CLASS VII. Unit - 9. CBSE-i. Student s Material. Representing. 3D in 2D. Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi India

Transcription

1 CBSE-i CLASS VII Unit - 9 Student s Material Representing 3D in 2D Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi India

2

3 CBSE-i S T U D E N T S M AT E R I A L Representing 3D in 2D VII CLASS Unit - 9 Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi India

4 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 may be taken are duly mentioned. In case any thing 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.

5 The 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 schools affiliated to it and over 158 schools situated in more than 23 countries outside India. 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 nonevaluative 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 Joshi Chairman

6 Advisory Conceptual Framework Shri Vineet Joshi, Chairman, CBSE Shri G. Balasubramanian, Former Director (Acad), CBSE Dr. Sadhana Parashar, Director (Training), Ms. Abha Adams, Consultant, Step Dr. Sadhana Parashar, Director (Training) Ideators VI-VIII Ms Aditi Mishra Ms Preeti Hans Ms. Charu Maini Ms. Malini Sridhar Ms Guneet Ohri Ms Neelima Sharma Dr. Usha Sharma Ms. Leela Raghavan Ms. Sudha Ravi Ms. Gayatri Khanna Prof. Chand Kiran Saluja Dr. Rashmi Sethi Ms. Himani Asija Ms. Urmila Guliani Dr. Meena Dhani Ms. Seema Rawat Ms. Neerada Suresh Ms. Anuradha Joshi Ms. Vijay Laxmi Raman Ms. Suman Nath Bhalla English : Ms Neha Sharma Ms Dipinder Kaur Ms Sarita Ahuja Ms Gayatri Khanna Ms Preeti Hans Ms Rachna Pandit Ms Renu Anand Ms Sheena Chhabra Ms Veena Bhasin Ms Trishya Mukherjee Ms Neerada Suresh Ms Sudha Ravi Ms Ratna Lal Ms Ritu Badia Vashisth Ms Vijay Laxmi Raman Chemistry Ms. Poonam Kumar Mendiratta Ms. Rashmi Sharma Ms. Kavita Kapoor Ms. Divya Arora Material Production Groups: Classes VI-VIII Physics : Ms. Vidhu Narayanan Ms. Meenambika Menon Ms. Patarlekha Sarkar Ms. Neelam Malik Biology: Mr. Saroj Kumar Ms. Rashmi Ramsinghaney Ms. Prerna Kapoor Ms. Seema Kapoor Mr. Manish Panwar Ms. Vikram Yadav Ms. Monika Chopra Ms. Jaspreet Kaur Ms. Preeti Mittal Ms. Shipra Sarcar Ms. Leela Raghavan Mathematics : Ms. Deepa Gupta Ms. Gayatri Chowhan Ms. N Vidya Ms. Mamta Goyal Ms. Chhavi Raheja Hindi: Mr. Akshay Kumar Dixit Ms. Veena Sharma Ms. Nishi Dhanjal Ms. Kiran Soni CORE-SEWA Ms. Vandna Ms.Nishtha Bharati Ms.Seema Bhandari, Ms. Seema Chopra Ms. Madhuchhanda MsReema Arora Ms Neha Sharma Geography: Ms Suparna Sharma Ms Aditi Babbar History : Ms Leeza Dutta Ms Kalpana Pant Ms Ruchi Mahajan Political Science: Ms Kanu Chopra Ms Shilpi Anand Economics : Ms. Leela Garewal Ms Anita Yadav CORE-Perspectives M s. M a d h u c h h a n d a, RO(Innovation) Ms. Varsha Seth, Consultant Ms Neha Sharma Coordinators: Ms. Sugandh Sharma, E O Dr. Srijata Das, E O Dr Rashmi Sethi, E O Ms.S. Radha Mahalakshmi, (Chief Co-ordinator, CBSE-i) E O Mr. Navin Maini, R O Ms. Madhu Chanda, R O (Inn) Shri Al Hilal Ahmed, AEO Mr. R P Singh, AEO (Tech) Ms. Anjali, AEO Shri R. P. Sharma, Ms. Neelima Sharma, Mr. Sanjay Sachdeva, S O Consultant (Science) Consultant (English)

