NCERT Laboratory Manuals Mathematics

ఆట అనేది అభ్యసన వ్యాసంగాలను(Attention towards learning) దెబ్బ తీస్తుందని భావించే చాదస్తులు ఇప్పటికి వున్నారు. బాల్య దశలో ఆట, అభ్యసనం అనేవి వేర్వేరు కావు. ఆట అనేది భావనల్ని స్పష్టం చేస్తుంది. పరిశీలనకు, ఊహకు అవకాశాలు కల్పిస్తుంది. తమ అనుభవాన్ని అర్ధవంతమైన రూపంలోకి  మార్చుకొనే అవకాశం ఇస్తుంది. పిల్లలు  ఏదైనా నేర్చుకువాలంటే వాళ్ల మీద మనకు ప్రేమ ఉందని, వాళ్లకు భద్రత ఉందనీ వాళ్ళకు అనిపించాలి. పిల్లల్ని ప్రేమించడమంటే వారితో కలిసి మాట్లాడడం, వారి కార్యకలాపాల్లో పాల్గొనడం, పిల్లల్లో,  పిల్లలుగా మారడం.  - జకియా మీరియన్ 

Activities for Classes I to V 

  1. To add two one-digit numbers
  2. To develop the sense of estimation in addition and subtraction of numbers
  3. To understand tens and ones
  4. To explore even and odd numbers in a playful manner
  5. To form two-digit numbers from any two-digits and to compare them
  6. To perform addition and subtraction using even and odd numbers(Game)
  7. To add and subtract two digit numbers with carrying
  8. To form three-digit numbers using digits
  9. To develop a sense of grouping(Game)
  10. To do multiplication of numbers using concrete objects
  11. To understand division by grouping
  12. To make a tangram and to form different shapes using its pieces
  13. To learn number operations in a known context
  14. To convert expanded form of a number into its usual form
  15. To collect, display and interpret data
  16. To find the multiples of numbers 2, 3, 4, 5,....,9   
  17. To construct a 3 × 3 Magic Square of Magic Constant 15
  18. To construct a 3 × 3 Magic Square of Magic Constant 15
  19. To find multiples and factors
  20. To find the factors of a given number (say 18)
  21. To compare the lengths of palms of students
  22. To make nets of cubes and cuboids using different objects
  23. To identify 2-D shapes in 3-D shapes
  24. To complete the pyramids by observing the pattern.(Game)
  25. To fill up the empty boxes(Game)
  26. A number puzzle(Puzzle) 
  27. A cross number game(Game)
  28. Some short-cut methods of calculation (Project)
  29. Suggested List of Projects

 Download the detailed copy part-1(1-16)

 Download the detailed copy part-2(17-29)

Activities for Classes VI, VII and VIII

    Activities for VI to VIII(1 - 27)

