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

 

Prerequisite Knowledge

Understanding Quadrilaterals: Class VIII Practical Geometry: Class VIII Triangles: Class IX

Short Description Of The Lesson

In this lesson, students will learn about different types of quadrilaterals and their properties, especially the properties of parallelograms. They will also learn to prove various theorems related to quadrilaterals and parallelograms.

Objectives

  Describe the types of quadrilaterals and their properties

  Prove the angle sum property of quadrilaterals

  Describe the types of parallelograms and their properties

  Prove that the diagonal of a parallelogram divides it into two congruent triangles

  Prove that if each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram

  Prove that if each pair of opposite angles of a quadrilateral is equal, then it is a parallelogram

  Prove that if a pair of opposite sides is equal and parallel in a quadrilateral, then it is a parallelogram

  Prove that if diagonals of a quadrilateral bisect each other, then it is a parallelogram

  Prove the mid-point theorem and its converse

Aids

Audio Visual Aids

Relevant Modules from Teach Next

  Quadrilateral and its Types

  Parallelogram and its Types

  Properties of a Parallelogram

  Mid-point Theorem

Other Audio Visual Aids

Access the videos relevant to the chapter ‘Quadrilaterals’ from the Library resources.

 

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.