7 Contents Preface Acknowledgment 1. Syllabus 1 2. Study Material 2 3. Student's Support Material 26 CSW 1: Warm Up Activity (W1) 27 Two Dimensional Figures CSW 2: Pre-content Worksheet (PC1) 29 Three Dimensional Figures CSW 3: Content Worksheet (CW1) 30 Faces, Vertices and Edges CSW 4: Content Worksheet (CW2) 33 Nets of 3D Solids CSW 5: Content Worksheet (CW3) 37 Cross Sections of Solids CSW 6: Post Content Worksheet (PCW1) 39 Skill Drill CSW 7: Post Content Worksheet (PCW2) 41 Test Your Progress 4. Suggested Videos/ Links/ PPT's 44

8 Syllabus 2D and 3D figures Identification 3-D figures Components of 3-d figures Drawing 3-D and 2-D figures in 2-D showing all the faces Identifying 3 D pictures of various objects and matching them with their names Identification and counting of vertices, edges and faces; nets (for cubes, cuboids, cylinders and cones) 1

9 STUDY MATERIAL 2

10 REPRESENTING 3D IN 2D Introduction So far, you have mainly learnt about plane figures such as triangles, rectangles, circles and so on. All these figures wholly lie in a plane and are referred to as two dimensional figures (2D figures). However, most of the objects you see around in your environment do not lie wholly in the same plane. For example, houses, cupboards, persons, fruits, flowers, tables, animals and so on do not lie wholly in the same plane. Figures representing such objects are called solid figures or three dimensional figures (3D Figures). In this unit, we shall discuss some ways of representing 3D objects (figures) in the form of 2D figures. Horizontal and vertical cross sections of solid objects/figures shall also be discussed in this unit. 1. 2D Figures and 3D objects (Figures) You are already familiar with plane figures like rectangles, squares, triangles, circles, etc., All of these figures wholly lie in a plane. Something common in these figures is that they have some length and breadth. That is, they have two dimensions. For this reason, these figures are called two dimensional figures (2D figures). You have also learnt about some solid objects such as hall, almirah, drum, joker s cap, match box, football, tea packet, and so on. These objects were of one of the shapes, namely sphere, cuboid, cylinder, cone and so on. One thing common in all these objects is that they have some length, breadth (thickness) and height (or depth). Therefore, they are known as three dimensional (3D) objects or figures. Obviously, none of these lie wholly in a plane. To have a quick recall, identify the 2D figures and 3D objects in the following figures and write the names of the corresponding figures/objects: 3

11 Fig.1 You can easily identify as follows: 2D figures : (i) triangle, (vi) rectangle, (viii) circle, (x) square 3D Objects :(ii) cuboid; (iii) sphere; (iv) cone; (vii) cylinder, (ix) cube 2. Drawing 3D objects in 2D shapes As a 3D object figure does not lie wholly in a plane, therefore it is not possible to draw a 3D object exactly on a paper (or blackboard), which is a flat surface (i.e., a 2D figure). But 3D objects are drawn in 2D sheet of paper (or blackboard) by observing some conventions. For example, some solid objects are drawn as follows: 4

12 Fig.2 You can note, from the above figure, that by using the dotted edge (s), it has become possible to visualize all the faces and surfaces of the corresponding solid figures. It is a convention to use dotted edges for this purpose. Drawing cuboids and cubes using squared dot papers and Isometric dot papers We explain the process through some examples. Example 1: Draw a sketch of a cuboid of dimensions 5x4x3 on a squared dot paper. Solution: A squared dot paper is a paper on which dots are marked such that they form a number of squares (See Fig. 3). 5

13 Fig.3 Mark point A on a dot on squared dot paper and move 5 dots to the right to reach at the fifth dot from A and mark it as B. From A, move 3 dots vertically words and mark the resulting dot as D and then complete the rectangle ABCD as shown in Fig. 3(i). Now, take one more point E on squared dot paper and complete the rectangle EFGH as was done for rectangle ABCD [Fig. 3 (ii)] Join AE, BF, CG and DH [Fig. 3 (iii)] Finally, show EF, BF and GF dotted [Fig 3(iv)] Then, Fig 3(iv) is the required cuboid. It may be observed that in this case the dimension 4 of the cuboid is not visible. It appears to be 2. For this reason, such a sketch is referred to as an oblique sketch of the cuboid. 6

