# CBSE CLASS 10 MATH

LESSON PLAN FOR CBSE CLASS 10 MATHEMATICS TEACHERS

 www.onlinepsa.in LESSON PLAN FOR MATHEMATICS TEACHERS OF CLASS X Board: CBSE | Class: X | Subject: Maths Chapter Name: Real Numbers

 Time Allotted For The Lesson This lesson is divided across five modules. It will be completed in five class meetings. Prerequisite Knowledge Rational Numbers: Class VIII Number System: Class IX Short Description Of The Lesson This lesson will introduce learners to Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic. Further, they will learn to calculate the highest common factor (HCF) of numbers using Euclid’s Division Lemma and the HCF and the least common multiple (LCM) of numbers using the prime factorisation method. They will also recall the properties of rational and irrational numbers and study a few theorems pertaining to these numbers. Objectives Euclid’s Division Lemma/Algorithm eorem of Arithmetic to calculate the HCF and LCM of numbers where is a positive number √ is an irrational number properties of rational numbers and their decimal expansions – terminating decimal expansions of rational numbers Aids Audio Visual Aids Relevant Modules from Teach Next on Lemma

 Other Audio Visual Aids Access the videos relevant to the chapter ‘Real Numbers’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities   A.  Warm-up Session Begin the lesson by recalling the concepts pertaining to the real number system. You may show the diagram of the real number system and ask the students the definitions of different types of numbers. You may also conduct a quiz covering the concepts, such as the properties of rational and irrational numbers and representing rational and irrational numbers on a number line     Real Number System   B.   Euclid’s Division Lemma or Division Algorithm: Practice Questions In this activity, students will learn to calculate the HCF of given numbers using Euclid’s Division Lemma. Teacher’s Notes Provide the historical and biographical details about Euclid. He was a Greek mathematician, who lived around 300 BC and was popularly known as Euclid of Alexandria. Euclid is also known as the Father of Geometry owing to his significant contribution to the subject. He wrote a treatise consisting of 13 books called ‘Elements’, which served as the main textbook for teaching mathematics even till the early 20th century. ‘Elements’ is mainly known for its geometric results and number

 Arithmetic and Applying the Fundamental Theory of Arithmetic, to the students. Thereafter, give questions to the students to calculate the HCF and LCM of given numbers using the prime factorisation method. Get the students to solve these questions in their maths exercise books.   D. Presentations: Rational and Irrational Numbers In this activity, learners will make presentations on the theorems pertaining to irrational and rational numbers. Teacher’s Notes Divide the class into groups and ask them to make presentations on the following theorems: Group A: Prove that if the prime number p divides a2, then p divides a, where a is a positive number. Group B: Prove that √2 is an irrational number. Group C: Theorem on Terminating Decimal Expansion: Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form p/q, where p and q are coprime, and the prime factorisation of q is in the form 2n5m, where, n, m are non-negative integers. Group D: Theorem on terminating decimal expansions: Let x=p/q be a rational number, such that the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. Then x has a decimal expansion which terminates. Group E: Theorem on non-terminating repeating decimal expansions: Let x=pq be a rational number, such that the prime factorisation of q is not of the form 2n 5m, where n, m are non- negative integers. Then, x has a decimal expansion which is non-terminating repeating (recurring). Supplemental Activities Ask the students to find out about the RSA algorithm, an internet encryption and authentication system, and the use of prime numbers in it. Expected Outcome After studying this lesson, students will be able to explain Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic. They will they be able to calculate the HCF of numbers using Euclid’s Division Lemma and the HCF and LCM of numbers using the prime factorisation method. They will be able to recall the properties of rational and irrational numbers and prove a few theorems pertaining to these numbers. Student Deliverables given by the teacher irrational numbers Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan Board: CBSE | Class: X | Subject: Maths Chapter Name: Polynomials

 Time Allotted For The Lesson This lesson is divided across five modules. It will be completed in five class meetings. Prerequisite Knowledge Polynomials: Class IX Short Description Of The Lesson In this lesson, learners will recall the basic terminology of polynomials, their categories and the method to calculate their zeroes. They will also learn to find the zero or zeroes of a polynomial by studying its graph. Moreover, they will study the relationship between the zeroes and the coefficients of linear, quadratic and cubic polynomials. Further, they will learn about the division algorithm for polynomials and also verify the division algorithm. Aids Relevant Modules from Teach Next Polynomials – Basic Terminology –  Linear Polynomials –  Cubic Polynomials Other Audio Visual Aids Access the videos relevant to the lesson ‘Polynomials’ from the Library resources. Aids Non-Technical None Procedure Teacher-Student Activities   A. Warm-up Session Begin the session with a simple activity to help students recall their prior knowledge about polynomials. Teacher’s Notes

 E.  Finding the Zeroes of Cubic Polynomials In this activity, students need to find the sum of zeroes, product of zeroes and sum of the products of zeroes taken two at a time for a given cubic polynomial. Teacher’s Notes Write down a cubic polynomial on the board along with its zeroes. Ask the students to find the sum of zeroes, product of zeroes and sum of the products of zeroes taken two at a time for the given cubic polynomial. Once done, ask them to verify the relationship between the zeroes and the coefficients of the polynomial.   F.  Division Algorithm Activity In this activity, students need to verify the division algorithm after performing the polynomial division. Teacher’s Notes Discuss the division algorithm in the class. Then, write down two polynomials on the board and ask the students to divide one by the other. Once done with the division, ask the students to verify the division algorithm. Each student should do the division and the verification in his/her notebook. Supplemental Activities Conduct a quiz in the class covering the important concepts covered in the topic. Expected Outcome After studying this lesson, learners will be able find the zero or zeroes of a polynomial by studying its graph. They will also be able to verify the relationship between the zeroes and the coefficients of linear, quadratic and cubic polynomials. Further, they will be able to verify the division algorithm. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Math Chapter Name: Pair of Linear Equations in Two