  1. To verify that addition of whole numbers is commutative
  2. To verify that multiplication of whole numbers is commutative
  3. To verify distributive property of whole numbers
  4. To verify distributive property of multiplication over addition of whole numbers
  5. To find HCF of two numbers 
  6. To find L.C.M. of two numbers
  7. To find fractions equivalent to a given fraction
  8. To find the sum of fractions with same denominators [say, 1/5 + 3/5]
  9. To find the sum of fractions with different denominators say, 1/4 + 2/3
  10. To subtract a smaller fraction from a greater fraction with the same denominator [say, 4/7 - 2/7 ]
  11. To subtract a smaller fraction from a greater fraction with different denominators [say, 5/7 – 2/3 ]
  12. To add integers
  13. To subtract integers
  14. Addition of decimals
  15. To construct a 4 × 4 Magic Square of Magic Constant 34
  16. To form various polygons by paper folding and to identify convex and concave polygon
  17. To obtain areas of different geometric figures using a Geoboard and verify the results using known formulas
  18. To establish the fact that triangle is the most rigid figure
  19. To represent a decimal number using a grid paper
  20. To make a ‘protractor’ by paper folding
  21. To obtain angle bisector of an angle by paper folding
  22. To make a parallelogram, rectangle, square and trapezium using set squares.
  23. To draw a perpendicular to a line from a point not on it, by paper folding
  24. To obtain formula for the area of a rectangle
  25. To obtain the perpendicular bisector of a line segment by paper folding
  26. To find the lines of symmetry of a figure (say, a rectangle) by paper folding
  27. To see that shapes having equal areas may not have equal perimeters  
      Download the detailed  copy
    Activities for VI to VIII(28 - 51) 
28.To multiply a fraction by a number [say, 3/4 × 7 ]
 29.To divide integers using unit squares of different colour
 30.To explain SAS criterion for congruency of two triangles
 31.To explain the SSS criterion for congruency of two triangles 
 32.To explain ASA criterion for congruency of two triangles 
 33.To explain RHS criterion for congruency of two right triangles
 34.To explain RHS criterion for congruency of two right triangles
 35.To multiply two fractions ( say, 3/4 and 5/6 ) 
 36.To divide a fraction by another fraction [ say, 2/3 ÷ 1/6 ]   
 37.To divide a fraction by a natural number. [say, 1/3 ÷ 4] 
 38.To multiply integers using unit squares of different colours
 39  To divide a natural number by a fraction
 40.To divide a mixed fraction by a proper fraction [say, 1 3/4 ÷ 1/4 ] 
 41.To multiply two decimals (say 0.3 and 0.4) using a grid
 42.To find the value of a n (where a and n are natural numbers) using paper folding
 43.To verify exterior angle property of a triangle
 44.To verify that the sum of any two sides of a triangle is always greater than the third side 
 45.To verify that in a triangle sides opposite equal angles are equal
 46.To draw altitudes of a triangle using paper folding
 47.To find the ratio of circumference and diameter of a circle
 48.To understand the meaning of less likely and more likely of the outcomes of an experiment 
 49.To verify that congruent triangles have equal area but two triangles with equal areas may not be congruent.
  50.To verify that when two lines intersect, vertically opposite angles are equal    
  51.To find the order of rotational symmetry of a given figure 
        Download the detailed copy-2 

 Activities for VI to VIII(52 - 74)

52.To obtain a formula for the area of a circle 
53.To verify that vertically opposite angles are equal
54.To add two algebraic expressions (polynomials) using different strips of cardboard
55.To subtract a polynomial from another polynomial 
56.To collect data and represent this through a bar graph
57.To verify that a minimum of three sides are required to construct a polygon 
58.To make medians of a triangle by paper folding
59.To obtain a formula for area of a rhombus
60.To verify Pythagoras Theorem for any right triangle
61.To verify Pythagoras Theorem using a grid paper
62.To verify Pythagoras Theorem for an isosceles right triangle
63.To verify Pythagoras Theorem for a right triangle with one angle 30º
64.To verify that if two parallel lines are intersected by a transversal, then
(i) the pairs of corresponding angles are equal.
(ii) the pairs of alternate interior angles are equal.
(iii) the pairs of interior angles on the same side of the transversal are
supplementary
65.To verify that the sum of three angles of a triangle is 180º
66.To obtain formula for the area of a parallelogram
67.To make a rhombus by paper folding and cutting 
68.To make a rectangle by paper folding
69.To make a square by paper folding
70.To obtain a parallelogram by paper folding
71.To draw regular polygons, using circles
72.To make a kite by paper folding and cutting
73.To verify that the sum of four angles of a quadrilateral is 360º
74.To verify that sum of exterior angles of a triangle and quadrilateral taken in order is 360° or four right angles
  Download the detailed copy

Activities for VI to VIII(75 - 93) and Projects

75.To make different types of prisms and pyramids and verifying Euler’s formula
76. To verify the algebraic identity : (a + b)² = a² + 2ab + b²
77.To verify the algebraic identity : (a – b)² = a² – 2ab + b²
78.To verify the algebraic identity : a² – b² = (a + b)(a – b)
79.To obtain a formula for the area of a trapezium
80.To form a cube and obtain a formula for its surface area
81.To form a cuboid and obtain a formula for its surface area
82.To obtain a formula for finding the volume of a cuboid
83.To establish a formula for the volume of a right circular cylinder
84.To obtain a formula for the curved surface area of a right circular cylinder
85.To verify that the opposite sides of a parallelogram are equal
86.To verify that adjacent angles of a parallelogram are supplementary
87.To verify that the diagonals of a parallelogram bisect each other
88.To multiply two linear algebraic expressions (polynomials) using different strips of cardboard
89.To verify that opposite angles of a parallelogram are equa
90.To factorise a polynomial, say (2x² + 4x)
91.To factorise a polynomial , say (x² + 4x + 3)
92.To solve a linear equation, say 2x + 3 = 5
93.To sketch a cube on an isometric dot paper and also to draw its oblique sketch on the square paper

Model Projects:

1.Perimeters and areas of rectangles
2.Methods for finding value of π

Suggested list of  Projects  

1.About an Indian mathematician and his/her contributions to mathematics.
2. Verification of Pythagoras theorem in different ways.
3. Magic squares : 3 × 3, 4 × 4, and 5 × 5.
4. Congruent shapes.
5. Exploring Pythagorean Triplets.
6. Drawing map of your school/locality.
7. Collection of data and its pictorial representation in different ways.
8. Decimal system versus other number systems with base 5, 8 and 2.
9. Divisibility Tests with special reference to 7, 11 and 13.
10. Verification of Euler’s formula for different 3 D shapes (polyhedra).
11. Application of direct and inverse proportions in day to day life.
12. Use of double bar graph in different situations.
13. Hardy – Ramanujan Numbers.
14. Use of algebraic identities in solving problems.
15. Areas of different polygons.
16. Graphs in day to day life.

Download the detailed copy

Activities for Class IX (1 to 10)

A.The Purpose of the Mathematics Laboratory
B.Role of Mathematics Laboratory in Teaching Learning
C.Management and Maintenance of Laboratory
D.Equipment for Mathematics Laboratory at Secondary Stage
E.Activities for Class IX
1.To construct a square-root spiral.
2.To represent some irrational numbers on the number line.
3.To verify the algebraic identity : (a + b)2 = a2 + 2ab + b2
4.To verify the algebraic identity :(a – b)2 = a2 – 2ab + b2
5.To verify the algebraic identity :a2 – b2 = (a + b)(a – b)
6.To verify the algebraic identity :(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
7.To verify the algebraic identity :(a+b)3 = a3 + b3 + 3a2b + 3ab
8.To verify the algebraic identity:(a – b)3 = a3 – b3 – 3(a – b)ab
9.To verify the algebraic identity:(a – b)3 = a3 – b3 – 3(a – b)ab
10.To verify the algebraic identity :a3 – b3 = (a – b)(a2 + ab + b2)

  Download the detailed copy-1 
Activities for Class IX (11 to 20)

  Download the detailed copy-2 
Activities for Class IX (21 to 34)

  Download the detailed copy-3 
Projects

  Download the detailed copy-4

 Activities for Class X (1 to 10)

 1.To find the HCF of two numbers experimentally based on Euclid Division Lemma.
2.To draw the graph of a quadratic polynomial and observe:
(i) The shape of the curve when the coefficient of x2 is positive. (ii) The shape of the curve when the coefficient of x2 is negative. (iii) Its number of zeroes.
3.To verify the conditions of consistency/ inconsistency for a pair of linear equations in two variables by graphical method.
4.To obtain the solution of a quadratic equation (x2 + 4x = 60) by completing the square geometrically.
5.To identify Arithmetic Progressions in some given lists of numbers (patterns).
6.To find the sum of first n natural numbers
7.To find the sum of the first n odd natural numbers.
8.To find the sum of the first n-even natural numbers.
9.To establish a formula for the sum of first n terms of an Arithmetic Progression.
10.To verify the distance formula by graphical method.1.Activities for Class X (1 to 10)
  Download the detailed copy

 Activities for Class X (11 to 20)


  Download the detailed Copy-2
Activities for Class X (21 to 32)


 Download the detailed copy-3
Projects
 1.ARYABHAT – THE MATHEMATICIAN AND ASTRONOMER
2.SURFACE AREAS AND VOLUMES OF CUBOIDS
3.GOLDEN RECTANGLE AND GOLDEN RATIO
4.π - WORLD'S MOST MYSTERIOUS NUMBER
LIST OF PROJECTS
Download the detailed copy

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