14 Example 2: Draw a sketch of a cuboid of dimentions 5x4x3 on a isometric dot paper. Solution: An isometric dot paper is a paper on which dots are marked such that they form a number of equilateral triangles (See Fig. 4) Mark a point A on an isometric dot paper and move 5 dots towards left to make AB = 5. Now, move 4 dots right upwards to r each the dot at the point C and then move three dots upwards as shown in Fig. (i) to reach at point F. Complete the parallelogram CFDG. Then Fig. 4 (ii) shows the required cuboid. Fig.4 You may note here that dimensions of the cuboid are 5x4x3 as desired. It is for this reason, this type of sketch is referred to as an isometric sketch of the cuboid. As a cube is also a cuboid with all its three edges equal, oblique and isometric sketches for a cube can be drawn on squared dot papers and isometric dot papers respectively by following the same steps as adopted for a cuboid. 3. Identification of 3D objects You are already familiar with many objects in you surrounding which have different shapes. For example, some of them are of spherical shape, some are of cuboidal shape, some are of cylindrical shape and so on. By observing the object, you can easily identify its shape. Let us consider an example to check this knowledge. 7

15 Example 3: Match the objects with the name of their shapes in the following: (a) Cube (b) Cuboid (c) Cone (d) Sphere (e) Prism (f) cylinder (g) Pyramid (h) Hamisphere 8

16 Solution: The required matching is as follows: (i) (b); (vii) (c); (xiii) (c); (ii) (d); (viii) (a); (xiv) (d); (iii) (b); (ix) (c); (xv) (e); (iv) (f); (x) (h); (xvi) (g); (v) (f); (xi) (b); (xvii) (b); (vi) (e); (xii) (f); 4. Faces, Edges and Vertices of 3D shapes You are already familiar with the terms faces, edges and vertices from your earlier classes. They are considered as the components of the solid shapes. Out of these components, the two dimensional shapes involved in a 3D shapes are known as faces, line segments or boundary of a curve known as edges and the corners are 9

17 called its vertices. Let us now take different solid shapes one by one and discuss about these components. (i) Cuboid: Look at Fig.5. It is a cuboid. It is made of six rectangles ABCD, EFGH, ADHE, BCGF, ABFE and DCGH. Fig. 5 Out of these rectangles, ABCD and EFGH are identical (Congruent), ADHE and BCGF are identical and CDHG and ABFA are identical. These are known as the opposite faces of the cuboid. Thus, there are 6 faces in a cuboid and out of these faces, opposite faces are identical. Clearly, the line segments involved are AB, DC, EF, HG, AD, BC, FG, EH, AE, DH, BF, and CG. Thus, these are 12 edges in a cuboid. You can see that: AB = DC = EF = HG; AD = BC = FG = EH and AE = DH = BF = CG. The corners A, B, C, D, E, F, G are the 8 vertices of the cuboid. Thus, a cuboid has 8 vertices or corners. (ii) (iii) Cube: As a cube is a specific cuboid in which length = breadth = height, so a cube also has Six faces (they are squares) twelve edges and eight vertices. Cylinder : Look at Fig. 6. It represents a cylinder. It has two flat surfaces and one curved surface. 10

18 Fig.6 The base and top of the cylinder are flat and circular in shape. We say that a cylinder has two faces. These faces are circular. The boundries of the circles corresponding to these faces are known as edges of the cylinder. It means that a cylinder has two circular edges. Obviously, a cylinder has, no corner or vertex. (iv) Cone: Look at Fig 7. It represents a cone. You can easily see that a cone has a curved surface, a circular face (base), a circular edge and a corner or vertex. Fig.7 11

19 (v) Prism: Let us now look at Fig. 8. Fig. 8 In (i), base and top are congruent triangles and the remaining three faces are rectangles. This figure represent a solid called a triangular prism. It has 2 +3 (bases + tops), i.e., five faces. Further, it has 9 (i.e. 3x3) edges and 6 (i.e. 3x2) vertices. Similarly, in (ii), base and top are congruent pentagons and the remaining five faces are rectangles. This figure represents a solid known as a pentagonal prism. It has (2+5), i.e., 7 faces, 15 i.e. (3x5) edges and 10 i.e. (5x2) vertices. From the above, if can be said that a prism with base a polygon of n sides will have: (2+n) faces, 3n edges and 2n vertices. (vi) Pyramid: Let us now look at Fig.9. In (i), base is a triangle and the remaining faces are also triangles. 12