 Time Allotted For The Lesson This lesson is divided across seven modules. It will be completed in seven class meetings. Prerequisite Knowledge Linear Equations in Two Variables: Class IX Short Description Of The Lesson In this lesson, learners will study about the general form of a pair of linear equations in two variables. They will learn to solve  a pair of linear equations in two variables by using the graphical method as well as the algebraic methods, such as substitution, elimination and cross-multiplication. They will also learn to solve non-linear equations. Objectives two variables method consistent or inconsistent by comparing the ratios of the coefficients of the equations substitution method elimination method – multiplication method -linear equations by reducing it to a pair of linear equations

 Aids Audio Visual Aids Relevant Modules from Teach Next Conditions of Pair of Linear Equations -Multiplication Method -Linear Equations Other Audio Visual Aids Access the videos relevant to the lesson ‘Pair of Linear Equations in Two Variables’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities A.  Warm-up Session Begin the lesson by conducting a simple activity to help students recall their prior learning of linear equations in two variables. Write an equation in two variables on the board and ask the students to find its solution. You can also ask them to graphically find the solution of the equation. Then, present the students with a simple word problem, which can be represented by a pair of linear equations in two variables. Help the students to represent this situation with a pair of linear equations in two variables. Thereafter, ask them to recall the general form of a linear equation in two variables and write it on the board. Now, explain to the students the general form of a pair of linear equations in two variables. B.  Graph Activity In this activity, students need to graphically find the solution of a pair of linear equations in two variables. Teacher’s Notes Write a word problem on the board and ask each student to represent the information in the problem by a pair of linear equations in two variables and then graphically solve the equations. Thereafter, ask them to study the graphs, and determine if the equations are consistent or inconsistent. Additionally, write down a few word problems on the board and ask the students to represent them by the pairs of linear equations in two variables. They also need to determine if the equations are consistent or inconsistent by comparing the ratios of the coefficients of the equations. C.  Chit Activity

 In this activity, students need to algebraically find the solutions of pairs of equations. Teacher’s Notes Divide the class into a few groups. Prepare chits with word problems (which can be situations) written on them. Also, mention the method (substitution, elimination or cross- multiplication) to be used to find the solution. Present the chits to the groups and ask a student from each group to pick up a chit. Now, the members of a group can discuss the problem (situation) amongst themselves. Once done, ask a student from the group to represent the given situation as a pair of linear equations in two variables on the board. The student also needs to solve the equations using the method mentioned in the chit. Supplemental Activities Ask the students to do the following activity. Frame a word problem and exchange your question with your neighbour in the class. Represent the situation in the word problem by a pair of linear equations in two variables and solve the equations using any of the algebraic methods learnt in the lesson. Expected Outcome After studying this lesson, learners will be able to solve a pair of linear equations in two variables by using the graphical method as well as the algebraic methods, such as substitution, elimination and cross-multiplication. They will also be able to solve non-linear equations. Student Deliverables – Solutions of non-linear equations Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Quadratic Equations

 Time Allotted For The Lesson This lesson is divided across three modules. It will be completed in three class meetings. Prerequisite Knowledge Polynomials: Class X Short Description Of The Lesson This lesson will introduce learners to quadratic equations and the different methods to find their roots. They will also learn to derive the quadratic formula and use it to find the roots of a quadratic equation. Further, they will learn to find the nature of the roots of a quadratic equation as well as the sum and the product of the roots. Objectives given situation in the form of a quadratic equation completing the square the solution of a quadratic equation using the quadratic formula equation Aids Audio Visual Aids Relevant Modules from Teach Next Other Audio Visual Aids

 Student Deliverables ons given by the teacher Assessment Class Test and extra sums from refreshers and Teach Next Modules. Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Arithmetic Progression

 Time Allotted For The Lesson This lesson is divided across two modules. It will be completed in two class meetings. Prerequisite Knowledge None Short Description Of The Lesson In this lesson, learners will be introduced to the concept of arithmetic progression or AP. They will learn about the general form of an AP. They will also learn about the first term, the common difference and the nth term of an AP. Additionally, they will learn to find the sum of the first n terms of an AP. Objectives progression or AP given AP AP Aids Audio Visual Aids Relevant Modules from Teach Next Other Audio Visual Aids Access the videos relevant to the lesson ‘Arithmetic Progression’ from the Library resources. Aids No technical

