Guidelines for Mathematics
 Laboratory in Schools Class X

1. Introduction

Taking into consideration the national aspirations and expectations reflected in the recommendations of the National Curriculum Framework developed by NCERT, the Central Board of Secondary Education had initiated a number of steps to make teaching and learning of mathematics at school stage activity-based and experimentation oriented. In addition to issuing directions to its affiliated schools to take necessary action in this regard, a document on ‘Mathematics Laboratory in Schools – towards joyful learning’ was brought out by the Board and made available to all the schools. The document primarily aimed at sensitizing  the schools and teachers to the concept of Mathematics Laboratory and creating awareness among schools as to how the introduction of Mathematics Laboratory will help in enhancing teaching – learning process in the subject from the very beginning of school education. The document also included a number of suggested hands-on activities.  

With the objective of strengthening the concept further, the Board brought out another document ‘Guidelines for Mathematics Laboratory in Schools – Class IX’ in the year 2005. The document aimed at providing detailed guidelines to schools with regard to the general layout, physical infrastructure, material and human resources, etc for a Mathematics Laboratory. Besides, the document included a list of hands-on activities and projects, detailed procedure to be followed for carrying out these activities and the scheme of evaluation. In the meantime, the Board had issued two circulars to all its schools with regard to establishing Mathematics Laboratory and introduction of the scheme of internal assessment in the subject. Circular number 10 dated March 2, 2005 clarified that the internal assessment of 20% is to be given on the basis of performance of an individual in activity work, project work and continuous assessment. The schools were also informed through the same circular that the scheme would be effective for Class IX from the academic session 2005-2006 and for Class X from the academic session starting April 2006 i.e. from March, 2007 Examination. 

2. About the present document

The present document includes details of all Class X activities to be carried out by the students during the full academic session. Description of a few sample projects has also been included. Since Class X is a terminal stage, great care has been taken to ensure that these activities are directly related to the syllabus, can be easily performed and do not require expensive equipment or materials. A detailed evaluation scheme has also been given. A sincere attempt has been made to ensure that the students or teachers are not put to any kind of stress due to time constraint, curriculum load or any other difficulties in carrying out the proposed activity work. For the sake of completeness and reinforcement of the concept, the present document reiterates the general features of a Mathematics Laboratory given in the earlier document for Class IX. 

3. Mathematics Laboratory

3.1 What is a Mathematics Laboratory ? 
Mathematics Laboratory is a place where students can learn and explore mathematical concepts and verify mathematical facts and theorems through a variety of activities using different materials. These activities may be carried out by the teacher or the students to explore, to learn, to stimulate interest and develop favourable attitude towards mathematics. 

3.2 Need and purpose of Mathematics Laboratory 

Some of the ways in which a Mathematics Laboratory can contribute to the learning of the subject are: 

• It provides an opportunity to students to understand and internalize the basic mathematical concepts through concrete objects and situations. 

• It enables the students to verify or discover several geometrical properties and facts using models or by paper cutting and folding techniques. 

• It helps the students to build interest and confidence in learning the subject. 

• The laboratory provides opportunity to exhibit the relatedness of mathematical concepts with everyday life. 

• It provides greater scope for individual participation in the process of learning and becoming autonomous learners. 

• It provides scope for greater involvement of both the mind and the hand which facilates cognition. 

• The laboratory allows and encourages the students to think, discuss with each other and the teacher and assimilate the concepts in a more effective manner. 

• It enables the teacher to demonstrate, explain and reinforce abstract mathematical ideas by using concrete objects, models, charts, graphs, pictures, posters, etc. 

3.3 Design and general layout 

A suggested design and general layout of laboratory which can accommodate about 32 students at a time is given here. The design is only a suggestion. The schools may change the design and general layout to suit their own requirements. 

3.4 Physical infrastructure and materials 

It is envisaged that every school will have a Mathematics Laboratory with a general design and layout as indicated with suitable change, if desired, to meet its own requirements. The minimum materials required to be kept in the laboratory may include furniture, all essential equipment, raw materials and other necessary things to carry out the activities included in the document effectively. The quantity of different materials may vary from one school to another depending upon the size of the group. 

3.5 Human Resources 

It is desirable that a person with minimum qualification of graduation (with mathematics as one of the subjects) and professional qualification of Bachelor in Education be made incharge of the Mathematics Laboratory. He/she is expected to have special skills and interest to carry out practical work in the subject. The concerned mathematics teacher will accompany the class to the laboratory and the two will jointly conduct the desired activities. A laboratory attendant or laboratory assistant with suitable qualification and desired knowledge in the subject can be an added advantage. 

3.6 Time Allocation for activities 

It is desirable that about 15% - 20% of the total available time for mathematics be devoted to activities. Proper allocation of periods for laboratory activities may be made in the time table. The total available time may be divided judiciously between theory classes and practical work. 

