Viva Mathematics Lab Manual, Class 9

Contents:

Activity 1. Square Root • To construct a square-root spiral that depicts square roots of natural numbers like v2,v3,v5, etc

Activity 2. Algebraic Identity I • To verify the identity (a + b)² = a² + 2 ab + b² for simple cases using squaresand rectangles

Activity 3. Algebraic Identity II • To verify the identity a^{2 •} b² = (a + b) (a • b) geometrically

Activity 4. Algebraic Identity III • To verify the identity (a + b)³ = a³ + 3ab² + 3a²b + b³ using a set of unit cubes

Activity 5. Algebraic Identity IV • To verify the identity (a • b)³ = a³ • 3a²b + 3ab² • b³ using a set of unit cubes and cuboids

Activity 6 Algebraic Identity V • To verify the identity a³ + b³ = (a + b) (a² • ab + b²) using a set of unit cubes and cuboids

Activity 7. Algebraic Identity VI • To verify the identity a^{3 •} b³ = (a • b) (a² + ab + b²) using a set of unit cubes and cuboids

Activity 8. Factorisation of Polynomials • To interpret geometrically the factors of a quadratic expression of the type x² + bx + c using square grids, strips paper strips

Activity 9. Coordinate Geometry • To obtain the mirror image of a given geometrical figure with respect to x-axis and y-axis

Activity 10. Geoboard • To carry out the following activities using geoboard • To find the area of any triangle • To find the area of any polygon by completing the rectangles • To obtain a square on a given line segment • Given an area, to obtain different polygons of the same area

Activity 11. Area of Parallelogram • To show that the area of a parallelogram is the product of its base and height, using paper cutting and pasting

Activity 12. Area of Triangle • To show that the area of a triangle is half the product of the base and the height, using paper cutting and pasting

Activity 13. Area of Trapezium • To show that the area of a trapezium is equal to half the product of its altitude and the sum of its parallel sides, using paper cutting and pasting

Activity 14. Mid-Point Theorem • To verify the mid-point theorem for a triangle, using paper cutting and pasting

Activity 15. Triangle Inequality • To verify that • (a) The sum of any two sides of a triangle is always greater than the third side • (b) The difference of any two sides of a triangle is always less than the third side

Activity 16. Properties of Parallelogram • To verify the properties with respect to diagonals of the following quadrilaterals a square, a rectangle, a rhombus and parallelogram

Activity 17. Properties of Quadrilateral • To show that the figure obtained by joining the mid-points of the consecutive sides of any quadrilateral is a parallelogram

Activity 18. Centroid of Triangle • To illustrate that the medians of a triangle concur at a point (called the centroid) which always lies inside the triangle, using the method of paper folding

Activity 19. Incentre of Triangle • To illustrate that the internal bisectors of the angles of a triangle meets at a point (called the incentre), which always lies inside the triangle

Activity 20. Area of Circle • To verify that the area of a circle is half the product of its circumference and radius

Activity 21. Angle by an Arc • To verify that the angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle, using the method of paper cutting/folding

Activity 22. Cyclic Quadrilateral Theorem • To verify that in a cyclic quadrilateral • (a) The sum of either pair of opposite angles is 180?? • (b) The exterior angle is equal to the interior opposite angle, using the method of cutting, pasting and folding

Activity 23 Area of a Right Triangular Prism and a Pyramid • To make the net for a right triangular prism and a right triangular pyramid (regular tetrahedron) and obtain the formulae for the total surface area

Activity 24. Euler's Formula • To verify Euler's formula for different polyhedra: Prism, Pyramid and Octahedron

Project 1. Comparison • Comparison of the performance of two teams in a one-day international cricket match

Project 2. A Measuring Task • To investigate to your athletics track to see whether it is marked fairly for runners who start on different lines or not

Project 3. Data Collection • To find out the number of graduates (male and female) in each family having age 21 years to 30 years group

Project 4. Investigation of Pythagoras Theorem and p • To study various aspects of Pythagoras and his famous theorem, called Pythagoras Theorem • Investigation of various historical aspects of p

Group Activity 1. Percentage • To find the percentage of the students in a class who write faster with their right hand/left hand.

Group Activity 2. Measurement • To help the students establish interesting mathematical relationship by measuring some features of the body or body parts

Important Terms and Definitions

Formulae/Identities

About the Author:

Ajay Kumar, Head, Department of Mathematics, St. Mary's School, Dwarka (New Delhi).