 Divide the class into three groups. Ask each group to make a presentation. The first group needs to derive the formula for the nth term of an AP, the second group has to derive the formula for the sum of the first n terms of an AP and the third group has to derive the formula for the sum of first n positive integers. D. Chit Activity In this activity, students need to answer questions on AP. Teacher’s Notes Divide the class into a few groups. Create chits with different types of questions written on them. Now, present the chits to a group and ask a student from the group to pick up a chit. Then, ask the student to read out the question and solve the problem on the board. Include questions wherein the students need to find the nth term of a given AP. Additionally, give an AP and ask the students to find the sum of the first n terms of the AP. You can also ask them to find the sum of the first n positive integers given to them. Continue the activity with other groups as well. Supplemental Activities Ask the students to work on the following activities: Observe the pattern of the graph. Extrapolate the graph to estimate the next numbers in the series. arithmetic progression. numbers in a finite AP. Aryabhata, a great Indian mathematician- astronomer, gave the method to express the arithmetic series in one of his most famous works ‘Aryabhatiya’. Expected Outcome After studying this lesson, learners should be able to identify an AP. They should also be able to identify the first term and the common difference of an AP and find the nth term of an AP. Additionally, they should be able to find the sum of the first n terms of an AP and the sum of the first n positive integers. Student Deliverables Review questions given by the teacher Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Triangles

 Time Allotted For The Lesson This lesson is divided across seven modules. It will be completed in seven class meetings. Prerequisite Knowledge Triangles: Class IX Short Description Of The Lesson This lesson will introduce learners to the concept of similarity. They will learn about the similarity of different figures and the similarity of triangles. They will also learn important theorems  like the basic proportionality theorem and its converse, the AAA similarity criterion, the SSS similarity criterion and the SAS similarity criterion. Further, they will study theorems related to the areas of similar triangles as well as the Pythagoras Theorem and its converse. Objectives the same number of sides ic proportionality theorem triangles e the Pythagoras Theorem

 Aids Audio Visual Aids Relevant Modules from Teach Next   y Criterion Other Audio Visual Aids Access the videos relevant to the lesson ‘Triangles’ from the Library resources. Aids Non-Technical None Procedure Teacher-Student Activities   A.  Warm-up Session Begin the lesson by conducting a simple activity to help students recall prior knowledge on congruency and triangles. Get a few paper cutouts of geometrical figures to the classroom. For example, you can get the cutouts of three triangles. Of these triangles, two triangles must be of the same shape and size, while one can be of a larger or a smaller size, but of the same shape. Now, ask the students to choose the congruent figures of the three. Thereafter, explain the concept of similarity with the help of the third triangle. Additionally, you may conduct an activity wherein the students will study the changing size of shadows made by a triangle. Focus the light from a torch or any other source of light on a wall. Place a triangular cardboard between the light source and the wall. Keep moving the triangle towards and away from the light source. Each time, observe the shadow cast on the wall. You may also ask the students to take the measurements of the shadows. The shadows would be of different sizes but similar to each other and the triangular cardboard. You can also get several similar figures or objects to the classroom to explain the concept of similarity. Ask the students to find similar figures or objects in the classroom. In the session, also discuss the ASA congruence rule and the SSS congruence rule.   B.  Similarity of Polygons and Triangles

 In this activity, students need to explain the conditions of similarity for polygons and triangles. Teacher’s Notes Divide the class into two groups and assign a topic to each group. Ask one of the groups to explain the conditions of similarity for polygons with the same number of sides and the other group to explain the conditions of similarity for triangles. The students can use cutouts of triangles and polygons or draw out the triangles and polygons on the board to explain the conditions of similarity. Also, ask each student to get at least one pair of similar objects to the class. C.  Proving Theorems In this activity, students need to prove a few theorems and similarity criteria. Teacher’s Notes Divide the class into five groups and ask each group to prove a theorem or similarity criterion. The theorems and similarity criteria to be proved are as follows: the basic proportionality theorem D.  Areas of Similar Triangles and Pythagoras Theorems In this activity, students need to prove theorems related to the areas of similar triangles as well as the Pythagoras Theorem and its converse. Teacher’s Notes Divide the class into four groups and ask them to prove the following theorems: Group A: Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Group B: Prove that if a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and to each other. Group C: Prove the Pythagoras Theorem. Group D: Prove the converse of the Pythagoras Theorem. Supplemental Activities Ask the students to measure the height of a flag pole, building or tree using the properties of similar triangles. You can ask the students to choose an object whose height may be difficult to measure. For measuring the height of such objects, ask the students to measure the length of the shadow cast by the object. Next, ask them to measure the length of the shadow cast by a ruler or a yardstick (or any other object of known height)

 standing straight up on the ground. Note that the lengths of the shadows of the objects of known height and unknown height should be measured at the same time of the day. Now, the lengths of the shadows of the objects of known height and unknown height and the length of the ruler or the yardstick are known. As the sun’s rays are almost parallel over such a small distance, the triangles formed will be similar. Therefore, the unknown height can be found using the following proportion. Expected Outcome After studying this lesson, learners will be able to explain the concept of similarity. They will be able to prove the basic proportionality theorem and its converse, the AAA similarity criterion, the SSS similarity criterion and the SAS similarity criterion. Further, they will be able to prove the theorems related to the areas of similar triangles as well as the Pythagoras Theorem and its converse. Additionally, the learners will be able to use the results obtained from the theorems and solve problems. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Coordinate Geometry

 Time Alloted For The Lesson This lesson is divided across three modules. It will be completed in three class meetings. Prerequisite Knowledge Coordinate Geometry: Class IX Short Description Of The Lesson In this lesson, the learners will learn to find the distance between two points whose coordinates are given. They will also learn to find the coordinates of a point that divides a line segment joining two points of known coordinates internally in a given ratio. Further, they will learn to calculate the area of a triangle using the coordinates of its vertices.

