmath/geometry/support/lmg2.pdf

http://ellerbruch.nmu.edu/classes/cs255f01/cs255students/rbudek/P10/quadworksheet.pdf

http://ellerbruch.nmu.edu/classes/cs255f01/cs255students/rbudek/P10/quadworksheet.pdf

164

http://books.google.co.in/books?id=jzgWL4ahqukC&pg=PA213&lpg=PA213&dq=qua

drilateral+worksheet&source=bl&ots=MgekNrN7Y3&sig=NffVR-

5LYglEmTnDUc0k1TCKzDU&hl=en&ei=putGTePWAcnQccz4gY8O&sa=X&oi=book_r

esult&ct=result&resnum=8&ved=0CD8Q6AEwBzjKAg#v=onepage&q=quadrilateral%

20worksheet&f=false

http://www.enslow.com/product_images/worksheets/Geometry.pdf

http://www.geogebra.org/en/upload/files/MSP/HarryMarshall/Investigating_Qua

drilaterals.pdf

http://www.lessonsnips.com/docs/pdf/comparing3d.pdf

http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1472&CurriculumID=4

http://3dshapes.org/faces-edges-a-vertices-explained-for-3d-shapes.html

http://www.numeracyworld.com/shape-and-space-worksheets.php

http://math.buffalostate.edu/~it/projects/Fiden.pdf

http://www.suite101.com/content/how-to-make-tessellations-with-kids-

a201851#ixzz1CizC7Y1N

https://leecountyschools.wikispaces.com/.../Tessellation+Project+Directions.doc

http://books.google.co.in/books?id=jzgWL4ahqukC&pg=PA213&lpg=PA213&dq=quadrilateral+worksheet&source=bl&ots=MgekNrN7Y3&sig=NffVR-5LYglEmTnDUc0k1TCKzDU&hl=en&ei=putGTePWAcnQccz4gY8O&sa=X&oi=book_result&ct=result&resnum=8&ved=0CD8Q6AEwBzjKAg#v=onepage&q=quadrilateral%20worksheet&f=false





http://www.enslow.com/product_images/worksheets/Geometry.pdf

http://www.geogebra.org/en/upload/files/MSP/HarryMarshall/Investigating_Quadrilaterals.pdf

http://www.geogebra.org/en/upload/files/MSP/HarryMarshall/Investigating_Quadrilaterals.pdf

http://www.lessonsnips.com/docs/pdf/comparing3d.pdf

http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1472&CurriculumID=4

http://3dshapes.org/faces-edges-a-vertices-explained-for-3d-shapes.html

http://www.numeracyworld.com/shape-and-space-worksheets.php

http://math.buffalostate.edu/~it/projects/Fiden.pdf

http://www.suite101.com/content/how-to-make-tessellations-with-kids-a201851#ixzz1CizC7Y1N

http://www.suite101.com/content/how-to-make-tessellations-with-kids-a201851#ixzz1CizC7Y1N

https://leecountyschools.wikispaces.com/.../Tessellation+Project+Directions.doc

165

Suggested videos:

Name Tiltle/Link

Video clip 1

shapes around us

http://www.youtube.com/watch?v=Gclsis-A1sw&feature=related

shapes and basic geometry

http://www.youtube.com/watch?v=Ru61Z8XQp9Q&feature=related

Video clip 2

song on polygon

http://www.youtube.com/watch?v=9cKN2jk2vDI&feature=related

polygons introduction

http://www.youtube.com/watch?v=JTVPQEYN_10

Video clip 3 classification of triangles

http://www.youtube.com/watch?v=7KqFwUSot7k

Video clip 4 types of quadrilaterals

http://www.youtube.com/watch?v=nt1d93aSRr8

Video clip 5 Names of 3d figures

http://www.youtube.com/watch?v=wlvn4anF-fI&feature=fvwrel

Web link 1 edges , vertices and faces of 3D objects

http://www.youtube.com/watch?v=9T-HsKXzkLc&feature=related

Web link 2 symmetry

http://www.youtube.com/watch?v=BX4cx-9zT1A

Web link 3 http://www.primaryschool.com.au/mathematicslessonsresults.php?strand=Space%20and%20Geometry&unit=3D&grade=56

Web link 4 http://www.learnanytime.co.uk/Maths/Shape.htm

Web link 5 http://www.onlinemathlearning.com/geometry-math-games.html

Web link 6 http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#Symm

http://www.youtube.com/watch?v=Gclsis-A1sw&feature=related

http://www.youtube.com/watch?v=Ru61Z8XQp9Q&feature=related

http://www.youtube.com/watch?v=9cKN2jk2vDI&feature=related

http://www.youtube.com/watch?v=JTVPQEYN_10

http://www.youtube.com/watch?v=7KqFwUSot7k

http://www.youtube.com/watch?v=nt1d93aSRr8

http://www.youtube.com/watch?v=wlvn4anF-fI&feature=fvwrel

http://www.youtube.com/watch?v=9T-HsKXzkLc&feature=related

http://www.youtube.com/watch?v=BX4cx-9zT1A

http://www.primaryschool.com.au/mathematicslessonsresults.php?strand=Space%20and%20Geometry&unit=3D&grade=56

http://www.primaryschool.com.au/mathematicslessonsresults.php?strand=Space%20and%20Geometry&unit=3D&grade=56

http://www.learnanytime.co.uk/Maths/Shape.htm

http://www.onlinemathlearning.com/geometry-math-games.html

http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#Symm

http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#Symm

Unit-7- Understanding Shapes 2D and 3D

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Transcript of Unit-7- Understanding Shapes 2D and 3D