20 Fig. 9 They are three in number. It is known as a pyramid with a triangular base or a triangular pyramid. Thus, there are in all four faces in a triangular pyramid. It is for this reason, a triangular pyramid is also known as a tetrahedron. In (ii), base is a rectangle and the remaining faces are triangles. They are four in number. Thus, there in are all five (1+4) faces in a pyramid with a rectangular base. The number of edges in (i) is 6 (2x3) and in (ii) is 8 (2x4). Clearly, the number of vertices in (i) is 4 i.e., (1+3) and in (ii) is 5 i.e., (1+4). In view of the above, we can say that: A pyramid with a polygon of n sides will have (n+1) faces, 2n edges and (n+1) vertices. It is easy to see that a sphere has one curved surface, no face, no edge and no and a hemisphere vertex. Further, a hemisphere has a curved surface, one (circular) face, one (circular) edge and no vertex. Let us consider an example to check the understanding of these concepts. 13

21 Example 4: Fill in the blanks: (i) (ii) (iii) (iv) (v) (vi) (vii) A cuboid has vertices, faces and edges. A cylinder has curved surface (s), edges and faces. A triangular pyramid has edges, vertices and faces. A hexagonal prism has edges, vertices and faces. Out of these faces, are. A cube has faces, vertices and edges. A cone has edge(s), face(s) and vertiex (ces). A pentagonal pyramid has faces vertices and edges. (viii) A sphere has one surface, faces vertices and edges. Solution: (i) 8, 6, 12 (ii) one, 2, 2 (iii) 6, 4, 4 (iv) 18, 12, 8; 6, 2, congruent hexagons (v) 6, 8, 12 (vi) 1, 1, 1 (vii) 6, 6, 10 (viii) curved, 0, 0, 0 5. Nets of Solid (3D) Figures Cuboids and Cubes Activity : Take a thin cradboard sheet and on it, draw a figure made of six rectangles as shown in Fig.10. In this figure, rectangles 1 and 2 must be congruent rectangles 3 and 4 must be congruent and rectangles 5 and 6 must be congruent. 14

22 Fig. 10 Cut this figure out using a pair of scissors. Now, fold this cutout along the dotted lines. What do you obtain? You will obtain a box of the shape of a cuboid as shown in Fig.11. Fig. 11 We say that shape of Fig. 10. is a net of a cuboid of Fig.11. Note that for the same cuboid, we can also have a net as given below: Fig

23 Thus, for the same cuboid, we can have more than one nets. Now, draw a figure made up of six congruent squares on a cardboard sheet and cut it out as shown in Fig.13. Fold this figure along the dotted lines. What do you obtain? Fig. 13 In this case, you will obtain the shape of a cube. Thus, shape given in Fig.13 is a net of a cube. Like a cuboid, for the same cube, we can have more than one nets. For example, shape given in Fig.14 is also a net for the same cube which is obtained from Fig.13. Fig. 14 Cylinders and Cones Activity : On a thin cardboard sheet or a chart paper, draw a rectangle of say length 22 cm and breadth 10cm. Cut it out (Fig.15) 16

24 Fig. 15 Draw two circles of radius 3.5 cm each and attached these with the rectangle of Fig.15 as shown in Fig. 16. Fig.16 Fold the shape (rectangle) of Fig. 16 so that side of length 22cm takes the form of a circle. What do you observe? You will find that, on folding, we obtain the shape of a cylinder. Now paste the two circles of Fig.16 at the base and top of this cylinder to make it closed (Fig.17). Fig. 17 Se, we can say that shape given in Fig. 16 is a net of the cylinder given in Fig. 17. Now, let us perform another activity as given below: 17

25 Activity : Draw a circle of radius say 28 cm and from it, cut a sector of arc length 22 cm (See Fig. 18) on a chart paper. Cut it out [See Fig.18 (iii)] Fig. 18 Now draw a circle of radius 3.5 cm (this makes the its circumference = 22 cm) and attach it with the sector of Fig.18 (iii) as shown in Fig. 19. Fig. 19 Fold the sector OAB such that A and B coincide to form the shape of a cone (Fig. 20). Paste the circle of radius 3.5 cm to the base of this cone to make it closed. Thus, the shape of Fig.19 is a net of the cone of Fig

26 Fig. 20 Let us take an example to understand these concepts. Example 5: Match the nets of column I with the 3D shapes of column II: 19