 Objectives e the distance formula to find the distance between any two points whose coordinates are given coordinates are given whose coordinates are given segment joining two points of known coordinates internally in a given ratio using the coordinates of its vertices three vertices are given Procedure Teacher-Student Activities   A.  Warm-up Session Begin the lesson by conducting a simple activity to help students recall their prior knowledge of coordinate geometry. You can draw the Cartesian plane on the board and ask the students to identify the axes and name them. Then, ask them to identify and name the four quadrants into which the axes divide the plane. Mention the coordinates of a few points and ask the students to mark the points on the Cartesian plane. Thereafter, you can discuss a few applications of coordinate geometry. On a map, the location of a city or a country is usually given as a set of coordinates. Another application of coordinate geometry is to determine the latitude and longitude of a place/object, for example, the location of a ship at sea. Computer graphic designers also refer to the coordinates on the computer screen to create figures and computer animations. Additionally, coordinate geometry is widely used in art, buildings, design and cloth manufacturing, space exploration and so on.   B.  Graph Activity In this activity, students need to find the distance between two points marked on a graph paper and calculate the area of a triangle drawn on a graph paper. Teacher’s Notes Ask each student to get two sheets of graph paper to the class. Ask them to draw the Cartesian plane on both the papers. Thereafter, they need to mark two points in the first quadrant of one of the graph papers. Now, ask the students to exchange their graph papers with their neighbours. Next, ask the students

 Supplemental Activities Ask the students to solve the questions given in ‘Summative Assessment’ in the CCE/Activities section. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Introduction to Trigonometry

 Time Allotted For The Lesson This lesson is divided across nine modules. It will be completed in nine class meetings. Prerequisite Knowledge Triangles: Class X Short Description Of The Lesson This lesson will introduce students to the concept of trigonometry. They will learn about the trigonometric ratios of an acute angle in a right angled triangle. They will also learn about the trigonometric ratios of specific angles such as 00, 900, 450, 600 and 300 and the trigonometric ratios of complementary angles. They will also study different trigonometric identities.

 Objectives os of an acute angle of a right angled triangle such as ‘adjacent side’, ‘hypotenuse’ and ‘opposite side’ the ratios is known 0 0 0 0 ic ratios of 300 angles trigonometric identities Aids Audio Visual Aids Relevant Modules from Teach Next     Other Audio Visual Aids Access the videos relevant to the chapter ‘Introduction to Trigonometry’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities   A. Warm-up Session Begin the lesson by recalling the Pythagoras theorem. Introduce the concepts of the angle of elevation and the angle of depression using some practical examples. For example, a girl is looking at a plane from her garden and a boy is looking down from the balcony of his apartment at a festival procession at one end of the street. Explain how a right angled triangle can be imagined to be formed and used to calculate heights and distances with the help of trigonometry in these situations. Thereafter, explain the concept of trigonometry and talk briefly about its history. Ancient Egyptians used the ideas from trigonometric functions and similar triangles while building

 pyramids. In ancient Greece, trigonometric functions were used to observe the position of the stars to predict the time of the day or the period of the year. Tell the students about some practical applications of trigonometry. It is used in physics, engineering, astronomy and chemistry. Trigonometry helps in various fields such as optics and statics. In mathematics, it is used in linear algebra and statistics.   B.  Flash Card Activity In this activity, students will calculate the trigonometric ratios of an acute angle of a given right angled triangle. Teacher’s Notes Teach the students about the trigonometric ratios of the acute angle of a right angled triangle. Prepare flash cards with an image of a right angled triangle on every card and some questions regarding the calculation of its trigonometric ratios. Divide the class into two teams and show them a card with the questions. The team members will discuss amongst themselves and then one volunteer will announce the answers. You may show the same card to both teams and ask them to work out the answer or show different cards to both teams. The team getting maximum correct answers will be the winner.   C.  Presentations on Trigonometric Ratios In this activity, students will deliver presentations on trigonometric ratios of 00, 900, 450, 600 and 300. Teacher’s Notes Divide the class into three groups and assign them presentations on the following topics: 0 0 and 600 os of 00 and 900   Ask the groups to take the example of a right angled triangle. In their presentations, they have to explain how to arrive at the trigonometric ratios of the angles assigned to them. Once a group is done with its presentation, students from the other groups can ask pertinent questions. After the activity is over, give questions based on the trigonometric ratios of various angles to all groups. . D.  Grid Activity In this activity, students will have to write the values of the trigonometric ratios of specific angles. Teacher’s Notes

 Create a grid with angles and trigonometric ratios. Leave some blanks in the grid for trigonometric ratios and ask the students to fill in these blanks. You can either show the grid to the students or draw it out on the board.   E.    Board Activity: Trigonometric Ratios of Complementary Angles In this activity, students will solve a few questions using the trigonometric ratios of complementary angles. Teacher’s Notes Teach the students to derive the trigonometric ratios of complementary angles of a right angled triangle. Thereafter, write a question on the board regarding the trigonometric ratios of complementary angles. Ask all students to solve the questions in their notebook. You may ask any student from the class to solve the question on the board. Similarly, give more questions to the students. . F.       Charts on Trigonometric Ratios and Trigonometric Identities In this activity, students will prepare charts on trigonometric ratios and trigonometric identities. Teacher’s Notes Divide the class into three groups and ask them to prepare charts on the following topics: right angled triangle. es of trigonometric ratios of 00, 900, 450, 600 and 300. complementary angles. Make another table with trigonometric identities.

 Supplemental Activities Ask the students to perform the following activities: how it is used to determine distances in astronomy. Then, share your information with the class. mathematician of the Gupta age, and his contribution to trigonometry. Expected Outcome After studying this lesson, students should be able to cite the trigonometric ratios of an acute angle of a right angled triangle. They should also be able to work out the trigonometric ratios of specific angles such as 0⁰ , 90⁰ , 45⁰ , 60⁰ and 30⁰ and the trigonometric ratios of complementary angles. Moreover, they should be able to use different trigonometric identities to solve questions. Student Deliverables ons on trigonometric ratios Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Some Applications of Trigonometry

 Time Allotted For The Lesson This lesson has one module. It will be completed in one class meeting. Prerequisite Knowledge Introduction to Trigonometry: Class X

 Short Description Of The Lesson This lesson will introduce students to the various concepts related to trigonometry, such as line of sight, angle of elevation and angle of depression. They will also learn to solve word problems pertaining to heights and distances using the trigonometric ratios. Objectives angle of depression ratios Aids Audio Visual Aids Relevant Modules from Teach Next Other Audio Visual Aids Access the videos relevant to the chapter ‘Some Applications of Trigonometry’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities A.  Warm-up Session Begin the lesson by recalling the concepts of trigonometric ratios. You may create flash cards with some angles mentioned on one side and the value or trigonometric ratio of the angles on the other side of the cards. For example, you can write Sin 90o on one side of a flash card and its value ‘1’ on the other side. Conduct a quiz in the class using these flashcards. Thereafter, talk about the angle of elevation, angle of depression and line of sight. Ask the students to cite a few practical examples of angle of elevation and depression. Two examples are provided here: –metre high light house. Her eyes are making an angle of depression with the rock, which is lying near the base of the light house. of sight of the man will form an angle of elevation. B.  Measuring Height with an Inclinometer In this activity, students will learn to make an inclinometer or clinometers and measure the angle of elevation and the height of an object. Teacher’s Notes Tell the students how to make an inclinometer and then explain its working to them. Materials Required: r washer)

 Procedure Attach the straw to the protractor (using the adhesive) as shown in the diagram. Then, attach the thread (with the mass tied at its end) to the middle of the protractor. The thread should hang vertically as shown in the diagram.     Now, you can use the inclinometer to measure the height of various objects, such as a tree or a building. Here are the steps that need to be followed: 1.  Choose an object whose height is to be measured. 2.   Stand at a distance from the object and look at its top through the straw. On looking at something above your head the inclinometer will tilt. Read and record the value of the angle marked by the thread on the protractor. This will be the angle of elevation or . Refer to the image   3.   Measure the distance between you and the object. You may call this distance l   4.   Use your readings to calculate the height of the object using

 the following formula. The total height (or ) of the object will be , where refers to the height of the observer from the ground C. Heights and Distances: Practical Questions In this activity, students will learn to solve the questions based on height and distances. Teacher’s Notes Divide the class into two groups and give them questions based on heights and distances. Supplemental Activities Ask the students to use their inclinometers to measure the angles of inclination and depression of different objects in their neighbourhood. Expected Outcome After studying this lesson, students should be able to know about various concepts related to trigonometry, such as line of sight, angle of elevation and angle of depression. They should also be able to solve word problems pertaining to heights and distances using the trigonometric ratios. Student Deliverables height of an object Assessment Class Test and extra sums from refreshers and Teach Next Modules. Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Circles

 Time Alloted For The Lesson This lesson has one module. It will be completed in one class meeting. Prerequisite Knowledge Circles: Class IX Short Description Of The Lesson In this lesson, students will learn about tangents and secants to a circle. Moreover, they will also prove theorems and conduct a few activities related to the tangents of a circle.

 Objectives circle perpendicular to the radius through the point of contact external point to a circle are equal outside a circle Aids Audio Visual Aids Relevant Module from Teach Next Other Audio Visual Aids Access the videos relevant to the chapter ‘Circles’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities A.  Warm-up Session Begin the lesson by drawing the following illustration on the board     Thereafter, ask the learners to identify the radius, diameter, sector, secants and tangents present in the illustration. After the learners have answered, lead into the module.   B.  Charts and Activities: Theorems on Tangents to a Circle In this activity, learners will prove theorems and solve exercises related to tangents to a circle. Teacher’s Notes Part 1 Divide the class into two groups – A and B. Assign the following topics to the groups and ask them to prepare charts. These charts can be later displayed in the class. any point of a circle is perpendicular to the radius through the point of contact. an external point to a circle are equal.

 Part 2 After the learners have prepared the charts, provide questions based on the theorems on tangents to a circle and ask them to solve these questions in the class. Expected Outcome After studying this lesson, learners will be able to explain the concepts of a tangent and a secant to a circle. Moreover, they will be able to prove theorems and solve exercises related to the tangents of a circle. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Constructions

 Time Allotted For The Lesson This lesson is divided across three modules. It will be completed in three class meetings. Prerequisite Knowledge Constructions: Class IX Triangles: Class X Circles: Class X Short Description Of The Lesson In this lesson, learners will be taught to divide a line segment in a given ratio using a compass. They will learn the construction of a triangle similar to a given triangle as per the specified scale factor. The learners will also learn the construction of the pair of tangents from an external point to a given circle. Moreover, they

 will mathematically prove these constructions. Objectives e segment is divided as per the given ratio specified scale factor constructed as per the specified scale factor a given circle to a given circle are constructed Aids Audio Visual Aids Relevant Modules from Teach Next Other Audio Visual Aids Access the videos relevant to the chapter ‘Constructions’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities A. Warm-up Session   Begin the lesson by holding a quiz pertaining to the following topics learnt previously: •  Similarity of triangles •  Criteria for similarity of triangles You may also draw triangles (with the measurements of lengths and angles) on the board. Then, ask the learners to identify whether the triangles are similar and the criterion they used to come to the conclusion. After the learners have answered, lead into the lesson.   B. Division of a Line Segment: Construction and Verification In this activity, learners will divide a line segment in a given ratio using a compass and then mathematically prove the construction. Teacher’s Notes Part 1 Draw two line segments of equal measurements on the board. The lengths of the line segments should be in decimals. For

 example, you may draw two line segments, each measuring 15.7 cm. Then, select two learners and ask them to divide the given line segments using only a ruler. Ask one of the learners to divide the line segment in the ratio 1:1 and the other learner to divide the other line segment in the ratio 2:3. Thereafter, ask the learners to measure the divisions to check if the line segments are divided according to the given ratios. You may also ask the learners to share the difficulties they faced while dividing the line segment. Part 2 After the learners have answered, demonstrate the division of a line segment in a given ratio using a compass. Thereafter, mathematically prove the construction. Finally, ask the learners if they found this method simpler than the earlier method. Part 3 After the demonstration, divide the class into pairs. Provide each pair with the length of a line segment and a ratio. The learners need to draw the line segment in their books and then divide it in a given ratio using a compass (both the methods covered in Part 2). Also, ask each pair to mathematically prove the constructions. Thereafter, randomly select learners and ask them to demonstrate the construction and proof to the class.   C.         Activity: Construction and Verification of Similar Triangles In this activity, learners will construct a triangle similar to a given triangle as per the specified scale factor (using a compass) and then mathematically prove the same. Teacher’s Notes Divide the class into a few pairs. Provide each pair with the measurements of a triangle and two scale factors such that one of the constructed triangles is smaller and the other larger than the given triangle. For instance, you may provide the following measurements: Sides of a triangle: 5 cm, 7 cm and 6 cm Scale factors: and First, the learners have to construct the triangle in their exercise books and then construct triangles similar to it as per the specified scale factors. Thereafter, the learners have to mathematically prove the constructions. Later, you may randomly select learners and ask them to demonstrate the construction and the proof to the class.   D.    Activity: Construction and Verification of Tangents to a Circle In this activity, learners will construct tangents to a circle and then

 mathematically prove the constructions. Teacher’s Notes Demonstrate the constructions of tangents to a circle (from a point on the circumference and outside the circle) using a compass. Thereafter, ask the learners to draw two circles of any radius. Tell them to mark a point on one of the circles and then construct a tangent at this point. Thereafter, ask the learners to mark a point outside the other circle and construct the pair of tangents to the circle from this external point. The learners also need to mathematically prove their constructions. Supplemental Activities Ask the learners to do the following activities: Expected Outcome Studying this lesson, learners will be able to divide a line segment in a given ratio using a compass. They will be able to construct a triangle similar to a given triangle as per the specified scale factor. The learners will also be able to construct a pair of tangents from an external point to a given circle. Moreover, they will be able to mathematically prove these constructions. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Areas Related to Circles

 Time Allotted For The Lesson This lesson is divided across four modules. It will be completed in four class meetings.

 Prerequisite Knowledge Perimeter and Area: Class VII Mensuration: Class VIII Introduction to Trigonometry: Class X Some Applications of Trigonometry: Class X Short Description Of The Lesson In this lesson, learners will recall various geometrical terms related to a circle, such as chord, radius, diameter, arc, segment, sector and circumference. They will also be taught to calculate the length of an arc of a circle and the areas of a sector and a segment of a circle. Additionally, they will learn to calculate the areas of combinations of plane figures. Objectives ‘segment’ in relation to a circle Aids Relevant Module from Teach Next nations of Plane Figures Other Audio Visual Aids Access the videos relevant to the chapter ‘Areas Related to Circles’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities A. Warm-up Session Begin the lesson by drawing the following illustration on the board.   Divide the class into small groups. Ask each group to label the chords, radii, diameters, major and minor arcs, major and minor segments and major and minor sectors in the circle B.

 B.  Activities: Area of a Sector and Length of an Arc In this activity, learners will calculate the area of a sector of a circle and the length of an arc of a circle. Teacher’s Notes Note: This activity is divided into three parts. Part 1 Show or draw the image provided on the boar   Then, highlight the circles that are either completely green or brown coloured. Now, recall that if the learners know the radius of each of these circles, then they can easily calculate the corresponding areas. You may ask one of the learners to write the equation to calculate the area of a circle on the board. Part 2 Thereafter, highlight the circles with sectors. Now, ask the learners to list the measurements required to calculate the area of a sector of a circle. After the learners have answered, write the equation to calculate the area of a sector of a circle on the board. Thereafter, provide the measurements of the radii and angles of the sectors and ask the learners to calculate the areas of the sectors. Part 3 After the learners have calculated the areas of the sectors, highlight the lengths of the arcs of the sectors. Now, ask the learners to list the measurements required to calculate the length of an arc of a sector of a circle. After the learners have answered, write the equation to calculate the length of an arc of a sector of a circle. Thereafter, ask the learners to calculate the lengths of the arcs of the sectors based on the measurements provided in Part 2. C.  Activity: Area of a Segment In this activity, learners will calculate the area of a segment of a circle. Teacher’s Notes Show the image provided or draw a similar image on the board.

 Then, ask the learners to identify the chords in the image. Now, shade a segment of the circle and then ask the learners to list the measurements required to calculate the area of this segment. After the learners have answered, write the equation to calculate the area of a segment of a circle on the board. Thereafter, provide the required measurements for each segment of the circle and ask the learners to calculate the area. D. Activity: Areas of Combinations of Plane Figures In this activity, learners will calculate the areas of combinations of plane figures. Teacher’s Notes Tell the learners that there are several everyday objects, which are a combination of two or more geometrical shapes. For example, a quilt with circular designs, a wall with a circular window and a clock with a circular dial. You may also show the images provided or draw similar images on the board

 Thereafter, mention that calculating the areas of these figures may look difficult. However, if we know the measurements (the length and breadth of the quilt and walls, the sides of a triangle and the radii of each circle), then it is possible to calculate the areas of such combinations of plane figures. After the explanation, show the class how to calculate the area of the white cloth seen in the quilt. Supplemental Activities Slice a circular pizza base, cake or paper. Now, ask the learners to calculate the length of an arc of a sector, the area of a sector and the area of a segment. Expected Outcome After studying this lesson, learners will be able to describe various geometrical terms related to a circle, such as chord, radius, diameter, arc, segment, sector and circumference. They will also be able to calculate the length of an arc of a circle and the areas of a sector and a segment of a circle. Additionally, they will be able to calculate the areas of combinations of plane figures. Student Deliverables Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN
 Chapter Name: Surface Areas and Volumes
 Time Allotted For The Lesson This lesson is divided across three modules. It will be completed in three class meetings. Prerequisite Knowledge Perimeter and Area: Class VII Visualising Solid Shapes: Class VII Visualising Solid Shapes: Class VIII Mensuration: Class VIII Surface Areas and Volumes: Class IX Short Description Of The Lesson In this lesson, learners will calculate the surface areas and the volumes of the combination of solids. They will also learn that when a solid is converted to another solid or multiple solids, either of the same or different shapes, the surface area changes but the volume remains constant. Moreover, they will also be taught to calculate the surface area and the volume of the frustum of a cone. Objectives combination of solids solid or multiple solids, either of the same or different shapes, the surface area changes but the volume remains constant frustum of a cone Procedure Teacher-Student Activities A. Warm-up Session Begin the lesson by recalling the prior knowledge of students on the following topics:   Recall the formulae to calculate the surface areas and the volumes of different basic solids. Then, show different objects (or their images) that are made by the combination of different solids.

 Round  Bottom  Flask Test Tube Conical Flask Ask them if they can calculate the surface areas and the volumes of these solids. Then, explain the method to calculate the surface areas and the volumes of these objects by calculating the surface areas and the volumes of different basic solids that form these objects.   B.  Surface Areas and Volumes: Activity In this activity, students will calculate the surface areas and the volumes of the combination of solids. Teacher’s Notes Divide the class into groups. Each group needs to bring an object to the class that is formed by the combination of basic solids. They need to identify the basic solids that make up the object. Then, they should take the measurements of these basic solids and calculate their surface areas and volumes. Based on these calculations, they should work out the surface areas and the volumes of the objects. C.  Clay Activity In this activity, students will calculate the change, if any, in the surface area and the volume of a solid when it is converted into different solid or multiple solids, either of the same or different shapes. Teacher’s Notes Divide the class into two groups. Bring some modelling clay to the classroom. Ask a group to shape the clay in any of the basic solids, such as cube, cuboid, cylinder and sphere. They need to take the required measurements and calculate the surface area and the volume of the solid that they have made. Now, the other group should break the solid and make numerous smaller solids from the clay. Then, they need to take the required measurements and calculate the surface area and the volume of the smaller shapes. Thereafter, ask both groups to analyse the relation between the surface area and the volume of the original solid and the new solids. Conduct a similar activity to prove that when the shape of a

 solid object is changed, its surface area changes but the volume remains constant. For this activity, change the original basic solid into the basic solid of a different shape. For example, change a cube into a cylinder and compare the surface area and the volume of the cube with the cylinder. Supplemental Activities Ask the students to do the following activities: cubes to your friends to arrange them in the form of a cuboid. Ask them how many different cuboids they can make with 12 cubes. You will notice that all these cuboids would have different surface areas but the same volume. Find the cuboids with the smallest surface area and the largest surface area. Expected Outcome After completing the lesson, learners should be able to calculate the surface areas and the volumes of the combination of solids. They should also be able to explain that when a solid is converted to another solid or multiple solids, either of the same or different shapes, the surface area changes but the volume remains constant. Moreover, they should also be able to calculate the surface area and the volume of the frustum of a cone. Student Deliverables None Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Statistics

 Time Allotted For The Lesson This lesson is divided across seven modules. It will be completed in seven class meetings. Prerequisite Knowledge Statistics: Class IX Short Description Of The Lesson This lesson will introduce the students to the various methods used to calculate the mean and mode of grouped data. They will also learn to find the median of grouped and ungrouped data. Moreover, they will learn to graphically represent cumulative frequency curves. Objectives grouped data method  mean method he step deviation method observations observations requency distribution as an ogive Aids Audio Visual Aids Relevant Modules from Teach Next -Direct Method -Assumed Mean Method -Step Deviation Method Mode of Grouped Data

 Other Audio Visual Aids Access the videos relevant to the chapter ‘Statistics’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities   A.  Warm-up Session Begin the session by holding a quiz about the concepts that students have learnt in the previous classes. For example, mean, mode and median. You may divide the class into two groups and give them questions based on the calculation of mean, mode and median from ungrouped data. You may also ask them to interpret data from different types of graphs and frequency distribution tables. Thereafter, show a grouped frequency distribution table to the students and teach them to calculate mean using different methods.   B.  Calculating the Mean of Grouped Data In this activity, students will calculate mean using the direct method, assumed mean method and step deviation method. Teacher’s Notes Give questions to the students to calculate mean using the direct method, assumed mean method and step deviation method. You can also show some frequency distribution tables to the students and ask them which method of mean calculation they would use in each case and the reasons behind their decision.   C.  Calculating the Mode of Grouped Data In this activity, students will calculate the mode of grouped data. Teacher’s Notes Give questions to the students to calculate the mode of grouped data. You may also give some scenarios to the students and ask them which measure of central tendency (mean or mode) should be used in each scenario. For example: the workers.   D.  Calculating the Median of Grouped/Ungrouped Data In this activity, students will calculate the median of ungrouped/grouped data. Teacher’s Notes Give the students some questions to calculate the median of ungrouped data with odd and even number of observations.

 Thereafter, give some practice questions to the students where they have to calculate the median of grouped data.   E.  Cumulative Frequency Curves In this activity, students will learn to graphically represent cumulative frequency distribution. Teacher’s Notes Give a few questions to the students where they have to calculate the median of grouped data by working out the cumulative frequency. Thereafter, ask the learners to graphically depict the frequency distribution by making a cumulative frequency curve or ogive. Tell the students more about ogive. Statistically, ogive refers to the cumulative distribution function. The term was applied by the English statistician Francis Galton to describe the curve of cumulative distribution. Galton had borrowed the term ’ogive’ from architecture, where ‘ogee’ was the name of a typical decorative element used in the English churches in 1400 AD. Ogival curves are used a lot in buildings made in Gothic architecture. Refer to the images of the buildings given here. Chhatrapati Shivaji Terminus, Mumbai Ogival Arches     F.  Charts In this activity, students will make charts on the concepts learnt by them in the class. Teacher’s Notes Divide the class into three groups and ask them to prepare charts on the following topics: used to calculate the mean of grouped data. mean of grouped data.

 (grouped data) and median (grouped and ungrouped data). Supplemental Activities in the class: their houses to the school Expected Outcome After studying this lesson, students should be able to calculate the mean and mode of grouped data. They should also be able to calculate the median of grouped and ungrouped data. Moreover, they should be able to represent cumulative frequency distribution as an ogive. Student Deliverables Charts on various methods to calculate mean, mode and median Assessment Class Test and extra sums from refreshers and Teach Next Modules.

 Lesson Plan ONLINEPSA.IN Board: CBSE | Class: X | Subject: Maths Chapter Name: Probability

 Time Allotted For The Lesson This lesson has one module. It will be completed in one class meeting. Prerequisite Knowledge Probability-An Experimental Approach: Class IX Short Description Of The Lesson This lesson will introduce students to the concept of theoretical probability. They will also learn about various terms, such as equally likely outcomes, elementary event, complement of an event, sure event and impossible event. Moreover, they will be able to solve questions based on theoretical probability. Objectives outcomes, elementary event, complement of an event, sure event and impossible event Aids Relevant Modules from Teach Next Theoretical Approach to Probability Other Audio Visual Aids Access the videos relevant to the chapter ‘Probability’ from the Library resources. Aids No technical None Procedure Teacher-Student Activities   A. Warm-up Session Begin the session by recalling the concepts learnt by students in the previous class. You may ask questions regarding terms, such as experiment, trial, event and outcome. You may also give some questions where the students have to calculate the probability of an event. Thereafter, explain the concept of

 theoretical probability. Simply put, it is the ratio between the number of ways in which an event can occur and the total number of possible outcomes in the sample space.   B.  Experiment In this activity, students will perform an experiment to understand the difference between experimental probability and theoretical probability. Teacher’s Notes Divide the class into a few groups and ask them to perform an experiment as follows. Give three coins to each group and ask them to find the experimental probability of getting at least two heads. The students should record the outcomes of their experiment in a sheet. Then, ask the students to check the outcome of the experiment using theoretical probability. Guide the students in the right direction by asking them about the possible outcomes. Once the activity is done, discuss the difference between the experimental and theoretical probability.   C.  Presentation In this activity, students will perform experiments and explain various concepts, such as equally likely outcomes, elementary event, complement of an event, sure event and impossible event. Teacher’s Notes Divide the class into three groups. The groups have to use different examples to explain the concepts. They can use charts or show experiments in the class. After the presentation, give the students questions (word problems) pertaining to the concepts of probability. Supplemental Activities Ask the students to perform the following activity: the different diseases/ailments they have faced in a given year. Then present the findings in a tabular form and calculate the probability of the most common disease for the children of different age groups. example, the toss of a coin between the captains to decide which team would bat/ball first. as healthcare insurance, advertising, farming and weather forecasting. Share your findings with the class.

 Expected Outcome After studying this lesson, students should be able to understand the concept of theoretical probability. They should also be able to explain various terms, such as equally likely outcomes, elementary event, complement of an event, sure event and impossible event. Moreover, they should be able to solve questions based on theoretical probability. Student Deliverables Presentations on concepts of probability Assessment Class Test and extra sums from refreshers and Teach Next Modules.