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**The Students may be provided with opportunities individually/in groups and encouraged to –**

- Extend the methods of finding LCM and HCF of large numbers learnt earlier to general form.
- discuss different aspects of polynomials, such as - their degree, type (linear, quadratic, cubic), zeroes etc., relationship between their visual representation and their zeroes.
- Play a game which may involve a series of acts of factorising a polynomial and using one of its factors to form a new one. For example, one group factorising says, (x
^{3}– 2x^{2}– x – 2) and using one of its factor x-1 to construct another polynomial which is further factorised by another group to continue the process. - Discuss different aspects of linear equations by engaging students in the activities of the following nature:
- One group may ask another to form linear equation in two variables with coefficients from a particular number of systems i.e. natural numbers/ numbers that are not integers etc.
- Graphically representing a linear equation in 1D or 2 D and try to explain the difference in their nature.
- Encouraging students to observe identities & equations and segregate them.

- Use graphical ways to visualise different aspects of linear equations such as visualising linear equations in two variables or to find their
**NCERT Solution for Class 10 Mathematics**. - Observe and analyse patterns in their daily life situations to check if they form an Arithmetic Progression and, if so, find rule for getting their nth term and sum of n terms. The situations could be - our savings/ pocket money, games such as playing cards and snakes & ladders, etc.
- Analyse and compare different geometrical shapes, charts, models made using paper folding and tell about their similarity and congruence.
- Discuss in groups different situations such as constructing maps etc. In which the concepts of trigonometry are used.
- Work in projects related to heights and distances, that may include situations in which methods have to be devised for measuring the angle of inclination of the top of a building and their own distance from the building.
- Device ways to find values of different trigonometric ratios for a given value of a trigonometric ratio.
- Observe shapes in the surroundings that are a combination of shapes studied so far such as cone, cylinder, cube, cuboid, sphere, hemisphere etc. They may work in groups and may provide formulas for different aspects of these combined shapes.
- To determine areas of various materials, objects, designs around them. For e.g. design on a handkerchief, design of tiles on the floor, geometry box etc by doing Worksheets and referring to
**NCERT Books for Class 10** - Discuss and analyse situations related to surface areas and volumes of different objects such as, (a) given two boxes of a certain shape with different dimensions, if one box is to be changed exactly like another box , which attribute will change, surface area or volume? (b) By what percent will each of the dimensions of one box have to be changed to make it exactly of the same size as the other box?
- Discuss and analyse the chance of happening of different events through simple activities like tossing a coin, throwing two dice simultaneously, picking up a card from a deck of 52 playing cards etc.
- Generalise the formulas of mean, median and mode read in the earlier classes by providing situations for these central tendencies
**Sample papers for Class 10 Mathematics** - To draw tangents to a circle from a point which lies outside and a point which lies inside the circle. They may be motivated to evolve different ways to verify the properties of such tangents.

**What are the two levels of mathematics in Class 10 ?**

The CBSE Board has introduced two levels of examination in Mathematics for the students who are going to appear in the Board examination for class 10. The details of this scheme are as under:

- Two levels of Examination will be held in the subject of Mathematics in the Board examination for Class 10 and the same shall not be applicable to the internal assessment in class 10.
- First level would be the same as the existing one, and the other would be an easier level.
- There shall not be two levels of Assessment/Examination for class IX.
- The nomenclature for the two Examinations will be; Mathematics-Standard for the existing level of examination, and Mathematics-Basic for the easier level of examination.
- The syllabus, class room teaching and internal assessment for both the levels of examination would remain the same so that the students get an opportunity to study the whole range of topics throughout the year and are able to decide the level of Board examination depending upon their aptitude and abilities.
- The Standard level will be meant for students who wish to opt for Mathematics at Sr. Secondary level and the Basic level would be for students not keen to pursue Mathematics at higher levels.
- A student will have the right to choose between the two levels of Examination at the time of submission of List of Candidates (LoC) by the affiliated school to the Board through online.
- In case student fails at any level of Mathematics, he/she can appear at the compartment examination as per norms of the Board.
- A student, who qualifies the Mathematics-Basic, shall be given an option to appear in Mathematics-Standard at the time of Compartment exams as per norms of the Board, in case he/she changes his/her mind to pursue Mathematics at Senior Secondary level.

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