# CLASS 9 MATH

LESSON PLAN FOR CBSE CLASS 9 MATH TEACHERS

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Areas of Parallelograms And Triangles

 Prerequisite Knowledge: The Triangle and its Properties: Class VII Congruence of Triangles: Class VII Perimeter and Area: Class VII Understanding Quadrilaterals: Class VIII Practical Geometry: Class VIII Mensuration: Class VIII Triangles: Class IX Quadrilaterals: Class IX Short description of lesson In this lesson, learners will study about the geometrical figures that have the same base and lie between the same parallels. They will also learn that the parallelograms having the same base and lying between the same parallels are equal in area, while the different geometrical figures having the same base and lying between the same parallels may not be equal in area. They will also learn to prove various theorems related to the areas of parallelograms and triangles. Objective      Identify the geometrical figures that have the same base and lie between the same parallels    Explain that the parallelograms having the same base and lying between the same parallels are equal in area    Explain that the different geometrical figures having the same base and lying between the same parallels may not be equal in area     Prove that the parallelograms having the same base and lying between the same parallels are equal in area     Prove that the parallelograms having the same base and equal in area lie between the same parallels     Prove that the area of a triangle is equal to half the  area of a parallelogram if they have the same base and lie between the same parallels    Prove that two triangles having the same base or equal

 bases and lying between the same parallels are equal in area    Prove that two triangles having the same base or equal bases and equal in area lie between the same parallels     Prove that the area of a triangle is equal to half the product of its base and the corresponding height     Prove that a median of a triangle divides it into two triangles of equal areas Aids / Audio Visual Aids Relevant Modules from TeachNext   Figures on Same Base and Between Same Parallels   Theorems Related to Areas of Parallelograms   Theorems Related to Areas of Triangles Access the videos relevant to the chapter ‘Areas of Parallelograms and Triangles’ from the Library resources. Supplemental Activities Ask the students to make various geometrical figures by sticking matchsticks. A few figures should have the same base and lie between the same parallels. While, the other figures should have the same base, but they should lie between different parallels. Additionally, the students should make figures that lie between the same parallels but have different bases. They should bring these matchstick figures to the classroom and then discuss various theorems learnt in the lesson. Expected Outcome After completing the lesson, learners should know about the figures that have the same base and lie between the same parallels. They should also know that the parallelograms having the same base and lying between the same parallels are equal in area, while the different geometrical figures, having the same base and lying between the same parallels may not be equal in area. They should also be able to prove various theorems related to the areas of parallelograms and triangles. Student Derivable   Presentations on theorems related to the areas of parallelograms   Presentations on theorems related to the areas of triangles Assessment Class Test and extra sums from Teach Next Module and Refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Heron’s Formula

 Prerequisite Knowledge Areas of Parallelograms and Triangles: Class IX Short Description Of The Lesson In this lesson, learners will be introduced to Heron’s formula. Moreover, they will learn to calculate the area of a triangle and a quadrilateral using Heron’s formula. Objectives   Calculate the area of a triangle using Heron’s formula   Calculate the area of a quadrilateral using Heron’s formula Aids Audio Visual Aids Relevant Module from TeachNext  Heron’s Formula Access the videos relevant to the chapter ‘Heron’s Formula’ from the Library resources. Supplemental Activities   Ask learners to check the triangular objects in their houses. Then, ask them to record the lengths of the sides of these objects. Thereafter, the learners need to calculate the areas of these triangular objects in their books.   Ask the learners to research on the following topics: o Proofs of Heron’s formula o  Heronian triangle o  Brahmagupta’s formula Expected Outcome After studying this lesson, learners will be able explain Heron’s formula. Moreover, they will be able to calculate the area of a triangle and a quadrilateral using Heron’s formula. Student Deliverables  Review questions given by the teacher Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Polynomials