4. Scheme of Evaluation (Class X)

4.1 Internal assessment 

Theory Examination : 80marks 
Internal Assessment : 20 marks 

Internal assessment of 20 marks, based on school-based examination, will have the following break-up: 

Year-end assessment of activities : 10 marks 
Assessment of project work : 05 marks 
Continuous assessment : 05 marks 

4.2 Assessment of Activity Work 

The year-end assessment of activities and project work will be done during an organized session of an hour and a half with intimation to the Board. The following parameters may be kept in mind for the same: 

a) The proposed internal examination may be organized in the month of February as per the convenience of the schools. 

b) Every student may be asked to perform two given activities during the allotted time. Special care may be taken in choosing these two activities to ensure that the students are not put to any kind of stress due to time constraint. 

c) The students may be divided into small groups of 20-25 as per the convenience of the schools. 

d) The assessment may be carried out by a team of two mathematics teachers including the teacher teaching the particular section. 

e) The break-up of 10 marks for assessment of a single activity could be as under: 

• Statement of the objective of activity : 01 mark 
• Design or approach to the activity : 02 marks 
• Actual conduct of the activity : 03 marks 
• Description/explanation of the procedure : 03 marks 
• Result and conclusion : 01 mark 

The marks for assessment of two activities (10+10) may be added and then reduced to be out of 10. 

Every student may be asked to complete the activities given in this document during the academic year and maintain a proper activity record of this work. 

The schools would keep a record of the activity notebook and project work of the students’ work as well as answer scripts of this examination for verification by the Board, whenever necessary, for a period of six months. 

4.3 Evaluation of project work 

Every student will be asked to do at least one project, based on the concepts learnt in the classroom. The project should be preferably carried out individually and not in a group. The project may not be mere repetition or extension of the laboratory activities, but should aim at extension of learning to real life situations. Besides, it should also be somewhat open-ended and innovative. The project can be carried out beyond the school working hours. Some sample projects are given in the document but these are only illustrative in nature. The teacher may encourage the students to take up new projects. 

The weight age of five marks for project work could be further split up as under Identification and statement of the project Design of the project Procedure/processes adopted Write-up of the project  Interpretation of result : 

01 mark 
01 mark 
01 mark 
01 mark 
01 mark 

4.4 Continuous Assessment 

The procedure given below may be followed for awarding marks for continuous assessment in Class X. 

a) Reduce the marks of Class IX annual examination to be out of ten marks. 

b) Reduce the marks of Class X first terminal examination to be out of ten marks. 

c) Add the marks of (a) and (b) above and get the achievement of the student out of twenty marks. 

d) Reduce the total in (c) above to the achievement out of five marks 

The marks (out of 5) may be added to the score of year-end assessment of activities and project work (10 + 5) to get the total score out of 20 marks. 

Activities 

1. To obtain the conditions for consistency of a system of linear equations in two variables by graphical method. 

2. To verify that the given sequence is an arithmetic progression by paper cutting and pasting method. 

3. To verify that the sum of first n natural numbers is n(n + 1) / 2, that is Sn = n (n + 1) / 2, by graphical method. 

4. To verify the Basic Proportionality Theorem using parallel line board and triangle cut-outs. 

5. To verify the Pythagoras Theorem by the method of paper folding, cutting and pasting 

6. To verify that the angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the  circle, using the method of paper cutting, pasting and folding. 

7. To verify that the angles in the same segment of a circle are equal, using the method of paper cutting, pasting and folding. 

8. To verify, using the method of paper cutting, pasting and folding that 
a. the angle in a semicircle is a right angle, 
b. the angle in a major segment is acute, 
c. the angle in a minor segment is obtuse. 

9. To verify, using the method of paper cutting, pasting and folding that 
a. the sum of either pair of opposite angles of a cyclic quadrilateral is 1800. 
b. in a cyclic quadrilateral the exterior angle is equal to the interior opposite angle.

10. To verify using the method of paper cutting, pasting and folding that the lengths of tangents drawn from an external point are equal.

13. To determine the area of a given cylinder. To obtain the formula for the lateral surface area of a right circular cylinder in terms of the radius (r) of its base and height (h).

14. To give a suggestive demonstration of the formula for the volume of a right circular cylinder in terms of its height (h) and radius (r) of the base circle.

15. To make a cone of given slant length (l) and base circumference (2pr) .

16. To give a suggestive demonstration of the formula for the lateral surface area of a cone.

17. To give a suggestive demonstration of the formula for the volume of a right circular cone.

18. To give a suggestive demonstration of the formula for the surface area of a sphere in terms of its radius.

19. To give a suggestive demonstration of the formula for the volume of a sphere in terms of its radius.

20. To get familiar with the idea of probability of an event through a double colour card experiment.

More Info Click Here...........

Courtesy : CBSE.NIC.IN