27 Solution: The required matching is as follows: (i) (ii) (iii) (iv) (d); (c); (b); (a); 6. Cross-Sections of 3D Shapes You must have observed the cross-sections of different vegetables, while cutting them with a knife. Note that every vegetable is a 3D object. What about its crosssection? Clearly, it is a 2D shape. Thus, we may say that (cross-section) of every 3D object is a 2D shape. 20

28 Here, we shall consider the horizontal and vertical cross-sections of some familiar 3D shapes. (i) Cuboid: Cut a cuboid by a plane parallel to its base (Fig. 21). You will see that the cross-section is a rectangle. Thus, the horizontal cross-section of a cuboid is a rectangle. Fig. 21 Similarly, if we cut a cuboid by a vertical plane, then again we shall obtain its cross-section as a rectangle. (ii) Cube: Recall that all the faces of a cube are congruent squares. So, if we cut a cube by a horizontal plane, then the cross-section obtained will be a square (Fig. 22). Fig. 22 Similarly, if we cut a cube by a vertical plane, the cross-section will again be a square. 21

29 (iii) Cylinder: Let us take a cylinder and cut it by a horizontal plane i.e., by a plane parallel to its base (Fig.23). Fig. 23 What do you observe about its cross-section? You will find that the cross-section is a circle. Now, cut the same cylinder by a vertical plane (Fig.24). Fig. 24 What do you observe about its cross-section? You will find that the cross-section is a rectangle. (iv) Cone: Cut a cone by plane parallel to its base (Fig.25). What do you observe about its cross-section? Clearly, it is a circle smaller then the base circle of the cone. 22

30 Fig. 25 Now, let us cut the same cone by a vertical plane. What do you observe about its cross-section? You will find that it is a triangle Fig. 26 (v) Sphere: Let us cut a sphere by a plane in any direction (Fig.27). We shall always find that the cross-section is a circle. Fig. 27 Now, let us take an example to check our understanding 23

31 Example 6: Fill in the blanks: (i) (ii) (iii) (iv) (v) (vi) The vertical cross-section of a cylinder is a The vertical cross-section of a cube is a The horizontal cross-section of a cone is a The horizontal cross-section of a cuboid a The vertical cross-section of a sphere is a The horizontal cross-section of a cylinder is a Solution: (i) rectangle (ii) square (iii) circle (iv) rectangle (v) circle (vi) circle Example 7: What is the name of the shape given in Fig.28? Write its Fig. 28 (i) (ii) horizontal and vertical cross-sections. Solution: This shape has a pentagonal base. Its all other faces are triangles. So, this shape is a pentagonal pyramid. (i) (ii) Its horizontal cross-section is a pentagon (See Fig 29(i)] Its vertical cross-section is a triangle [See Fig.29(ii)] 24

32 Fig. 29 Note: (i) (ii) Vertical and horizontal cross-sections of 3D objects can also be obtained on a screen by placing that object in between the screen and a source of light (See Fig.30). Many a times, we obtain same cross-sections for different 3D objects. So, it is not always possible to indicate the 3D objects for a given cross-section. Fig

33 Student s Support Material 26

34 Worksheet - 1 Two Dimensional Figures Warm Up (W1) Name of the student Date Activity 1- Identify and match Match the flashcards with 2D shape and their definition: Definitions: A 2D closed shape with four sides and with only one pair of opposite sides parallel. 27

35 Activity 2 Guess the shape and draw: i) I am flat shape. I have one curved side. I have no corners. What shape am I?.. ii) I am flat shape. I have three straight sides. I have three corners. What shape am I?.. iii) I am flat shape. I have four straight sides. I have four corners. All my sides are of equal length. What shape am I?.. iv) I am flat shape. I have one curved side. I have one straight side. I have two corners. What shape am I?.. 28

36 Student s Worksheet -2 Three Dimensional Figures Pre-content Worksheet (P1) Name of the student Date Activity 1- Put your thinking caps on!! Write the names of five familiar objects that have following shapes. i) Sphere ii) Rectangular prism iii) Cone iv) Cylinder Activity 2- Look at the pictures below. What shape(s) do you recognize in each picture? a. f. b. g. c. h. h. d. i. 29