 Prerequisite Knowledge Algebraic Expressions and Identities: Class VIII Short Description Of The Lesson In this lesson, learners will be taught about polynomials, a type of algebraic expression. They will study about the zero of a polynomial as well as the Remainder Theorem and the Factor Theorem. Additionally, they will be introduced to a few standard identities and will learn to use these identities to factorise and evaluate algebraic expressions. Objectives   Identify if a given algebraic expression is a polynomial   Name a polynomial based on its degree   Find the zeroes of a given polynomial   Prove the Remainder Theorem   Find the remainder using the Remainder Theorem when a polynomial is divided by a linear polynomial   State the Factor Theorem   Verify if a linear polynomial is the factor of a given polynomial   Factorise polynomials using the Factor Theorem or the splitting method   Derive the given algebraic identity   Evaluate polynomials using algebraic identities   Factorise polynomials using algebraic identities Aids Aids Relevant Modules from TeachNext   General Form of a Polynomial in One Variable   Zero of a Linear Polynomial   Remainder Theorem   Factor Theorem   Factorisation Using Algebraic Identities Access the videos relevant to the lesson ‘Polynomials’ from the Library resources

 Supplemental Activities Ask the students to research on polynomials. The research can include the meaning of the term and the  different areas of maths and science where polynomials are widely used. It could also include any other interesting information or facts about polynomials. Expected Outcome After studying this lesson, learners will be able to identify polynomials and its degree. They will be able to find the zeroes of polynomials. They will also be able to prove the Remainder Theorem and state the Factor Theorem and use these theorems to solve problems. Additionally, they will be able to derive a few standard identities and use these identities to factorise and evaluate algebraic expressions. Student Deliverables Review questions given by the teacher Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Lines and Angles

 Prerequisite Knowledge Lines and Angles: Class VII The Triangles and its Properties: Class VII Introduction to Euclid’s Geometry: Class VIII Short Description Of The Lesson In this lesson, learners will revise basic geometrical terms and definitions. They will also learn about the linear pair axiom. The learners will recall knowledge about the different types of angles and the angles formed by a transversal on a pair of parallel and intersecting lines. Moreover, they will be taught to prove theorems related to lines, angles and triangles. Objectives   Explain the terms ‘line’, ‘ray’, ‘line segment’, ‘collinear points’, ‘intersecting lines’ and ‘parallel lines’   Describe the different types of angles   Explain the terms ‘adjacent angles’, ‘linear pair of angles’, ‘complementary angles’, ‘supplementary angles’ and ‘vertically opposite angles’   Prove that vertically opposite angles are equal   Describe the angles formed by a transversal   Explain the corresponding angles axiom   Prove that if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal   Prove that if a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary   Prove that the lines which are parallel to the same line are parallel to each other   Prove that the sum of three angles of a triangle is 180o Aids Relevant Modules from TeachNext   Introduction to Lines and Angles   Pair of Angles   Angles Made by Transversal   Theorems on Parallel Lines – I   Theorems on Parallel Lines – II Other Audio Visual Aids

 Access the videos relevant to the chapter ‘Lines and Angles’ from the Library resources. Supplemental Activities Ask the learners to read how properties of lines and angles are used by professionals. For example, engineers and architects apply the properties of lines and angles while making designs or blueprints for buildings. Expected Outcome After studying this lesson, learners will be able to describe basic geometrical terms and definitions. They will also be able to explain the linear pair axiom. The learners will be able to solve exercises based on the different types of angles and the angles formed by a transversal on a pair of parallel and intersecting lines. Moreover, they will be able to prove related to lines, angles and triangles Student Deliverables   Review questions given by the teacher   Scrapbook on types of angles   Presentation on theorems Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Circles

 Prerequisite Knowledge Basic Geometrical Ideas: Class VI Short Description Of The Lesson This lesson introduces students to circles and the terms related to circles. They will also learn various theorems pertaining to circles. Moreover, they will learn about concyclic points, cyclic quadrilaterals and the theorems associated with these concepts. Objectives   Define a circle   Define various terms, such as centre, circumference, radius, chord, diameter, arc, segment and sector, in relation to a circle   Describe the features of the diameter of a circle   Describe various areas covered by a circle on a plane  Prove that a perpendicular from the centre of a circle to a chord bisects the chord   Prove that the line drawn from the centre of a circle to bisect a chord is perpendicular to the chord   Prove that the equal chords of a circle are equidistant from the centre of a circle   Prove that the chords equidistant from the centre of a circle are equal in length   Prove that the equal chords of a circle subtend equal angles at the centre   Prove that the chords that subtend equal angles at the centre of a circle are equal in length   Define the congruent arcs of a circle and their properties   Prove that the congruent arcs of a circle subtend equal angles at the centre of a circle   Prove that the angle subtended by an arc at the centre is double the angle subtended by the arc at any other point on the remaining part of the circle   Prove that angles subtended by an arc at all points within the same segment of a circle are equal

   Prove that all angles formed in a semicircle are right angles   Define concyclic points   Prove that a circle can pass through three points that form a triangle   Prove that if a line segment joining two points subtends equal angles at two other points on the same side of the line segment, then all the four points are concyclic   Describe the properties of cyclic quadrilaterals   Prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 1800   Prove that if the sum of the opposite angles of a quadrilateral is 180,then the quadrilateral is cyclic Aids Relevant Modules from TeachNext   Basic Concepts   Properties of Perpendicular Bisector of a Chord   Properties of Equal Chords   Angle Subtended By a Chord at the Centre   Theorems Based on Arcs-1   Theorems Based on Arcs-2   Theorems Based on Arcs-3   Concyclic Points   Properties of Cyclic Quadrilaterals Other Audio Visual Aids Access the videos relevant to the chapter ‘Circles’ from the Library resources. Supplemental Activities Ask the students to do the following activities:   Find out about the tangent and secant related to a circle and shares your findings with the class.   Find out why all celestial bodies (except asteroids) are spherical in shape Expected Outcome After studying this lesson, students will be able to explain all the terms related to circles. They will also be able to prove various theorems pertaining to circles, concyclic points and cyclic quadrilaterals. Student Deliverables   Presentations on theorems pertaining to arcs and chords of a circle   Presentations on concyclic points and cyclic quadrilaterals Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Introduction to Euclid’s Geometry

 Prerequisite Knowledge Lines and Angles: Class VII Short Description Of The Lesson This lesson will introduce learners to Euclid’s Geometry. They will learn a few of Euclid’s definitions and axioms. They will also learn about Euclid’s postulates. Objectives   Explain Euclid’s definitions of different terms, such as a point, line, straight line, surface and plane surface   Explain Euclid’s five postulates   Explain Euclid’s axioms Aids Relevant Modules from TeachNext   Euclid’s Definitions   Euclid’s Postulates   Euclid’s Axioms Other Audio Visual Aids Access the videos relevant to the lesson ‘Introduction to Euclid’s Geometry’ from the Library resources. Supplemental Activities Euclid has listed 23 definitions in his Book I of the ‘Elements’. Ask the students to research on the other definitions in Book I. Discuss a few of these definitions in the class. Expected Outcome After studying this lesson, learners will be able to explain some of Euclid’s definitions and axioms. They will also be able to explain Euclid’s five postulates. Student Deliverables Review questions given by the teacher Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Probability

 Prerequisite Knowledge Data Handling: VII Data Handling: VIII Short Description Of The Lesson This lesson will introduce students to the concept of probability. They will learn new terms, such as ’experiment’, ‘trial’, ‘event’ and ‘outcome’. They will also learn to calculate probability in different types of questions. Objectives  Define probability and experimental probability  List the practical applications of probability  Conduct experiments to measure probability  Define the terms ’experiment’, ‘trial’, ‘event’ and ‘outcome’   Calculate probability of an outcome in a given event Aids Relevant Modules from TeachNext Probability-An Experimental Approach Other Audio Visual Aids Access the videos relevant to the chapter ‘Probability’ from the Library resources. Supplemental Activities Ask the learners to perform the following activity:  Take a jar containing six blue marbles, five red marbles, eight green marbles and three yellow marbles. If one marble is chosen at random from the jar, find out the probability of choosing a blue marble, red marble green marble and yellow marble. Expected Outcome After completing this lesson, students will be able to describe the concept of probability and experimental probability. They will be able to explain new terms, such as ‘event’, ‘trial’ and ‘outcome’. Moreover, they will also be able to calculate probability in different types of questions. Assessment Class Test and extra sums from Trach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Constructions

 Prerequisite Knowledge Practical Geometry: Class VII Triangles: Class IX Short Description Of The Lesson In this lesson, learners will study the construction of an angle, an angle bisector and a perpendicular bisector of a line segment. They will also learn about the construction of triangles when specific measurements, like two base angles and perimeter, the length of base, base angle and the sum/difference of two sides are provided. Moreover, the learners will theoretically prove these constructions. Objectives   Construct a triangle when its two base angles and perimeter are known   Prove that the required triangle is constructed from its two base angles and perimeter   Construct the bisector of a given angle   Prove that the angle bisector of a given angle is constructed   Construct an angle measuring 60o at the initial point of a ray   Prove that the required 60o angle is constructed   Construct the perpendicular bisector of a given line segment   Prove that the required perpendicular bisector of a line segment is constructed   Construct a triangle when the length of its base, base angle and the sum of the two sides are known   Prove that the required triangle is constructed from the length of its base, base angle and the sum of two sides   Construct a triangle when the length of its base, base angle and the difference of two sides are known   Prove that the required triangle is constructed from the length of its base, base angle and the difference of two sides

 Aids Audio Visual Aids Relevant Modules from TeachNext   Construction of Triangles   Bisector of an Angle   Construction of 60 Degree angle at the Initial Point of a Ray   Perpendicular Bisector of a Line Segment   Construction of a Triangle Given its Base, Base Angle and Sum of Two Sides   Construction of a Triangle Given its Base, Base Angle and Difference of Two Sides Other Audio Visual Aids Access the videos relevant to the chapter ‘Constructions’ from the Library resources. Supplemental Activities Ask the learners to research on the following topics:   Alternate ways to prove the constructions of angle bisectors and perpendicular bisectors   Application of angle bisectors and perpendicular bisectors Expected Outcome After studying this lesson, learners will be able to construct an angle, angle bisector and the perpendicular bisector of a line segment. They will also be able to construct triangles when specific measurements, like two base angles and perimeter and the length of base, base angle and the sum/difference of the two sides, are provided. Moreover, the learners will be able to theoretically prove these constructions. Student Deliverables   Review questions given by the teacher   Charts on angle bisector and perpendicular bisector   Charts on construction of triangles Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Linear Equations in Two Variables

 Prerequisite Knowledge Linear Equations in One Variable: Class VIII Short Description Of The Lesson This lesson will introduce learners to linear equations in two variables. Further, they will learn to find the solutions of such equations. They will also learn to represent linear equations in two variables on the Cartesian plane. Additionally, they will study about the equations of lines that are parallel to the x-axis and the y-axis. Objectives   Explain the term ‘linear equation in two variables’   Identify if a given equation is a linear equation in two variables   Find solutions for the given linear equations   Represent a linear equation in two variables on the Cartesian plane   Represent the solutions of an equation on a number line and the Cartesian plane Aids Relevant Modules from TeachNext   Linear Equation in Two Variables   Graphical Representation Other Audio Visual Aids Access the videos relevant to the lesson ‘Linear Equations in Two Variables’ from the Library resources. Aids Non-Technical None Supplemental Activities Ask the students to research more about linear equations. Ask them to check if there are linear equations in more than two variables Expected Outcome After studying this lesson, learners will be able to identify linear equations in two variables and find the solutions of such equations. They will also be able to graphically represent linear equations. Student Deliverables   Review questions given by the teacher   Solutions of linear equations   Graphs of the linear equations Assessment Class Test and extra sums from Teach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Quadrilaterals

 Supplemental Activities Ask the students to make the Venn diagram of quadrilaterals that summarises the unique properties of various quadrilaterals. An example is given here. . Expected Outcome After completing the lesson, learners should be able to describe the different types of quadrilaterals and their properties, especially the properties of parallelograms. They should also be able to prove various theorems related to quadrilaterals and parallelograms. Student Derivable  Presentations on the theorems on quadrilaterals and parallelograms Assessment Class Test and extra sums from Trach Next Module and refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Triangles

 Prerequisite Knowledge The Triangles and its Properties: Class VII Congruence of Triangles: Class VII Short Description Of The Lesson In this lesson, learners will study congruent triangles and the criteria for their congruence. They will also be taught to prove the rules of congruence and the properties of triangles. The learners will be explained the non-criteria for the congruence of triangles. Moreover, they will also study a few theorems and conduct a few activities related to the inequalities in a triangle. Objectives  Describe congruent triangles  List the four criteria for the congruence of triangles  Explain the Side-Angle-Side (SAS) congruence rule  Prove the Angle-Side-Angle (ASA) congruence rule  Prove the Side-Side-Side (SSS) congruence rule  Prove the Right Angle-Hypotenuse-Side (RHS) congruence rule   Explain the non-criteria for the congruence of triangles   Prove that the angles opposite to the equal sides of an isosceles triangle are equal   Prove that the sides opposite to the equal angles of a triangle are equal   Prove that if two sides of a triangle are unequal, then the angle opposite to the longer side is larger   Prove that in any triangle, the side opposite to the larger angle is longer     Prove that the sum of any two sides of a triangle is greater than the third side Aids Relevant Modules from Teach Next   Criteria for Congruence of Triangles   Angle-Side-Angle (ASA) Congruence Rule   Side-Side-Side (SSS) Congruence Rule   Properties of Triangles   Inequalities in a Triangle Access the videos relevant to the chapter ‘Triangles’ from the

 Library resources. Supplemental Activities Ask the learners to read about the relationships between the measures of angles and the lengths of sides in triangles. Also, ask them to research on how the properties of triangles help in their construction. Expected Outcome After studying this lesson, learners will be able to describe congruent triangles and the criteria for their congruence. They will also be able to prove the rules of congruence and the properties of triangles. The learners will be able to explain the non-criteria for the congruence of triangles. Moreover, they will be able to prove theorems and solve exercises related to the inequalities in a triangle. Student Derivable   Review questions given by the teacher   Presentation on the congruence of triangles   Charts on the properties of triangles   Presentation on inequalities in a triangle Assessment Class Test and extra sums from Teach Next Module and Refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Coordinate Geometry

 Prerequisite Knowledge Introduction to Graphs: Class VII Short Description Of The Lesson In this lesson, students will be introduced to the Cartesian coordinate geometry. In addition, students will learn to write the coordinates of points given on the Cartesian plane as well as plot points by referring to their coordinates. Objectives   Describe the features of the Cartesian plane   Locate the quadrant of a given point on the Cartesian plane  Write the coordinates of the points marked on the Cartesian plane   Plot a point on the Cartesian plane if its coordinates are given Aids Audio Visual Aids Relevant Modules from Teach Next  Cartesian Plane Other Audio Visual Aids Access the videos relevant to the lesson ‘Coordinate Geometry’ from the Library resources. Supplemental Activities Ask the students to research on the use of coordinate geometry in finding the various features marked on a topographical map. Expected Outcome After studying this lesson, students will be able to explain the concept behind Cartesian coordinate geometry. In addition, they will also be able to write the coordinates of points given on the Cartesian plane. The students will also be able to plot points by referring to their coordinates. Student Deliverables  Presentation on Cartesian Plane Assessment Class Test and extra sums from Teach Next Module and Refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Number Systems

 Prerequisite Knowledge Rational Numbers: Class VIII Short Description Of The Lesson This lesson refreshes students’ knowledge about rational numbers and introduces them to the concept of irrational numbers. They will learn to represent irrational numbers on a number line. They will also learn about real numbers and their decimal expansions. Moreover, they will be taught various mathematical operations on real numbers. They will learn to rationalise the denominator of irrational numbers and will also learn to apply various laws of exponents to real numbers. Objectives   Describe the concept of irrational numbers   Represent irrational numbers on a number line   Describe the concept of real numbers   Find the decimal expansions of real numbers   Express the numbers with terminating decimal expansion and non-terminating recurring decimal expansion as rational numbers   Express a number with non-terminating and non- recurring decimal expansion as a rational number   Determine irrational numbers between two rational numbers   Represent real number on a number line using the process of successive magnification   Describe the results of various mathematical operations of irrational numbers   Describe the various properties with respect to the real numbers   Represent the square root of a real number on a number line   Verify the identities related to the square roots using examples  Rationalise the denominator of a given irrational number

   Verify the laws of exponents involving the same bases   Apply the laws of exponents to the real numbers   Verify the laws of exponents involving different bases but the same exponents Aids Relevant Modules from Teach Next   Irrational Numbers   Real Numbers   Decimal Expansion of Real Numbers in P/Q Form   Representation of Real Numbers on the Number Line   Operations on Real Numbers   Square Root of a Real Number on The Number Line   Rationalising Denominators of Irrational Numbers   Laws of Exponents Other Audio Visual Aids Access the videos relevant to the chapter ‘Number Systems’ from the Library resources. Supplemental Activities Find out about the golden ratio or divine proportion or golden proportion. The golden ratio, symbolised by the green letter (phi), is actually an irrational number, which is approximately equal to 1.618. Expected Outcome After studying the lesson, students will be able to understand the concepts of irrational numbers and rational numbers. They will be able to represent irrational numbers on a number line. They will also learn about real numbers and their decimal expansions. Moreover, they will be able to perform various mathematical operations on real numbers. They will also learn to rationalise the denominator of irrational numbers and apply various laws of exponents to real numbers. Student Deliverables   Review questions given by the teacher      Charts representing square roots and real numbers on a  number line    Presentations on the operations of various properties on real numbers, the identities of square roots and the laws of exponents Assessment Class Test and extra sums from Teach Next Module and Refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Surface Areas and Volumes

 Prerequisite Knowledge Perimeter and Area: Class VII Visualising Solid Shapes: Class VII Visualising Solid Shapes: Class VIII Mensuration: Class VIII Short Description Of The Lesson In this lesson, learners will calculate the surface areas and the volumes of different solids, such as cubes, cuboids, cylinders, cones and spheres. They will also derive the formulae for calculating the curved surface area, total surface area and volume of a cone. Objectives   State the formulae for the lateral surface area of a cuboid, cube and cylinder   State the formulae for the total surface area of a cuboid, cube and cylinder   Define the concepts of volume and capacity   State the formulae for the volume of a cuboid, cube and cylinder   Calculate the surface area and volume of a cuboid, cube and cylinder   Define the concept of a right circular cone   Derive the formulae for the curved surface area, total surface area and volume of a cone  Define the concepts of a sphere, its centre, radius and diameter   Calculate the surface area and volume of a sphere   Define the concept of a hemisphere   Calculate the curved surface area, total surface area and volume of a hemisphere Aids Relevant Modules from Teach Next   Surface Areas and Volumes   Surface Area and Volume of a Cone   Surface Areas and Volumes of a Sphere Other Audio Visual Aids Access the videos relevant to the chapter ‘Surface Areas and Volumes’ from the Library resources.

 Aids No technical None Supplemental Activities Ask the students to research on the explanation for the formula for calculating the volume of a sphere. The explanation is as follows: Consider that a sphere is divided into many small pyramids with their peaks at the centre of the sphere as shown in the image here. The volume of all these pyramids is times the sum of their base areas multiplied by their height ( ). Clearly, the volume of all these pyramids is equal to the volume of a sphere. We also know that the base areas of all these pyramids are equal to the surface area of the sphere or 4. Hence, the formula for the volume of the sphere is . Expected Outcome After completing the lesson, learners should be able to calculate the surface areas and volumes of different solids, such as cubes, cuboids, cylinders, cones and spheres. They should also be able to derive the formulae for calculating the curved surface area, total surface area and volume of a cone. Student Derivable  Presentations on the theorems/formulae related to volume Assessment Class Test and extra sums from Teach Next Module and Refreshers.

 Lesson Plan Onlinepsa.in Board: CBSE | Class: IX | Subject: Maths Chapter Name: Statistics

 Prerequisite Knowledge Data Handling: Class VIII Short Description Of The Lesson This lesson will introduce the learners to the different techniques used to collect and data, for example, frequency distribution table. They will learn to draw and interpret bar graphs, histograms and frequency polygons. They will also learn to calculate different measures of central tendency, such as mean, mode and median. Objectives Analyse different types of data Create a frequency distribution table to classify data Draw a bar graph to depict the given data Interpret data from the given bar graph Draw a histogram to depict the given data Interpret the data represented in a histogram Draw a frequency polygon with the help of a histogram Calculate the mean of the given data Calculate the mode of the given data Calculate the median Calculate the median of the data when the observations are in even number Aids Relevant Modules from Teach Next Collection and Presentation of Data Bar Graphs Histograms Frequency Polygons Measures of Central Tendency —Mean —Mode —Median Other Audio Visual Aids Access the videos relevant to the lesson ‘Statistics’ from the Library resources.

 Supplemental Activities You may ask the children to create an opinion poll plot the findings on a graph Expected Outcome After completing this lesson, the students will be able to use different techniques to collect and present the data. They will be able to draw and interpret bar graph. Moreover they will also  gain the expertise to calculate different measures of central tendency, such as mean, mode and median. Student Deliverables a.  Review Questions given by the teacher b.  Bar graphs, histogram and frequency polygon Assessment Class Test and extra sums from Teach Next Module and Refreshers.