37 e. j. On the basis of above, answer the following i) If we cut these shapes horizontally which of the new shapes have the shape as the original ones from which they were cut? Draw the new shapes obtained where ever relevant. ii) What are some differences between a prism and a pyramid? Also categorize if possible under a prism or pyramid. Student s Worksheet -3 Faces, Vertices and Edges Content Worksheet (CW1) Name of the student Date Activity 1- Visible Faces: Take an object like a cube. Each flat side of a cube is called a face. Now a) Hold the cube so that you see only one face. Draw the shape that you see. b) Hold the cube so that you see only two faces. Draw the shape that you see. c) Hold the cube so that you see only three faces. Draw the shape that you see. d) What happens when you try to hold the cube so that you can see four faces? 30

38 Activity 2- Complete the table given: Name Shape Type of Faces Number of faces Number of Vertices Number of Edges Triangular Pyramide/ (Tetrahedron) Cube (Square Prism) Octahedron Triangular Prism Hexagonal pyramid Pentagonal Prism Cuboid (Rectangular Prism) 31

39 A Swiss mathematician Leonhard Euler gave a relationship between the number of faces, vertices and edges Known as Euler s Formula given as Now verify it for all the above figures. Verification F + V E = 2 Name Shape Number of faces (F) Number of Vertices (V) Number of Edges (E) Verification of F+E-V=2 Triangular Pyramide (Tetrahedron) Cube (Square Prism) Octahedron Triangular Prism Hexagonal pyramid 32

40 Pentagonal Prism Cuboid (Rectangular Prism) Student s Worksheet -4 Nets of 3D Solids Content Worksheet (CW2) Name of the student Date Activity 1- Draw nets: All the faces of a shape are visible in a net i) Cube ii) Cuboid iii) Cylinder iv) Cone 33

41 Activity 2- The drawing of a cube-shaped box without a top is given below: Which of these nets can be folded to make the above box? (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) There are three more nets that could make the above box. Draw at least one of them and shade the bottom face. 34

42 Activity 3- Look at the prism given below: Only two faces are visible. i) How many faces are hidden? ii) How many faces are triangles? iii) How many faces are rectangles? iv) Draw a net of this prism. Activity 3- Name the solid whose net is given. Trace the nets and make the 3d figures out of them 35

43 36

44 Student s Worksheet -5 Cross Sections of Solids Content Worksheet (CW3) Name of the student Date Activity 1- Cross - Sections Visualize and draw the shapes obtained of the cross section horizontally and vertically, of the given solids. SOLIDS HORIZONTAL CROSS-SECTION VERTICAL CROSS-SECTION 37

45 38

46 Student s Worksheet -6 Skill Drill Post-Content Worksheet (PCW1) Name of the student Date Activity 1- Group Activity 1. Group students in their home groups. (About five-six) 2. Each group will be given a solid shape. 3. Students will collect information about it and complete the table on an A-3 sheet Name of Solid Sketch of Solid Number of flat surfaces Share your expert knowledge to fill in this table Number of Number curved of edges surfaces Number of vertices Is the shape a prism, What is the shape of pyramidthe base or (crosssection) neither?? Does the shape roll? (Yes/ No) Does the shape stack? If yes, draw its stacking. 4. Read the information about your shape. 5. Underline the words you do not understand. 39

47 6. Discuss the underlined word with the group to discover the meaning 7. Complete the worksheet called Building Technical Vocabulary about 3D shapes on an A-3 sheet. One sample is as follows: 8. The person with the shortest hair will collect the model of your shape from the teacher. 9. Pass the shape around the group. 10. The tallest person of the group will collect straws and connectors to build a model of your 3D shape. 11. All the group members will complete the model as a teamwork. 40

48 Student s Worksheet -7 Test Your Progress Post-Content Worksheet (PCW2) Name of the student Date Activity 1- Take the test: Q1. Draw the 3D figure whose net is given below. Also write its name. NET SOLID DRAWING 41

49 42

50 Q2. Does Euler s Formula work for the polyhedral below? a) b) c) d) 43

51 Acknowledgments Websites Referred to: Suggested Video links Name Video Clip 1 Video Clip 2 Video Clip 3 Video Clip 4 Video Clip 5 Video Clip 6 Video Clip 7 Weblink1 Weblink 2 Weblink 3 Weblink 4 Weblink 5 Names of 2D shapes Title/Link 2D shapes 3D shapes and their nets Teaching Kids the Basics: Shapes 3D shapes Introduction to Nets and 3D 3D geometry Review &%203D%20Shapes%20Bingo.ppt 44

52 CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi India