ANNEXURE I ACHIEVEMENT TEST IN CONTENT OF...

ANNEXURE I

ACHIEVEMENT TEST IN CONTENT OF MATHEMATICS

FOR PRIMARY SCHOOL TEACHERS

1. Write the smallest or biggest digit number given below.

............................ 1.1 the largest 4 digit number

............................ 1.2 the six digit number

............................ 1.3 the largest five digit number.

............................ 1.4 the largest eight digit number.

............................ 1.5 the smallest seven digit number.

2. Find the place value of the digits that are underlined in the following numbers.

2.1) 6 2 5084 2.2) 2 60854 2.3) 54 2 804

2.4) 2 356705 2.5) 5 2 34614

3. Some digits in the following numbers are underlined. Add with their place values.

3.1) 6 2 36 4 81 3.2) 9 8 3 4214 3.3) 5 2 148 7 3

3.4) 2 74 1 326 3.5) 1 6 293 2 4

4. Some digits in the following numbers are underlined. Subtract with their place values.

4.1) 2 9 37 4 51 4.2) 3 6982 2 0 4.3) 6 7 04 0 56

4.4) 9 4 6 5 142 4.5) 2 1481 0 9

5. Write the following numbers in words in the English system.

5.1) 48231645 5.2) 984621342 5.3) 2642361

5.4) 3746452 5.5) 793720

6. Write the Indo-Arabic numerals corresponding to

6.1) LVIII 6.2) XLIX 6.3) MCXIV

6.4) DCIV 6.5) MDCX

7. Write the roman numerals corresponding to

7.1) 235 7.2) 2004 7.3) 540

7.4) 1049 7.5) 667

8. Write the following numbers in the decimal system.

8.1) 1101(2) 8.2) 10010(2) 8.3) 1001(2)

8.4) 11001(2) 8.5) 11100(2)

II

9. Write the following numbers in the binary system.

9.1) 25 9.2) 36 9.3) 49

9.4) 81 9.5) 75

10. Do the following additions.

.................................... 10.1) 473215 + 23142 + 76915 + 94321

.................................... 10.2) 9872 + 64932 + 6723 + 27

.................................... 10.3) 100011 + 1001 + 272 + 8752

.................................... 10.4) 23764 + 897213 + 6731 + 256

.................................... 10.5) 36679 + 4513 + 9512 + 67019

11. Do the following problems.

.................... 11.1) which is added to 134753 to get 427568 ?


.................... 11.3) which is subtracted from 75635 to get 37562 ?

.................... 11.4) how much is more 44528 from 27536 ?

.................... 11.5) how much is more from 86287 from 35292 ?

12. Multiply the following

12.1) 432 x 245 12.2) 617 x132 12.3) 409 x 123

12.4) 711 x 201 12.5) 708 x 304

13. Do the following divisions.

13.1) 484 ÷ 22 13.2) 631 ÷ 25 13.3) 936 ÷ 39

13.4) 784 ÷ 43 13.5) 591 ÷ 51

14. Write the multiples of given numbers.

14.1) 25 14.2) 16 14.3) 22

14.4) 18 14.5) 31

15. Write the factors of given numbers.

15.1) 48 15.2) 61 15.3) 64

15.4) 47 15.5) 38

16. Fill in the blanks with a suitable digit to make the number divisible by 11?

16.1) 32...97 16.2) 123...75 16.3) 2...72032

16.4) 32...408 16.5) ...93161

17. Find the G.C.D of given numbers.

17.1) 16, 30 17.2) 120, 180, 240 17.3) 60, 90, 150

17.4) 36, 48, 60 17.5) 12, 16, 20

III

18. Find the L.C.M. of given numbers.

18.1) 6, 8, 12 18.2) 12, 16, 24 18.3) 50, 80, 90

18.4) 27, 45, 25 18.5) 35, 42, 36

19. Write the following rational numbers in the ascending order.

20. Add the following expression.

21. Subtract the rational numbers given below.

22. Simplify the following expression?

23. Express the following rational numbers as decimals?

23.1) 1/3 23.2) 10/11 23.3) 52/15

23.4) 1/7 23.5) 14/11

IV

24. Write the following decimals in ascending order?

24.1) 3.34, 3.33, 3.336 24.2) 5.09, 5.04, 5.61

24.3) 0.26, 6.05, 0.56 24.4) 0.5, 0.19, 0.259

24.5) 0.28, 0.31, 0.2

25. Simplify the following Decimals ?

25.1) 43.1 + 41.6 - 23.4 = 25.2) 4.36 - 2.57 + 1.57 =

25.2) 12.384 + 16.467 - 10.023 = 25.4) 1.03 + 0.452 - 0.08 + 0.92 =

25.5) 3.20 + 15.67 - 0.08 - 0.9 =

26. Multiply the following?

26.1) 0.36 x 8 26.2) 32.562 x 48 26.3) 14.674 x 32

26.4) 2.576 x 25 26.5) 2.59 x 15

27. Divide the following?

27.1) 48.75 ÷ 25 27.2) 34.65 ÷ 35 27.3) 91.80 ÷ 15

27.4) 115.92 ÷ 21 27.5) 16.48 ÷ 16

28. Reduce the following ratios into simplest form ?

28.1) 24 : 72 28.2) 75 : 150 28.3) 37 : 47

28.4) 80: 112 28.5) 85 : 102

29. Solve the following

29.1)Ifx : y = 2 : 3; y : z = 9 : 5 ,then find x : y : z ?

29.2) If a : b = 5 : 12; b : c = 8 : 7, then find a : b : c ?

29.3) If l : m = 3 : 4; m : n = 4 : 5 , then find l : m : n ?

29.4) If p : q = 5 : 4; q : r = 3 : 4, then find p : q : r ?

29.5) If a : b = ½ : 1/3 ; b : c = 1/3 : 1/4 then find a : b : c ?

V

30. Find the missing numbers in the following proportion?

30.1) 24 : 18 = .............. : 9 30.2) 12 : 16 = 9 : ..............

30.3) 9 : 12 = .............. : 48 30.4).............. : 20 : 5 : 2 ½

30.5) 10½ : .............. = 5½ : 2¾

31. Find the averages of the following?

31.1) 64, 6, 65, 35, 75, 37 31.2) 4, 6, 8, 10, 12

31.3) 20, 19, 18, 23, 25 31.4) 31, 39, 40, 38, 37

31.5) 327, 512, 450, 615

32. Convert the following common fractions into a percentage? 32.1) 2/3= 32.2) 5/8= 32.3) 5/12= 32.4) 3/4= 32.5) 4/5=

33. Convert the following percentages into a common fractions ?

33.1) 35% 33.2) 20% 33.3) 12 ½ %

33.4) 6¼ % 33.5) 62½ %

34. Express the, second number as a percentage of the first.

34.1) 60, 36 34.2) 500, 225 34.3) 45, 39

34.4) 625, 250 34.5) 48, 30

35. Find the amount when ?

...................35.1)Principal =2500 Rate =5% per annum, Time =6 months

...................35.2) Principal = 5000 Rate=18% per annum, Time=1 year 9 months

....................35.3) Principal =7000 Rate=16% per annum, 2 year 3 months

..............… .35.4) Principal = 2000 Rate=24% per annum,Time=11.2.04-5.6.04 to

....................35.5) Principal=1800 Rate=30% per annum,Time=26.1.04-15.8.04 to

36. Write the numerical co-efficient in each of the following?

36.1) 15a 36.2) 4x2y 36.3) -65a2b2c2

36.4) – ¾ abc 36.5) 123 xyz

37. Find the co-efficient of x in each of the following?

37.1) 39x 37.2) 2abx 37.3) 4 mnx

37.4) 61 lpx 37.5) 12 abcx

VI

38. Add and simplify the following terms?

38.1) 8xy, 10xy, 7xy,-9xy=……………………………………

38.2) -4x2, 3y ,4x2,-5y =…………………………………………

38.3) - 5 a2b, 8 b2a, - 6 a2b, 9 ab2 = ………………………………

38.4) 3 x2y2, 4 y2, 3x2, - 2y2 = ……………………………………..

38.5) 2x2, 4y2, 3x2, -2y2 = …………………………………………

39. Add the following expressions

39.1) 3a-2b, 10a - 4b, -2a + 5b

39.2) x + y + z, x - y + z, x + y - 2z

39.3) 2x3 + 3x2 - 5, x3 - 3x2 +6, 5 x3 + 2x2 + 10

39.4) x2 + y - 4 x2 - xy2, 5x2 - 5 xy2 , 7 x2y + 2x2

39.5) 6 xy + 10 yz - zx, 7 xy - 2 yz - 6 zx, - 2 xy - 3 yz + zx

40. Find the Zeroes of the following

40.1) 2x - 3 40.2) 3x - 2 40.3) - 4/3 x + 1

40.4) 2/13 x - 1/7 40.5) 4/7 x - 7/15

41. Rewrite each expression using exponents.?

41.1) b.b.b.c.c.c 41.2) (x+y) . (x+y) . (x+y) . (x+y)

41.3) x . x . x . x . x . x . y. y. y. y. 41.4) 2/3 .2/3. 2/3. 2/3. 2/3.

41.5) (a-b) . (a-b) . ( a-b) . (m+n) . (m + n)

42. Find the following in their simplest form?

VII

43. Find each of the following using the formula?

43.1) (x+y)2 43.2) (m-n)2 43.3) (x+10)2

43.4) (5m-7) (5m-7) 43.5) (3p+10) (3p+10)

44. Factorise the following expressions ?

44.1) (x+y)2- 9 44.2) (x-3)2 - 64 44.3) 3x2 - 27

44.4) x4 - x2 44.5) x3y - xy3

45. Draw the segments whose lengths are given below

__ __ ___ __

45.1) AB = 5 cm 45.2) PQ = 4.6 cm 44.3) MN = 7 45.4) XY = 6.3 cm

__

45.5) SR = 3.5 cm

46. Some angles are given below consider each of them and say what kind of angle it is?

VIII

47. In the following figures n is transversal of lines land m. consider each figure and give the name of the angle

48. Given below is the measurement of angles of a triangle state the type of the triangle obtained in each c ase.

48.1) 750, 450, 600 48.2) 1000, 600, 200 48.3) 300, 600, 900

48.4) 900, 450, 450 48.5) 550, 250, 1000

49. Give the names of the following quadrilaterals?

IX

50. Find the areas using formulas.

................................... 50.1) If b = 4 cm, h = 6 cm.,then find the area of a triangle?

................................... 50.2) The Square of a side is 10cm. Then find the area of a square.

................................... 50.3) In a quadrilateral, the diagonals interest at right and have lengths equal to 6 cm and 7 cm respectively find the area of the quadrilateral.

................................... 50.4) the lengths of the parallel sides of a trapezium are 10.4 cm and 6.6cm. The distance between them is 4 cm. find its area.

................................... 50.5) the radius of a circle is 14cm what is its area?

51. Read the bar graph and answer the questions given below

Egypt Canada USA India Japan Germany

Nations

Bar graph of birth and death rates of a few countries in 1978

............................................... 51.1) what does the diagram represent?

............................................... 51.2) what is the country in which both the birth and death rates are highest?

............................................... 51.3) what is the country in which both are lowest?

....................................... …… 51.4) what is the country in which the difference between the birth and death rates is maximum?

............................................... 51.5) what is the rank of India In terms of birth rates?

Birth Rate Scale Death Rate 1 cm = 5

X

ANNEXURE II

XXIV

ANNEXURE III

AN ACHIEVEMENT IN CONTENT OF MATHEMATICS FOR

PRIMARY SCHOOL TEACHERS

KEY (FIRST DRAFT) S.No Answer S.No Answer S.No Answer S.No Answer

1.1 9,000 1.2 1,00,000 12.4 142911 12.5 215232

1.3 99,999 1.4 9,99,99,999 13.1 22 13.2 25

1.5 1000000 2.1 20,000 13.3 24 13.4 18 2.2 2,00,000 2.3 2,000 13.5 11 14.1 25,50,75,100,…

2.4 2000,000 2.5 2,00,000 14.2 16,32,48,…. 14.3 22,44,66,….

3.1 200400 3.2 9030000 14.4 18,36,54,….. 14.5 31, 62,93, … 3.3 200070 3.4 2001000 15.1 1, 2,3, 4,6, 8,

12, 16, 48, 15.2 1,61

3.5 600020 4.1 899600 15.3 1, 2,4, 8, 16,32, 64

15.4 1, 47

4.2 29999980 4.3 699900 15.5 1, 2, 18, 38 16.1 1

4.4 395000 4.5 2000000 16.2 4 16.3 6 5.1 48millions231

thousands 6hundredand 45

5.2 984millions 621 thousands3 hundredand42

16.4 6 16.5 2

5.3 26millions42 thousands 3hundredand 61

5.4 37millions46 thousands 4hundredand 52

17.1 2 17.2 60

5.5 48millions231 thousands 6hundredand45

6.1 58 17.3 30 17.4 12

6.2 49 6.3 1114 17.5 4 18.1 24

6.4 604 6.5 1610 18.2 48 18.3 3600 7.1 CCXXXV 7.2 MMIV 18.4 675 18.5 1260

7.3 DXL 7.4 MIL 19.1 3/7 , 6/10, 5/8 19.2 3/7,7/16, 9/12

7.5 DCLXVII 8.1 13 19.3 1/5, 6/12, 7/10 19.4 9/16, 7/12, 5/8

8.2 18 8.3 9 19.5 9/16, 7/12, 5/8 20.1 78/72

8.4 25 8.5 28 20.2 776/360 20.3 71/60 9.1 11001(2) 9.2 100100(2) 20.4 1764/864 20.5 3159/1620

9.3 110001(2) 9.4 1010001(2) 21.1 1 21.2 38

9.5 1001011(2) 10.1 667593 21.3 8 21.4 2 10.2 81554 10.3 110036 21.5 2 22.1 121/60

10.4 927964 10.5 117723 22.2 176/21 22.3 107/20

11.1 292815 11.2 31546 22.4 7/40 22.5 1222/42 11.3 38073 11.4 19992 23.1 0.909090… 23.2 0.3333…

11.5 50995 12.1 105840 23.5 1.272727…… 24.1 3.34, 3.336, 3.33

12.2 81444 12.3 50307 24.2 5.61, 5.09,5.04 24.3 6.05, 0.56, 0.26

XXV

S.No Answer S.No Answer S.No Answer S.No Answer 24.4 0.5,0.259, 0.19 24.5 0.31, 0.28, 0.20 41.3 X6y4 41.4 (2/3)5 25.1 61.3 25.2 3.36 41.5 (a-b)3(m+n)2 42.1 -512/17875 25.3 18.82 25.4 2.32 42.4 1 42.5 1 25.5 18.69 26.1 2.88 43.1 x2+2xy+y2 43.2 (m2-2mn+n2 26.2 1562.976 26.3 469.57 43.3 X2+20x+100 43.4 25m2-70m+49 26.4 64.4 26.5 38.85 43.5 9p2+60p+100 44.1 (x+y+3)(x+y-3) 27.1 1.95 27.2 0.99 44.2 (x+5)(x-11) 44.3 3(x+3)(x-3) 27.3 6.12 27.4 5.52 44.4 (x2+x)(x2-x) 44.5 xy(x+y) 27.5 1.03 28.1 1:3 45.1 AB=5cm 45.2 PQ= 4.6cm 28.2 1:2 28.3 6:5 45.3 MN=7cm 45.4 XY=6.3cm 28.4 7:5 28.5 11:10 45.5 SR=3.5cm 46.1 Acute angle

29.1 6:9:5 29.2 40:96:84 46.2 Obtuse angle 46.3 Right angle 29.3 3:4:5 29.4 15:12:6 46.4 Reflective angle 46.5 Straight angle 29.5 1/2 : 1/3 :1/4 30.1 12 47.1 Alternative

interior angle 47.2 Corresponding

angle 30.2 12 30.3 36 47.3 Exterior angle 47.4 Alternative Exterior

angle 30.4 50 30.5 4 47.5 One side

interior angle

31.1 47 31.2 8 48.1 Acute Triangle 48.2 Obtuse triangle 31.3 31 31.4 37 48.3 Right angle

riangle 48.4 Right angle

Triangle 31.5 476 32.1 66% 48.5 Obtuse triangle 49.1 Parallelogram 32.2 62% 32.3 41.6% 49.2 Square 49.3 Trapezium 32.4 75% 32.5 8% 49.4 Rhombus 49.5 Rectangle 33.1 7/20 33.2 1/5 50.1 12 sq.cm 50.2 100sq.cm 33.3 7/20 33.4 1/16 50.3 21sq.cm 50.4 34sq.cm 33.5 5/8 34.1 60% 50.5 616sq,cm 51.1 Birth &death rates 34.2 45% 34.3 86 2/3% 51.2 Egypt 51.3 Germany 34.4 40% 34.5 62 ½% 51.4 Egypt 51.5 2 place 35.1 2562.50 35.2 6575 35.3 9520 35.4 2178.66 35.5 2115 36.1 15 36.2 4 36.3 -65 36.4 - 3/4 36.5 123 37.1 39 37.2 2ab 37.3 4mn 37.4 61 lp 37.5 12ab 38.1 16xy 38.2 -2y 38.3 -11a2+17b2a 38.4 3x2+3x2y2+2y2 38.5 5x2+2y2 39.1 11a-b 39.2 3x+y 39.3 8x3+2x2+1 39.4 12x2+2xy2 39.5 11xy+5yz-6zx 40.1 3/2 40.2 2/3 40.3 3/4 40.4 13/14 40.5 49/60 41.1 (bc)3 41.2 (x+4)4

XXVI

ANNEXURE IV

ACHIEVEMENT TEST IN CONTENT OF MATHEMATICS

FOR PRIMARY SCHOOL TEACHERS (FINAL STUDY TOOL)

1. Write the smallest or biggest digit number given below.

............................ 1.1 the largest 4 digit number

............................ 1.2 the six digit number

............................ 1.3 the largest five digit number.

............................ 1.4 the largest eight digit number.

2. Find the place value of the digits that are underlined in the following numbers.

2.1) 6 2 5084 2.2) 2 60854 2.3) 54 2 804

2.4) 2 356705

3. Some digits in the following numbers are underlined. Subtract with their place values.

3.1) 2 9 37 4 51 3.2) 3 6982 2 0 3.3) 6 7 04 0 56

3.4) 9 4 6 5 142

4. Write the Indo-Arabic numerals corresponding to

6.1) LVIII 6.2) XLIX 6.3) MCXIV

6.4) DCIV

5. Write the following numbers in the decimal system.

5.1) 1101(2) 5.2) 10010(2) 5.3) 1001(2)

5.4) 11001(2)

6. Do the following problems.



.................... 11.3) which is subtracted from 75635 to get 37562 ?

.................... 11.4) how much is greater than 44528 from 27536 ?

7. Multiply the following

7.1) 432 x 245 7.2) 617 x132 7.3) 409 x 123

7.4) 711 x 201

XXVII


8.1) 484 ÷ 22 8.2) 631 ÷ 25 8.3) 936 ÷ 39

8.4) 784 ÷ 43

9. Write the multiples of given numbers.

9.1) 25 9.2) 16 9.3) 22

9.4) 18

10. Write the factors of given numbers.

10.1) 48 10.2) 61 10.3) 64

10.4) 47

11. Find the G.C.D of given numbers.

11.1) 16, 30 11.2) 120, 180, 240 11.3) 60, 90, 150

11.4) 36, 48, 60

12. Find the L.C.M. of given numbers.

18.1) 6, 8, 12 18.2) 12, 16, 24 18.3) 50, 80, 90

18.4) 27, 45, 25

13. Write the following rational numbers in the ascending order.

13.1) 13.2) 13.3)

13.4)

14. Simplify the following expression?

15. Express the following rational numbers as decimals?

15.1) 1/3 15.2) 10/11 15.3) 52/15

15.4) 1/7

16. Write the following decimals in ascending order?

16.1) 3.34, 3.33, 3.336 16.2) 5.09, 5.04, 5.61

16.3) 0.26, 6.05, 0.56 16.4) 0.5, 0.19, 0.259

14.1) 14.2)

14.3) 14.4)

XXVIII

17. Simplify the following Decimals ?

17.1) 43.1 + 41.6 - 23.4 = 17.2) 4.36 - 2.57 + 1.57 =

17.2) 12.384 + 16.467 - 10.023 = 17.4) 1.03 + 0.452 - 0.08 + 0.92 =

18. Multiply the following?

18.1) 0.36 x 8 18.2) 32.562 x 48 18.3) 14.674 x 32

18.4) 2.576 x 25

19. Divide the following?

19.1) 48.75 ÷ 25 19.2) 34.65 ÷ 35 19.3) 91.80 ÷ 15

19.4) 115.92 ÷ 21


20.1) 24 : 72 20.2) 75 : 150 20.3) 37 : 47

20.4) 80: 112


21.1) 64, 6, 65, 35, 75, 37 21.2) 4, 6, 8, 10, 12

21.3) 20, 19, 18, 23, 25 21.4) 31, 39, 40, 38, 37

22. Convert the following common fractions into a percentage? 22.1) 2/3= 22.2) 5/8= 22.3) 5/12= 22.4) 3/4=

23. Find the amount when ?

...................23.1)Principal =2500 Rate =5% per annum, Time =6 months

...................23.2) Principal =5000 Rate=18% per annum, Time=1 year 9 months

....................23.3) Principal =7000 Rate=16% per annum, 2 year 3 months

..............… .23.4) Principal =2000 Rate=24% per annum,Time=11.2.04-5.6.04 to

24. Write the numerical co-efficient in each of the following?

24.1) 15a 24.2) 4x2y 24.3) -65a2b2c2

24.4) – ¾ abc

XXIX

25. Find the co-efficient of x in each of the following?

25.1) 39x 25.2) 2abx 25.3) 4 mnx

25.4) 61 lpx

26. Add the following expressions

26.1) 3a-2b, 10a - 4b, -2a + 5b

26.2) x + y + z, x - y + z, x + y - 2z

26.3) 2x3 + 3x2 - 5, x3 - 3x2 +6, 5 x3 + 2x2 + 10

26.4) x2 + xy2, 4 x2 - xy2, 5x2 - 5 xy2 , 7 x2y + 2x2

27. Rewrite each expression using exponents.?

27.1) b.b.b.c.c.c 27.2) (x+y) . (x+y) . (x+y) . (x+y)

27.3) x . x . x . x . x . x . y. y. y. y. 27.4) 2/3 .2/3. 2/3. 2/3. 2/3.

28. Find each of the following using the formula?

28.1) (x+y)2 28.2) (m-n)2 28.3) (x+10)2

28.4) (5m-7) (5m-7)

29. Draw the segments whose lengths are given below __ __ ___ __ 45.1) AB = 5 cm 45.2) PQ = 4.6 cm 44.3) MN = 7 45.4) XY = 6.3 cm

30. Some angles are given below consider each of them and say what kind of angle it is?

30.1) 30.2)

30.3) 30.4)

XXX

31. Give the names of the following quadrilaterals?

32. Find the areas using formulas. ................................... 32.1) If b = 4 cm, h = 6 cm.,then find the area of a triangle? ................................... 32.2) The Square of a side is 10cm. Then find the area of a

square. ................................... 32.3) In a quadrilateral, the diagonals interest at right and

have lengths equal to 6 cm and 7 cm respectively find the area of the quadrilateral.

................................... 32.4) the lengths of the parallel sides of a trapezium are 10.4 cm and 6.6cm. The distance between them is 4 cm. find its area.

51. Read the bar graph and answer the questions given below

Egypt Canada USA India Japan Germany

Nations Bar graph of birth and death rates of a few countries in 1978

............................................... 51.1) what does the diagram represent?

............................................... 51.2) what is the country in which both the birth and death rates are highest?

............................................... 51.3) what is the country in which both are lowest?

....................................... …… 51.4) what is the country in which the difference between the birth and death rates is maximum?

31.1) 31.2)

31.3)31.4)

Birth Rate Scale Death Rate 1 cm = 5

XXXI

ANNEXURE V

Final Study Tool (Telugu Version)

XXXIII

XXXVI

ANNEXURE VI

AN ACHIEVEMENT IN CONTENT OF MATHEMATICS FOR PRIMARY SCHOOL TEACHERS FINAL STUDY KEY

S.No Answer S.No Answer S.No Answer S.No Answer 1.1 9,000 1.2 1,00,000 1.3 99,999 1.4 9,99,99,999 2.1 20,000 2.2 2,00,000 2.3 2,000 2.4 2000,000 3.1 899600 3.2 29999980 3.3 699900 3.4 395000 4.1 58 4.2 49 4.3 1114 4.4 604 5.1 13 5.2 18 5.3 9 5.4 25 6.1 292815 6.2 31546 6.3 38073 6.4 19992 7.1 105840 7.2 81444 7.3 50307 7.4 149211 8.1 22 8.2 25.24 8.3 24 8.4 18.23 9.1 25,50,75,100.. 9.2 16,32,48.. 9.3 22,44, 66…. 9.4 18,36, 54.. 10.1 1,2, 3,46,8,12 10.2 1,61 10.3 1,2,4,8,16 10.4 1,47 11.1 2 11.2 60 11.3 30 11.4 12 12.1 24 12.2 48 12.3 3600 12.4 675 13.1 3/7,6/10,5/8 13.2 3/7,7/16,

9/12 13.3 1/5,

6/12,7/10 13.4 9/16, 7/12,5/8

14.1 2 1/60, 14.2 8 27/70, 14.3 5 7/20 14.4 7/40 15.1 0.333.. 15.2 0.9090… 15.3 3.4666.. 15.4 0.142.. 16.1 3.336, 3.34,

3.33 16.2 5.61, 5.09,

5.04 16.3 6.05,

0.56,0.26 16.4 0.5,0.259,0.19

17.1 61.3 17.2 3.36 17.3 18.828 17.4 2.322 18.1 2.88 18.2 1562.976 18.3 469.568 18.4 64.4 19.1 1.95 19.2 0.99 19.3 6.12 19.4 5.52 20.1 1:3 20.2 1:2 20.3 7:9 20.4 5:7 21.1 47 21.2 8 21.3 21 21.4 37 22.1 66.66 22.2 62.5 22.3 41.66 22.4 75 23.1 2562.50 23.2 6575 23.3 7520 23.4 2180 24.1 15 24.2 24.4 24.3 -65 24.4 -34 25.1 39 25.2 2ab 25.3 4mn 25.4 61lp 26.1 11a-b 26.2 3x+y 26.3 8x3+2x2+11 26.4 12x2+2xy2 27.1 (b3c3) 27.2 (x+y)4 27.3 X6y4 27.4 (2/3)5 28.1 x2+2xy+y2 28.2 m2-2mn+n2 28.3 X2+20x+100 28.4 25m2-70m+49 29.1 AB=5cm 29.2 PQ=4.6cm 29.3 MN=7cm 29.4 XY=6.3cm 30.1 Acute angle 30.2 Obtuse

angle 30.3 Right angle 30.4 Straight angle

31.1 Parallelogram 31.2 Square 31.3 Trapezium 31.4 Rhombus 32.1 12 32.2 100 sqcm 32.3 21sqcm 32.4 34sqcm 33.1 Egypt 33.2 Germany 33.3 Egypt 33.4 2 place

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ANNEXURE VII

AN ACHIEVEMENT TEST IN METHODOLOGY OF TEACHING MATHEMATICS

(First Draft)

I. Each item or question below describes a learning situation leading to discovery of a generalization mention the type of reasoning _ inductive reasoning or deductive reasoning that is used in the discovery of generalization.

1. If the numbers 5,10,15,20 are divisible by 5 & then the digits in the unit places are

0,5, the student concludes that the given numbers are divisible by 5. 2. The product of two odd numbers is an odd number. If a,b are two odd numbers then

ax b is also an odd number. 3. In the number if we move towards the left the value increases by 10 times, so in the

number 6425 the value of 2 is 10 times more than 5. 4. Observe the following: 1/5, 2/7, 7/11. …………….. The student generalizes that

denominator is greater than the numerator, the fractions are called proper fractions. 5. The student generalizes that if the ratios (2:3) X 4; (5:3) X 5; (1:3) X 2 are multiplied

by any whole number then the value does not change. 6. The line which starts from a point reaches the same point without intersecting more

than one time, the figure is closed figure. Thus we say circle, Rectangle and Triangles are closed figures.

7. By observation the student generalizes that “The average is obtained by dividing the sum of the quantities by the number of quantities”.

8. If the difference between the two primes is 2 then they are called Twin primes. 3,5 are prime numbers, their difference is 2. So they are called twin primes.

9. “If the sum of the two angles are 90 ° they are called complementary angles”. APB + Dac = 90° then P & Q are complementary angles.

10. By observing the squares of (a-b), (P-Q), (L-M), the student generalizes that the difference of the sum of the squares and the twice the product of the numbers are equal to the given numbers.

11. The area of the rectangle is A = l x b. If l=2,b=3 then the student finds out the area. 12. By observing many times the student generalizes that “The ratio of the circumference

& the diameter of a circle is constant”. II . GIVEN BELOW IS A SET OF GENERAL OBJECTIVES .SPECIFY THE AIMS -------UTILITARIAN, DISCIPLINARY ,AND CULTURAL TO WHICH THEY ARE SUBORDINATES . 13. Learning of Mathematics makes the student self confidence. Self respect &

simplicity. 14. The student angles that the culture and the secreates of sculpture are translated to the

next generation through Mathematics. 15. The student interpretates the bar diagrams from the Newspaper. 16. The student enjoys for the utilization of the principles of Mathematics in musical

instruments.

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17. The student uses the Profit &Loss, selling tax, Rate of interest of Mathematics in future business.

18. The study of Mathematics makes the student accurate in ideas and Attitudes in future. 19. The student enjoys and appreciates by doing games, puzzles in Mathematics. 20. From the given data the student evaluates the generalizations 21. The student deeply learns about the human achievements of great things in

Mathematics. 22. The student uses Mathematics in physical sciences & Biological Sciences.

III. CLASSIFY EACH OBJECTIVES BELOW AS BELONGING TO GENERAL OBJECTIVES (GO)AND SPECIFIC OBJECTIVE(SO) , WRITE UNDECIDED (UD ) IF YOU CANNOT DISGUISE INTO GENERAL OR SPECIFIC . 23. Student understands about the place values. 24. Student can apply the steps in Mathematics in their real life. 25. Student understood the concepts about prime numbers. 26. Student understood the concept about different types of triangles. 27. Students enjoy the symmetrical shapes of geometry by observing in nature. 28. Student understood the different concepts of Measurements. 29. Student classify different types of fractions. 30. Student uses the formulae of area of quadrilaterals in finding the areas like houses and

son on. 31. Student understand the angles formed by the transversal. 32. Students solve their problems by using the equations of Mathematics in daily life. 33. Students represent the details of their business in Statistics through circular graphs

and Bar diagrams. 34. Student interpretates about the development of the company through bar diagrams by

seeing the newspapers. 35. Student understood about the properties of Integers. 36. Student applies the terms of profit and loss problems, percentages, Rate of interests,

etc., in their business in future. 37. Student finds out the degree of the given polynomical. IV. CLASSIFY EACH OF THE FOLLOWING OBJECTIVES AS BELONGING TO THE COGNITIVE OR, AFFECTIVE OR PSYCHOMOTOR DOMAIN . 38. Student draws the square diagram from the given measurements. 39. Student separate the even prime numbers from the prime numbers. 40. Student participates in Maths clubs after their school time actively. 41. Student translates the expanded form of numbers to short form and vice versa. 42. Student read the numbers in the given table without any mistakes easily. 43. Student enjoys the symmetrical shapes in maths while seeing the flowers in nature. 44. Student finds out the L.C.M. of the numbers 2, 4, 8. 45. Student collects the cylindrical shaped instant sticks and cubical rods in Geometry

without the guidance of teacher. 46. Student uses the compass to draw the circle with the given measurements. 47. Student answer 1 m is equal to 100 cms. 48. For the value of (a+b)², the student answers a² + 2ab + b².

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49. Student appreciates Ramanujan by reading his life history. 50. The student opposes the fact of other student “The two parallel straight lines intersect

each other.” 51. If the area of the triangle A = ½ X b X h, and b = 2 cm, h = 4 cm. The student

substitutes the values of b and h in the given equation to find the area. 52. From the formula I = PTR/100, the student draws T = 100 X I/PR V. CLASSIFY THE FOLLOWING OBJECTIVES ACCORDING TO BLOOM’S

CLASSIFICATION . (1) Knowledge (2) Understanding/comprehension (3) Application, (4) Analysis (5) Synthesis (6) Evaluation. 53. If the length of a rectangular path is 20m, find area? The student explains that the

given data is not sufficient. 54. The student classifies even numbers and odd numbers from the given numbers.

1,2,3,4,5……… 55. “What is a multiple?” the student answers “The numbers obtained by the product of

the given number and 1,2,3,4,5 ……….. are called the multiples”. 56. The student explains the relationship between the circle and its radius? 57. The student illustrates rectangle, circle as closed figures. 58. For the question “are all the odd numbers are prime number?” 59. For the question “What is the formula for the area of a triangle? The student replies

Area, l = ½ x b x h. 60. A student buys ¾ lts. of milk everyday. So in the month of June how much he has to

buy? (30 days) is solved by the student? 61. In the following figure, student represents a ‘line’. 62. For the question “If a,b,c are Integers (whole numbers) then a + (b+c) = (a+b)+c

represents which property? Means he answer as associative. 63. Student generalizes that “ The circle has infinite diameters”. 64. A student compares the proper and improper fraction from the following: 9/4, 4/9,

5/9, 7/5 65. Student identifies the four sided figure?

(a) (b) (c) (d) 66. “What is the percentage of 25 kgs in one tonn.” The student converts into percentage? 67. For the question “what is a transitive axiom”. Student tells if x,y,z are rational

numbers and x > y, y > z then x > z.

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VI. CLASSIFY EACH STATEMENT GIVEN BELOW AS BELONGING TO THE KINDS OF SUBJECT MATTER IN MATHEMATICS (1 )CONCEPT ( 2) FACT (3)GENERALIZATION ( 4) RULE 68. The closure property does not obeys for whole numbers in subtraction. 69. “If the common factors for two numbers are not other than “I” then the numbers are

co-primes?” 70. a, b are two natural numbers and their L.C.M. and G.C.M. are L & G respectively

then a X b = L X G. 71. The largest two digit number is 99. 72. The sum of two even numbers is even. 73. If an object is divided into three parts then each part is 1/3.

74. The fractions having the denominator less than the numerator are called Improper fraction.

75. 1 rupee is equal to 100 paise. 76. 2 m is equal to 200 cms. 77. To convert days into hours, multiply days by 24. 78. The number of days in Leap year are 366. 79. If the four sides of a figure are equal, it is square. 80. The sides of a triangle are 3. 81. A line segment extended indefinitely on both sides is called straight line. 82. The product of two positive integers is always a positive integer. 83. If a, b are two positive integers and b � 0 then the form a/b is a rational number. 84. According to simple interest, to find the amount. Simple interest is to be added to

principal. 85. In X , 5 is exponent and X is base. 86. In a plane surface the lines drawn from the fixed point are infinite. 87. The right angle must be equal to 90 degree. 88. The sum of three angles in a triangle is 180 degrees. 89. Area of a sector is the half of the product of the arc and its radius. VII. REPRESENT THE TEACHING METHOD USED IN THE FOLLOWING TOPICS (INDUCTIVE, DEDUCTIVE, ANALYSIS, SYNTHESIS, LABORATORY, HEURISTIC, PLAYWAY, PROJECT METHOD)

90. The teaching method used to prove the theorems in Geometry. 91. The method used to find the formula for volume of a sphere. 92. The method used to say “The sum of three angles in a triangle is 180 degrees”. 93. The method used to evaluate R from I = PTR/100. 94. The method used in solving equations. 95. The method used to teach the properties of whole numbers. 96. The method used to introduce the shapes of quadrilaterals. 97. The method used to teach the lesson “Average” 98. The method used to the student to understand the concept “angle”

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99. The method used to deduce the formula of the area of a rectangle. 100. The method applied to learn multiplication table for 2. 101. The method used to estimate the expenditure to visit a factory. 102. The appropriate method to teach the measurement of length, weight and capacity.

103. The method used to teach the concepts of fractions. 104. The method suitable to explain “circumference is Ð times to its radius”. 105. The method to teach “the distance and speed of a train”. VIII. IN EACH OF THE GIVEN BELOW JUDGE WHETHER THE TEST ITEM MEASURES THE OBJECTIVE PREFIXED TO IT OR NOT. IF THE ITEM MEASURES THE OBJECTIVE INDICATE YOUR ANSWER BY ‘YES’ AND IF IT DOES NOT ‘NO’. 106. Objective : The students understand the set of numbers. Test item : Write elements in the set of numbers? 107. Objective : Students find out the place values. Test item : What is the biggest number in three digits? 108. Objective : Students use addition in daily life problems.

Test item : 23 + 545 = ? (How much) 109. Objective : Student understands multiplication as repeated addition.

Test item : 5 + 5 + 5 + 5 = 5 X ? 110. Objective : Student applies division in solving daily life problems. Test item : The cost of a pen is Rs.8/-, then find the number of pens Obtained for Rs.384/- 111. Objective : The students understand about the even and odd numbers. Test item : The only even prime number is 2. 112. Objective : Students learn the addition of like fractions. Test item : 1/3 + ¼ + 2/3 = ? 113. Objective : Students are able to do the basic operations in measurement of capacity. Test item: In a bag there are five paise coins, 7 ten paise coins, 15 twenty Five paise coins, 4 fifty paise coins. Find the total amount in a bag. 114 Objective : Student converts one form of unit to another. Test item : 1 km is equal to how many kilo meters? 115. Objective : Students says time from a clock. Test item : If today is May 1 st then what is the day on June 1 st. 116. Objective : The student says about the shapes of closed figures. Test item : What is the name of three sided closed figure. 117. Objective : Student converts Roman numerals to Hindu Arabic. Test item : Convert 100 to Roman numerals. 118. Objective : Student finds out L.C.M. of given numbers. Test item : What are the factors of 18, 20, 12. 119. Objective : Student applies the formula of average in daily life. Test item : Find the average of 45, 48, 50, 54.

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120. Objective : Students gain the knowledge of percentages. Test item : “Percentage” means? 121. Objective : Students apply the formulae of profit and loss in daily life? Test item : The cost price of an object is Rs.250/- extra expenditure is Rs.30/- and sold price is Rs.00/- whether it is gain or loss? What is the percentage? 122. Objective : Student understand the constructions of quadrilaterals. Test item : If the diagonal of a rectangle is 12 cms find its area? IX. FOLLOWING ARE THE TEST ITEMS. CLASSIFY THE OBJECTIVE IN COGNITIVE DOMAIN (KNOWLEDGE, COMPREHENSION, APPLICATION, ANALYSIS, SYNTHESIS, EVALUATION). 123. Instructional context : Students will be able to understand the place values by different methods. Question: In 26454 the place value of 6 is ? 124. Int. cont:Students will be able to understand the concept the concept of factors. Question: What are the common factors of 15, 35 ? 125. Int. cont : Students will be able to understand the divisibility tests. Question: Without dividing the number 1716 find out whether it is divisible by 33 or not. 126. Int. cont:Students will be able to understand the L.C.M. by the method of prime numbers. Question: Ramu, Rahim,Robert participates in running race. The time taken to complete one round to Ramu is 100 seconds, Rahim 110 seconds, and Robert is 120 seconds. If they all starts at the same time what is the Time taken by them to meet again? 127. Int. Cont: The student will be able to understand about fractions? Question: Write the fractions equal to 5/9? 128. Int. cont : Students will be able to understand decimal fractions. Question: Find the decimal fraction in the following: (a) ½ (b) 4/9 (c) 1/10 129. Int. cont : Students understand the measurement of weight. Question: How many grams makes 1 kilogram? 130. Int. cont:Students understand the concepts of percentages?

Question: The fraction equal to 20% is ? 131. Int.cont:Students will be explained about profit and loss. Question: Gain percentage formula is ? 132. Int.Cont:Students will be able to do problems about ratios. Question: In a school the pass and failures ratio is 5:3. If the number of failures Is 34. Find the pass students and the total number of students Attend for a test. 133. Int.cont: Students are able to convert Roman numerals to Hindu Arabic numerals. Question: The value of DMM in Hindu Arabic system is ? 134. Int. cont :Students are able to understand the types of triangles? Question : What is the triangle formed if no two sides are equal.

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135. Int. cont :Students are able to explain about circumference. Question: Find the circumference of a circle if its radius is 7 cms. X. CLASSIFY THE FOLLOWING TEACHING AID USED IN THE SITUATION APPROPRIATELY. (1) GRID PAPER, (2) CUBICAL RODS (3) CHINESE TONNGRAM (4) DOMINO CARDS (5) ABACUS (6) GEO BOARD (7) KUSINEER STRIPS (8) NAPIER STRIPS. 136. Aid used for students to teach the numbers. 137. The aid used to teach multiplication table. 138. Aid used to recognize the numbers. 139. Aid used to teach cube and cuboids. 140. Aid used to teach the concept of pictures in Geometry. 141. Aid by which we can teach additions and subtractions. 142. Aid by which we can teach the area of an irregular pictures. 143. Aid used to teach the concept even though the shapes are different the area is same. 144. Aid used to understand the decimal numbers. 145. Aid used to teach fractions. XI. Following are some of the difficulties may be confronted within learning/using mathematical each of the items. Indicate your response to each item by writing the numbers representing the kind of difficulty in the concept. Using these, identify the kind of difficulty manifested by the students response to teacher’s question in blank provided.

Kinds of learning difficulties

a. Not knowing the term designating the concept. b. Inability to state the meaning of the term designating a concept. c. Inability to remember the condition (s) necessary for a mathematical object to be

denoted by the term designating the concept. d. Misclassifying an example as a non-example of a concept or vice-versa. e. Inability to deduce useful information from a concept.

Teaching-Learning Situations

11.1 T : Can your (points to a student) Tell us a rectangle is ? S1 : Sorry, I can’t. 11.2 T : 22 is a composite number. But, why is it a composite number ? S2 : No response. 11.3 T : What do we call a point which is the point of concurrency of the altitude of triangle ? S3 : I have no idea. 11.4 T : Give an example of a quadratic equation. S4 : x + y = 9 11.5 T : What is the name of a line that intersects a circle in two points ? S5 : Sorry, I don’t remember.

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11.6 T : When do you say that a polygon is regular ? S6 : When the poly has equal sides. 11.7 T : What is an incentre ? S7 : It is point inside a triangle. 11.8 T : Yesterday we talked about a s pecial kind of geometric figure. We started

with a closed four-sided figure. What do we call these ? S8 : Sorry, I don’t remember. 11.9 T : ABCDEF is regular polygon. So what is the measure of an angle. S9 : I know that the angles are congruent, but I can’t tell the measure of an

angle. 11.10 T : What do you say that 5/2 is a proper fraction ? S10 : Because the numerator is greater than the denominator.

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ANNEXURE VIII

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(First Draft)

XLVIII

LVIII

ANNEXURE IX

PEDAGOGY OF TEACHING MATHEMATICS FINAL STUDY KEY

S.NO ANSWER S.NO ANSWER S.NO ANSWER

1.1 Inductive Reasoning 1.2 Inductive Reasoning 1.3 Deductive Reasoning

1.4 Deductive Reasoning 1.5 Inductive Reasoning 1.6 Deductive Reasoning

2.1 Disciplinary Value 2.2 Cultural Value 2.3 Utility Value

2.4 Cultural Value 2.5 Disciplinary Value 2.6 Utility Value

3.1 Specific Objective 3.2 General Objective 3.3 Specific Objective

3.4 General Objective 3.5 Specific Objective 3.6 General Objective

4.1 Cognitive Domain 4.2 Affective Domain 4.3 Cognitive Domain

4.4 Psychomotor Domain 4.5 Affective Domain 4.6 Psychomotor Domain

5.1 Knowledge 5.2 Knowledge 5.3 Application

5.4 Application 5.5 Knowledge 5.6 Comprehension

6.1 Rule 6.2 Fact 6.3 Generalization

6.4 Rule 6.5 Concept 6.6 Generalization

7.1 Deductive method 7.2 Analytical method 7.3 Play way method

7.4 Heuristic method 7.5 Laboratory method 7.6 Inductive method

8.1 Yes 8.2 No 8.3 No

8.4 Yes 8.5 No 8.6 Yes

9.1 Knowledge 9.2 Application 9.3 Application

9.4 Comprehension 9.5 Knowledge 9.6 Comprehension

10.1 Abacus 10.2 Napier stripes 10.3 Domino cards

10.4 Cuboids 10.5 Geo Board 10.6 Grid paper

11.1 B 11.2 C 11.3 A

11.4 C 11.5 C 11.6 C

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ANNEXURE X

AN ACHIEVEMENT TEST IN PEDAGOGY OF TEACHING MATHEMATICS (FINAL STUDY TOOL)

1. Each item or question below describes a learning situation leading to discovery of a generalization mention the type of reasoning - Inductive reasoning or Deductive reasoning that is used in the discovery of generalization.

1.1 The numbers 5,10,15,20 are divisible by 5 . These numbers have either 5 or 0 in the

units places. Therefore all numbers with ‘0’ or ‘5’ in the units place are divisible by ‘5’.

1.2 By observing many times the student generalizes that “the ratio of the circumferences and the diameter of a circle is constant”.

1.3 A student finds out the area of a parallelogram length X breadth by cutting into 2 equal triangles along one diagonal and from the formula of area of triangles.

1.4 All numbers with ‘2’ in the unit place are even numbers the number 17 does not have 2 in the unit place. Therefore ‘17’ is not an even number.

1.5 A student observes that the triads of any two even numbers the even numbers the answer is again in even number and hence concludes that the triads of consecutive numbers are even numbers.

1.6 Finding the product of (a+b) and (a-b) equal a2 – b2, a students concludes that the product of the sum and differences of two numbers is equal to the difference of their squares.

2 . GIVEN BELOW IS A SET OF GENERAL OBJECTIVES .SPECIFY THE AIMS -------UTILITARIAN, DISCIPLINARY ,AND CULTURAL TO WHICH THEY ARE SUBORDINATES . 2.1 Learning of Mathematics makes the student self confidence. Self respect &

simplicity. 2.2 The student analysis that the culture and the secretes of sculpture are translated to the

next generation through Mathematics. 2.3 The student interpretates the bar diagrams from the Newspaper. 2.4 The student enjoys for the utilization of the principles of Mathematics in musical

instruments. 2.5 From the given data the student draws the generalizations. 2.6 The student uses Mathematics in physical sciences & Biological Sciences.

3. CLASSIFY EACH OBJECTIVES BELOW AS BELONGING TO GENERAL OBJECTIVES (GO)AND SPECIFIC OBJECTIVE(SO) , WRITE UNDECIDED (UD ) IF YOU CANNOT DISGUISE INTO GENERAL OR SPECIFIC . 3.1 Student understands about the place values. 3.2 Student can apply the steps in Mathematics in their real life. 3.3 Student understood the concept about different types of triangles. 3.4 Students enjoy the symmetrical shapes of geometry by observing in nature.

LX

3.5 Student understood the different concepts of Measurements. 3.6 Student applies the knowledge of profit and loss problems, percentages, Rate of

interests, etc., in their business in future. 4. CLASSIFY THE FOLLOWING OBJECTIVES AS BELONGING TO THE COGNITIVE, AFFECTIVE AND PSYCHOMOTOR DOMAIN. 4.1 Student classifies given number into prime numbers and composite numbers. 4.2 Student classifies the even prime numbers from the prime numbers. 4.3 Student represents a given number in the expanded form. 4.4 Student read the numbers in the given table without any mistakes easily. 4.5 Student enjoys the symmetry. 4.6 Student draws a circle using protractor given the measure of its diameter. V. CLASSIFY THE FOLLOWING OBJECTIVES ACCORDING TO BLOOM’S

CLASSIFICATION . (1) Knowledge (2) Understanding/comprehension (3) Application, (4) Analysis (5) Synthesis (6) Evaluation. 5.1 “What is multiple?” the student answers “The numbers obtained by the product of the

given number and 1,2,3,4,5 ……….. are called the multiples”. 5.2 For the question “What is the formula for the area of a triangle? The student replies

Area = ½ x b x h. 5.3 A student buys ¾ lts. of milk everyday. So in the month of June how much he has to

buy? (30 days) is solved by the student? 5.4 Student generalizes that “ The circle has infinite diameters”. 5.5 Student identifies the four sided figure?

(a) (b) (c) (d) 5.6 “What is the percentage of 25 kgs in one tonn.” The student converts into percentage? 6. CLASSIFY EACH STATEMENT GIVEN BELOW AS BELONGING TO THE KINDS OF SUBJECT MATTER IN MATHEMATICS (1 )CONCEPT ( 2) FACT (3)GENERALIZATION ( 4) RULE 6.1 Co-primes are primes having one as common factor. 6.2 The largest two digit number is 99. 6.3 The improper fraction is a fraction in which whose numbers are greater than denominator. 6.4 To convert days into hours, multiply days by 24. 6.5 If the four sides of a figure are equal, it is square. 6.6 The product of two positive integers is a positive integer.

LXI

7. REPRESENT THE TEACHING METHOD USED IN THE FOLLOWING TOPICS (INDUCTIVE, DEDUCTIVE, ANALYSIS, SYNTHESIS, LABORATORY, HEURISTIC, PLAYWAY, PROJECT METHOD)

7.1 The method used to evaluate R from I = PTR/100. 7.2 The method used in solving equations. 7.3 The method used to the student to understand the concept “angle”. 7.4 The method applied to learn multiplication table for 2. 7.5 The appropriate method to teach the measurement of length, weight and capacity. 7.6 The method used to teach the concepts of fractions. 8. IN EACH OF THE GIVEN BELOW JUDGE WHETHER THE TEST ITEM MEASURES THE OBJECTIVE PREFIXED TO IT OR NOT. IF THE ITEM MEASURES THE OBJECTIVE INDICATE YOUR ANSWER BY ‘YES’ AND IF IT DOES NOT ‘NO’. 8.1. Objective : Student understands multiplication as repeated addition.

Test item : 5 + 5 + 5 + 5 = 5 X ? 8.2. Objective : Students learn the addition of like fractions. Test item : 1/3 + ¼ + 2/3 = ? 8.3 Objective : Student converts one form of unit to another. Test item : 1 km is equal to how many kilo liters ? 8.4. Objective : The student says about the shapes of closed figures. Test item : What is the name of three sided closed figure. 8.5. Objective : Student converts Roman numerals to Hindu Arabic. Test item : Convert 100 to Roman numerals. 8.6. Objective : Student gains the knowledge of percentages. Test item : “Percentage” means? 9. FOLLOWING ARE THE TEST ITEMS. CLASSIFY THE OBJECTIVE IN COGNITIVE DOMAIN (KNOWLEDGE, COMPREHENSION, APPLICATION, ANALYSIS, SYNTHESIS, EVALUATION). 9.1. Instructional context : Students will be able to understand the place values by different methods. Question: In 26454 the place value of 6 is ? 9.2. Int. cont : Students will be able to understand the divisibility tests. Question: Without dividing the number 1716 find out whether it is divisible by 33 or not. 9.3. Int. cont:Students will be able to understand the L.C.M. by the method of prime numbers. Question: Ramu, Rahim,Robert participates in running race. The time taken to complete one round to Ramu is 100 seconds, Rahim 110 seconds, and Robert is 120 seconds. If they all starts at the same time what is the Time taken by them to meet again?

LXII

9.4. Int. Cont:The student will be able to understand about fractions? Question: Write the fractions equal to 5/9?

9.5 Int. cont:Students will be explained about profit and loss. Question: Gain percentage formula is ? 9.6. Int. cont: Students are able to convert Roman numerals to Hindu Arabic numerals. Question: The value of DMM in Hindu Arabic system is ? 10. CLASSIFY THE FOLLOWING TEACHING AID USED IN THE SITUATION APPROPRIATELY. (1) GRID PAPER, (2) CUBICAL RODS (3) CHINESE TONNGRAM (4) DOMINO CARDS (5) ABACUS (6) GEO BOARD (7) KUSINEER STRIPS (8) NAPIER STRIPS. 10.1. Aid used for students to teach the numbers. 10.2. The aid used to teach multiplication table. 10.3. Aid used to recognize the numbers. 10.4. Aid used to teach cube and cuboids. 10.5. Aid used to teach the concept of pictures in Geometry. 10.6. Aid by which we can teach the area of an irregular pictures. 11. FOLLOWING ARE SOME OF THE DIFFICULTIES MAY BE CONFRONTED WITHIN LEARNING/USING MATHEMATICAL EACH OF THE ITEMS. INDICATE YOUR RESPONSE TO EACH ITEM BY WRITING THE NUMBERS REPRESENTING THE KIND OF DIFFICULTY IN THE CONCEPT. USING THESE, IDENTIFY THE KIND OF DIFFICULTY MANIFESTED BY THE STUDENTS RESPONSE TO TEACHER’S QUESTION IN BLANK PROVIDED.

Kinds of learning difficulties a. Not knowing the term designating the concept. b. Inability to state the meaning of the term designating a concept. c. Inability to remember the condition (s) necessary for a mathematical object to be

denoted by the term designating the concept. d. Misclassifying an example as a non-example of a concept or vice-versa. e. Inability to deduce useful information from a concept.

Teaching-Learning Situations 11.1 T : Can your (points to a student) Tell us a rectangle is ? S1 : Sorry, I can’t. 11.2 T : 22 is a composite number. But, why is it a composite number ? S2 : No response. 11.3 T : What is the name of a line that intersects a circle in two points ? S5 : Sorry, I don’t remember. 11.4 T : Yesterday we talked about a special kind of geometric figure. We started

with a closed four-sided figure. What do we call these ? S8 : Sorry, I don’t remember. 11.5 T : ABCDEF is regular polygon. So what is the measure of an angle. S9 : I know that the angles are congruent, but I can’t tell the measure of an

angle. 11.6 T : What do you say that 5/2 is a proper fraction ? S10 : Because the numerator is greater than the denominator.

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ANNEXURE XI

Final Study Tool – Telugu Version

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LXX

ANNEXURE XII

KEY Question no. Answer Question no. Answer

1 Inductive 41 Cognitive 2 Deductive 42 Psychomotor 3 Deductive 43 Affective 4 Inductive 44 Cognitive 5 Inductive 45 Affective 6 Deductive 46 Psychomotor 7 Inductive 47 Cognitive 8 Deductive 48 Cognitive 9 Deductive 49 Affective

10 Inductive 50 Affective 11 Deductive 51 Cognitive 12 Inductive 52 Cognitive 13 Disciplinary Value 53 Application 14 Cultural Value 54 Comprehension 15 Utilitarian Value 55 Knowledge 16 Cultural Value 56 Comprehension 17 Utilitarian Value 57 Comprehension 18 Disciplinary Value 58 Comprehension 19 Cultural Value 59 Knowledge 20 Disciplinary Value 60 Application 21 Disciplinary Value 61 Knowledge 22 Utilitarian Value 62 Comprehension 23 Specific 63 Application 24 General 64 Comprehension 25 Specific 65 Knowledge 26 Specific 66 Comprehension 27 General 67 Knowledge 28 Specific 68 Generalization 29 Specific 69 Rule 30 General 70 Rule 31 Specific 71 Fact 32 General 72 Generalization 33 General 73 Concept 34 Specific 74 Generalization 35 Specific 75 Fact 36 General 76 Fact 37 Specific 77 Rule 38 Psychomotor 78 Fact 39 Cognitive 79 Concept 40 Affective 80 Fact

LXXI

Question no. Answer Question no. Answer 81 Concept 115 No 82 Generalization 116 Yes 83 Concept 117 No 84 Rule 118 No 85 Concept 119 No 86 Generalization 120 Yes 87 Fact 121 Yes 88 Generalization 122 No 89 Rule 123 Knowledge 90 Analytic 124 Comprehension 91 Laboratory 125 .Application 92 Inductive 126 Application 93 Deductive 127 Comprehension 94 Analytic 128 Knowledge 95 Inductive 129 Comprehension 96 Laboratory 130 Comprehension 97 Inductive 131 Knowledge 98 Play-way 132 Application 99 Inductive 133 Comprehension 100 Heuristic 134 Knowledge 101 Project 135 Comprehension 102 Laboratory 136 Abacus 103 Inductive 137 Napier Strips 104 Laboratory 138 Domino 105 Deductive 139 Cubic Rod 106 Yes 140 Geo Board 107 Yes 141 Abacus 108 No 142 Grid Paper 109 Yes 143 Chinese Ton Gram 110 Yes 144 Cubic Rod 111 No 145 Grid Paper 112 No 146 b 113 No 147 c 114 No 148 a

149 d 150 a 151 c 152 b 153 c 154 e

155 c

LXXII

ANNEXURE XIII CLASSROOM OBSERVATION SCHEDULE FOR PRIMARY SCHOOL

TEACHERS (FIRST DRAFT)

1. Name of the Teacher : 2. Sex: Male/Female 3. Name of the School : 4. Location: Rural/Urban 5. Management : Mandal Parishad/Municipality 6. Class : V 7. Topic 8. Transaction Time /Duration: 9. Date : 10. Class situation : 11. 1. Multigrade class / 2. Mono grade

Components Observed Rating Scale 0000000000000000000000000000000000000000000000000000000000000

0000000 Yes/No

Exc

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Poo

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LESSON INTRODUCTION INTRODUCES EFFECTIVELY USING ONE OR MORE OF THE FOLLOWING. a. Focus on the topic b. Outlines the major points or tasks to be covered. c. States explicitly the aim of the lesson. d. Uses analogous situation e. Traces Historical development f. Reviews prerequisites g. States the utility of studying the topic.

I.

h. Presence a problem situation. DEVELOPMENT OF THE LESSON a. Uses appropriate teaching strategies. b. Presents or generalises content with accuracy and clarity c. Organises in logical and psychological order d. Provides opportunities for applying acquired knowledge

II. e. Budgets time according to task and importance objectives.

EXPLAINING a. Interprets by giving examples or instances/paraphrasing/Reviewing prerequisites. b. Describes the process and structure through demonstration. c. Establishes truth value of the knowledge using deductive arguments/counter example/experimentation d. Speaks with clarity and fluency. e. Uses appropriate Vo cabulary. f. Uses link words and phrases. g. Uses appropriate media and material

III. h. Provides emphasis and interest through stimulus variation.

Components(criteria/Teacher Behaviour ) QUESTIONING a. Clear, precise, relevant and grammatically correct. b. Delivers with appropriate speed and proper intonation and pitch. c. Provides desired pause for thinking. d. Distributes among ;volunteers and non volunteers. e. Handles pupils response using prompting seeking further information, refocusing and asking awareness questions

IV.

f. Avoids mass responses.

LXXIII

Components Observed Rating Scale

00000000000000000000000000000000000000000000000000000000000000000000

Yes/No

Exc

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USE OF BLACK BOARD a. Writes new points or pupils responses. b. Draws neat diagrams/sketches and labels. c. Writes legibly neatly, and systematically with adequate space and size. d. Gives sufficient time to take down.

V. e. Maintains continuity in communication while writing.

USE OF LEARNING MATERIAL INCLUDING SUPPORT MATERIAL a. Appropriate to the content and level of the children. b. Relevance to the various situations in the lesson/topic. c. Creates interest among the learner.

VI. d. Effectively used - Easy to handle/Use the material.

PUPILS PARTICIPATION a. Secures and sustains pupils attention through varied stimuli.

VII.

b. Increases pupils participation (responding and initiating) through asking questions and creating climate and using verbal and non verbal cues and reinforces.

Components(criteria/Teacher Behaviour ) CLOSURE OF THE LESSON a. Recollects/reviews major points of the lesson. b. Develops learning structures by relating present learning with previous and future learning. c. Creates sense of accomplishment in pupils.

VIII

d. Makes effective conclusion. CLASSROOM MANAGEMENT a. Reinforces attending behaviour. b. Reacts to misbehaviour. c. Responds to appropriate targets. d. Uses non-verbal behaviour to inhibit the development of potential problem. e. Avoids arguments to discourage antagonism between teacher and students.

IX

f. Takes punitive measures appropriate to the misdeeds. DIAGNOSING a. Using a variety of methods to determine student status. b. Integrating information from several sources to determine student needs. c. Determine student developmental level.

X.

d. Identifying non-instructional factors which may be limiting student progress. EVALUATION a. Establishing evaluation criteria. b. Evaluating personal teaching effectiveness. c. Critiquing student performance (Eg. Strengths, areas which need improvement.) d. Using evaluation results to improve instruction.

XI. e. Evaluating the ethical consequences of one's own actions.

LXXIV

ANNEXURE XIV CLASSROOM OBSERVATION SCHEDULE FOR

TEACHING MATHEMATICS AT PRIMARY LEVEL 1.Name of the Teacher: 2.Sex: Male / Female 3.Name of the school: 4.Name of the Mandal: 5.District: 6.Location : Rural /Urban 7.Management: Mandal Parishad / Municipality 8.Class : 9.Name of the lesson 10.Transaction Time : 30 minutes 11.(1).Multi grade / (2) Mono grade

Teaching Competence Scale Components (Criteria /Teacher Behaviour ) Observed

Rating Scale

Introduces effectively using one or more of the following In each components

Yes / No

Exce

llent

Ver

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od

Goo

d

Ave

rage

Poor

I INTRODUCTION OF LESSON A. Focus of on the topic B. Reviews prerequisites

B. Traces Historical developments C. States explicitly the aim of the lesion D. Out lines the major points to be covered E. States the utility of studying the topic F. Uses analogous situation G. Presents a problem situation H. Present a problem situation I. Apparatus of Devise used ---to the content ---to the target group ---to the contest ( Multi grade / Mono grade )

II DEVELOPMENT OF THE LESSON A. Uses appropriate teaching strategies

B. Presents or generalizes content with accuracy and Clarity

C. Organizes in Logical and Psychological order D. Provides opportunities for applying acquired

knowledge E. Budgets of time according task and importance

objectives F. Command on the content

III EXPLAINING A. Interprets by giving examples / instances / reviewing

Prerequisites B. Describes the process and structure through demonstration C. Establishes truth value of the knowledge using deductive D. Speaks with clarity and fluency E. Uses link words and phrases F. Uses appropriate media and material G. Provides emphasis and interest through stimulus variation H Uses appropriate vocabulary I. Appropriateness of beginning and closing statements J. Pausing

LXXV

Components (Criteria /Teacher Behaviour ) Observed

Rating Scale

Introduces effectively using one or more of the following In each components

Yes / No

Exce

llent

Ver

y go

od

Goo

d

Ave

rage

Poor

IV. QUESTIONING A. Clear, precise, relevant and grammatically correct

B. Provides desired pause to think and respond C. Distributes among volunteers D. Handles E. Avoids mass responses

USE OF BLACK BOARD a. Writes new points or pupils responses. b. Draws neat diagrams/sketches and labels. c. Writes legibly neatly, and systematically with adequate space and size. d. Gives sufficient time to take down.

V.

e. Maintains continuity in communication while writing. f. Space management

USE OF LEARNING MATERIAL INCLUDING SUPPORT MATERIAL

a. Appropriate to the content and level of the children. b. Relevance to the various situations in the lesson/topic. c. Creates interest among the learner.

VI.

d. Effectively used - Easy to handle/Use the material. e. Cost effectiveness f. Availability in immediate environment

PUPILS PARTICIPATION a. Secures and sustains pupils attention through varied stimuli. VII.

b. Increases pupils participation (responding and initiating) through asking questions and creating climate and using verbal and non verbal cues and reinforces.

CLOSURE OF THE LESSON a. Recollects/reviews major points of the lesson. b. Develops learning structures by relating present learning with previous and future learning.

VIII c. Makes effective conclusion.

CLASSROOM MANAGEMENT a. Reinforces attending behaviour. b. Responds to appropriate targets. c. Avoids arguments to discourage antagonism between teacher and students.

IX d. Takes punitive measures appropriate to the misdeeds.

EVALUATION a. Clarity, overall coverage, appropriateness with respect to objectives. b. Provides feedback by reinforcing the correct answers and correcting wrong answers c. Review to check overall achievement

X.

d. Assignment provides scope to practice and apply knowledge and skills

LXXVI

ANNEXURE XV

ATTITUDE TOWARDS TEACHING MATHEMATICS (First Draft)

Statements

1. Students behavior should be taken into consideration by the Mathematics teacher. 2. Teaching math’s influences our personality and character. 3. Teaching math’s makes the student more disciplined. 4. I feel, just one method of teaching is not suitable for all the students. 5. I feel, only trained teachers should have the right to teach Mathematics. 6. I feel, weak students gain a lot through the revi sion of the lesson by the Mathematics

teacher. 7. Mathematics teacher plans their works carefully. 8. Teaching Mathematics influences leadership qualities among students. 9. I like to clear students doubts in Mathematics. 10. I make the student to know the significance of Mathematics. 11. I am confident to do the exercises in Mathematics. 12. I teach Mathematics as a compulsory requirement. 13. I teach new topic / lesson/concept only after knowing the required knowledge. 14. I will take personal interest in each child to learn Mathematics. 15. I make the Mathematics class interesting by using activity based approach. 16. I have improved knowledge through Mathematics teaching. 17. I gained confidence by teaching Mathematics. 18. I am ready to spend any amount of time in teaching Mathematics to improve student

achievement. 19. I give attention to individual difference of the students in teaching Mathematics. 20. I adopt innovative techniques for effective teaching in Mathematics. 21. I refer resource material for Mathematics teaching. 22. I can inspire the student to learn Mathematics. 23. I can evaluate the effectiveness of Mathematics teaching. 24. I can identify learning difficulties in Mathematics. 25. I can provide appropriate remedial instruction to various learning difficulties in

Mathematics. 26. I try to make the pupil to feel Mathematics is an interesting an easy subject. 27. I get bored to do any planning before teaching Mathematics. 28. I can handle pupils responses effectively in teaching Mathematics. 29. I derive a great pleasure to answer the various questions, put forward by the students. 30. I am confident in teaching any topic in Mathematics. 31. I feel Mathematics important part of the school curriculum. 32. I work hard to improvise teaching techniques in Mathematics. 33. I like to teach Mathematics because the procedures are logical. 34. I trust the saying - : “Mathematics is the queen of all sciences”. 35. I plan / device interesting anecdotes for every new topic to be taught. 36. Teaching mathematics requires integration of real life situations.

LXXVII

Negative Statements 1. Individual differences among the students should not be paid much attention in

teaching Mathematics. 2. Mathematics teaching does not promote self-confidence among students. 3. I feel, the principles of “ learning by doing” cannot be implemented in Mathematics

teaching. 4. I feel very difficult to generalize about teaching procedures because each pupil

responds differently. 5. I feel so bothered teach Mathematics. 6. I avoid to teach the difficult mathematical problems. 7. Teaching Mathematics has no artistic value. 8. I teach Mathematics as a compulsory requirement. 9. I don’t spend more time on teaching difficult topics in Mathematics. 10. I don’t like to attend for any orientation program of teaching Mathematics. 11. I will not allow the pupils for independent thinking in problem solving. 12. I will not give importance to slow learners in Mathematics. 13. I will not help to clear the pupil’s doubts in Mathematics. 14. I discourage the students who come with alternative solution to the problem. 15. I am not aware of modern techniques of teaching Mathematics. 16. I am not aware of using achievement scores to improve Mathematics teaching. 17. I always blame under achievers in Mathematics. 18. Mathematics teaching is interesting in the beginning. 19. I do not like teaching Mathematics to the students. 20. Mathematics teaching makes teachers weak and incompetent. 21. I find difficult to adjust my Mathematics teaching according to the needs of the

learner. 22. I somehow manage to complete my Mathematics class. 23. I try to avoid bright students while teaching Mathematics. 24. I can’t teach Mathematics effectively when I have to deviate from my planned lesson. 25. I prefer to ignore pupils doubts and wrong answer. 26. I get bored to do any planning before teaching Mathematics. 27. I fail to arose and sustain student interest Mathematics teaching. 28. I prefer to teach easy topics in Mathematics. 29. I don’t get any satisfaction in teaching Mathematics. 30. I feel solving mathematical puzzles is uninteresting.

LXXVIII

ANNEXURE XVI

ATTITUDE TOWARDS TEACHING MATHEMATICS PILOT STUDY TOOL

Please read the following statements given below and give valuable opinion on each statement. Kindly select any one of the alternatives. Strongly agree (SD); Disagree (D), Undecided (U), Agree (A) and Strongly Agree (SA). Put tick mark (ü) in the space provided. Sl. No.

Statement SD D U A SA

1 The Mathematics teacher should take students’ behaviour into consideration

2 Individual differences among the students should not be paid much attention in teaching mathematics

3 Teaching Mathematics influences Teachers personality and character

4 Teaching Mathematics makes the student more disciplined

5 Mathematics teaching does not promote self confidence among students

6 7 Teaching Mathematics makes the student more

disciplined

8 It is difficult to generalize about teaching procedures because pupil responses are not uniform

9 Trained teachers should not have the right to teach mathematics

10 Teaching mathematics is bothered work 11 Weak students gain a lot through the revision of the

lesson by the mathematics teacher

12 Teacher should make the student to know the significance of mathematics

13 Teacher should avoid to teach the difficult mathematical problems

14 Teaching mathematics has no artistic value 15 Teacher teach new lessons after knowing the

prerequisites

16 Teacher should not spend more on teaching difficult topics

17 Teacher will take personal interest in each child to learn Mathematics

18 Teacher should not attend for any orientation programme related to mathematics

LXXIX

Sl. No.


19 Teacher will make the Mathematics class interesting by using activity based approach

20 Teacher improves knowledge through Mathematics teaching

21 Teacher should not give importance to slow learners

22 Teacher should discourage the students who come with alternative solution to the problem

23 Teacher should adopt innovative Techniques for effective teaching mathematics

24 Teacher should not aware of modern techniques of teaching mathematics

25 Teacher should refer resource material for Mathematics teaching

26 Teacher should not aware of using achievement scores to improve mathematics teaching

27 Teacher can inspire the student to learn Mathematics

28 Teacher can provide appropriate remedial instruction to various learning difficulties in mathematics

29 Teacher should blame under achievers in mathematics

30 Mathematics teaching is interesting only in the beginning

31 Teacher should try to create an interest in learning mathematics

32 Mathematics teaching makes teacher’s weak and incompetent

33 Teacher should plan before teaching mathematics 34 Teacher should feel difficult to adjust mathematics

teaching according to the needs of the learner

35 Teacher should handle pupils responses effectively in teaching mathematics

36 Teacher should avoid bright students while teaching

37 Teacher should feel pleasure to answer the students reactions

38 Teacher should confident in teaching any topic in mathematics

39 The teacher can’t teach mathematics effectively when he had to deviate from his planned lesson

40 Teacher should prefer to ignore pupils doubts and wrong answers

LXXX

Sl. No.


41 Teacher must feel mathematics as an important part of the school curriculum

42 Teacher should get bored to do any planning before teaching

43 Teacher must work hard to improvise teaching techniques in mathematics

44 Teacher failed arose and sustain student interest in mathematics

45 One should teach Mathematics because of its logical reasoning

46 Teacher should use anecdotes for introducing new topic to be taught

47 Teacher should prefer to teach easy topics in mathematics

48 Teacher should not get any satisfaction in teaching mathematics

49 Teaching mathematics requires integration of real life situations

50 Solving mathematical puzzles is uninteresting 51 Mathematics teacher plans his / her works carefully 52 Teacher teaches mathematics as a requirement of

the post

53 Teacher must give attention to individual difference of the students in teaching

54 Teaching mathematics influences leadership qualities among students

55 Teacher should not help to clear the pupil’s doubts in mathematics

56 Teacher can evaluate the effectiveness of Mathematics teaching

57 Teacher should confident to do the exercises in mathematics

58 Teacher can identify learning difficulties in Mathematics

59 Teacher should not allow the pupils for independent thinking

LXXXI

ANNEXURE XVII

Preliminary Tool for Pilot Study (Telugu Version)

LXXXII

LXXXIII

LXXXIV

ANNEXURE XVIII

ATTITUDE TOWARDS TEACHING MATHEMATICS FINAL STUDY TOOL

Sl. No.


1 The Mathematics teacher should take students’ behaviour into consideration

2 Individual differences among the students should not be paid much attention in teaching mathematics

3 Teaching Mathematics influences Teachers personality and character

4 Teaching Mathematics makes the student more disciplined

5 Mathematics teaching does not promote self confidence among students

6 7 Teaching Mathematics makes the student more

disciplined

8 It is difficult to generalize about teaching procedures because pupil responses are not uniform

9 Trained teachers should not have the right to teach mathematics

10 Teaching mathematics is bothered work 11 Weak students gain a lot through the revision of the

lesson by the mathematics teacher

12 Teacher should make the student to know the significance of mathematics

13 Teacher should avoid to teach the difficult mathematical problems

14 Teaching mathematics has no artistic value 15 Teacher teach new lessons after knowing the

prerequisites

16 Teacher should not spend more on teaching difficult topics

17 Teacher will take personal interest in each child to learn Mathematics

18 Teacher should not attend for any orientation programme related to mathematics

19 Teacher will make the Mathematics class interesting by using activity based approach

20 Teacher improves knowledge through Mathematics teaching

21 Teacher should not give importance to slow learners

LXXXV

Sl. No.


22 Teacher should discourage the students who come with alternative solution to the problem

23 Teacher should adopt innovative Techniques for effective teaching mathematics

24 Teacher should not aware of modern techniques of teaching mathematics

25 Teacher should refer resource material for Mathematics teaching

26 Teacher should not aware of using achievement scores to improve mathematics teaching

27 Teacher can inspire the student to learn Mathematics

28 Teacher can provide appropriate remedial instruction to various learning difficulties in mathematics

29 Teacher should blame under achievers in mathematics

30 Mathematics teaching is interesting only in the beginning

31 Teacher should try to create an interest in learning mathematics

32 Mathematics teaching makes teacher’s weak and incompetent

33 Teacher should plan before teaching mathematics 34 Teacher should feel difficult to adjust mathematics

teaching according to the needs of the learner

35 Teacher should handle pupils responses effectively in teaching mathematics

36 Teacher should avoid bright students while teaching

37 Teacher should feel pleasure to answer the students reactions

38 Teacher should confident in teaching any topic in mathematics

39 The teacher can’t teach mathematics effectively when he had to deviate from his planned lesson

40 Teacher should prefer to ignore pupils doubts and wrong answers

41 Teacher must feel mathematics as an important part of the school curriculum

42 Teacher should get bored to do any planning before teaching

43 Teacher must work hard to improvise teaching techniques in mathematics

LXXXVI

Sl. No.


44 Teacher failed arose and sustain student interest i n mathematics

45 One should teach Mathematics because of its logical reasoning

46 Teacher should use anecdotes for introducing new topic to be taught

47 Teacher should prefer to teach easy topics in mathematics

48 Teacher should not get any satisfaction in teaching mathematics

49 Teaching mathematics requires integration of real life situations

50 Solving mathematical puzzles is uninteresting

LXXXVII

ANNEXURE XIX

LXXXVIII

LXXXIX


XCIII

ANNEXURE XX

AN ACHIEVEMENT TEST IN CONTENT OF MATHEMATICS FOR V STANDARD (FIRST DRAFT)

Personal Information 1. Name of the student : 2. Gender : Boy/Girl 3. Age : 4. Caste : OC/BC/SC/ST/Minorities/Christians/Others 5. Father name : 6. Father education : Illiterate/Primary Inter/Education/S.SC/Inter/

Degree/P.G/Others 7. Mother name : 8. Mother education : Illiterate/Primary Education/S.S.C/Inter/Degree/

P.G/Other 9. Income : 10. School address :

11. Mathematics teacher name :

Instructions:

v Teachers are requested fill the above information.

v Students are advised to observed the questions carefully and give the answers.

v Each question gives subjections.

1. Express the following numbers in words

Ex:-25346 twenty five thousand three hundred on forty six

1.1) 74359

1.2) 98612

1.3) 59374

1.4) 81035

1. 5) 67541

2. Write the following numbers in the expand form

Ex :- 12345 = 10000+ 2000+ 300+ 40+ 5

2.1) 64527=

2.2) 87396 =

2.3) 96341 =

2.4) 72396 =

XCIV

3. Write the following numbers ascending order.

Ex: - 35490, 24927, 81426, 58974

Ascending order : - 24927, 35490, 58974, 81426.

3.1) 25084, 65248, 42561, 13274.

3.2) 67325, 23670, 75324, 53624.

3.3) 84615, 23684, 96353, 81383.

3.4) 55340, 52695, 31600, 77670.

3.5) 78123, 27356, 17975, 46795.

4. Find the place values of the underlined digits in the following numbers.

Ex :- 37645 How much the 7 place value 7000.

1) 75329 2) 92430 3)87643

4) 67542 5) 29354

5. Do the following Additions.

Ex:- 12345 15682 13212 41239

5.1) 12340+14462+16745=

5.2) 23871+36734+49852=

5.3) 85234+21673+62985=

5.4) 14259+63936+25326=

6. Do the following Substractions.

Ex: - 56275

(-) 23164

____________

33111__

6.1) 87425 6.2) 78758 6.3) 93568

(-) 36213 (-) 46345 ( -) 72356

__________ _______________ ______________

__________ ________________ _______________

6.4) 58976 6.5) 48627

(-) 36525 (-) 16516

____________ _______________

____________ ________________

XCV

7.


8.1) 30 ÷ 3 8.2) 26 ÷ 2 8.3) 36 ÷ 4

8.4) 49 ÷ 7 8.5) 56 ÷ 8


Ex :- 1345 ÷ 12

Divisibility 112

9.1) 360 ÷15 9.2) 793 ÷ 13

9.3) 848 ÷16 9.4) 462 ÷14

9.5) 714 ÷ 17

XCVI

10. Convert the additions into multiplications form.

Ex :- 5+5+5 = 5x3 10.1) 2+2+2+2 =

10.2) 9+9+9+9+9+9+9+9 =

10.3) 6+6+6+6+6 =

10.4) 8+8+8+8+8+8+8 =

10.5) 3+3+3+3+3+3 =

11. Convert the multiplication form into addition

Ex: 7 x 4 = 7+7+7+7

11.1) 4 x 6 =

11.2) 10 x 8 =

11.3) 11 x 3 =

11.4) 14 x 5 =

11.5) 16 x 7 =

12. Do the following multiplications

Ex :- 356 x 42

712

_1424

14952

12.1) 437 x 23 12.2) 254 x 45

12.3) 627 x 67 12.4) 987 x 57

12.5) 246 x 89

13. Write the Indo- Arabic numbers corresponding to. Ex : XXX = 10 + 10 + 10 = 30

13.1) XLV = 13.2) CDLIV =

13.3) CMXC= 13.4) MCDIV =

13.5) DMM =

XCVII

14. Write multiples of given numbers. Ex :- 4 Multiplies 4, 8, 12, 16................

14.1) 7 14.2) 9 4.3) 12 4.4) 5 14.5) 15

15. Write all the factors of given numbers Ex: - 16 factors 1, 2, 4, 8, 16..................

15.1) 12 15.2) 44 15.3) 18 15.4) 36 15.5) 21

16. Fill in the blanks with a suitable digit to make the numbers divisible by 9

EX :- 23........6 = 2316

16.1) 2345....... 16.2) 285 .....4

16. 3) 65 ...... 74 16.4) 5......07

16.5) ....8957

17. Find the L.C.M. of the following numbers.

EX: 6, 8, 12 L.C.M.

_2 6, 8, 12_ _3 3, 4, 6__ _2 1, 4, 2__ 1, 2, 1

L.C.M.= 2 x 3 x 2 x 2 x 1 x 1 = 24

17.1) 8, 12, 16 17.2) 12, 16, 20

17.3) 16, 20, 24 17.4) 10, 15, 20

17.5) 12, 18, 24

18. Write the fractions of the part shaded in the total.

Ex:

XCVIII

19. Tell whether the pair of fractions is equal or not in each of the questions given below.

Ex:

20. Put the symbols > or < Properly In the blanks below. ?

Ex:

21. Write each group of fractions in the ascending order?

Ex:

Ascending order:

XCIX

22. Add the following fractions.

Ex:

23. Subtract the second from the first.

Ex:

24. Work the following multiplications write down the production the simplest form.

Ex:

C

25. Simplify the following divisions?

26. Change into decimal fraction?

27. Change In to common fractions

Ex : 0.15 = 15/1000

27.1) 0.254 27.2) 4.67 27.3) 58.765

27.4) 65.403 27.5) 0.8643

28. In each of the following fill in the blanks with > or < to make the sentence true?

Ex: 36.546 ............36.346

28.1) 19.319 ............ 19.3116 28.2) 7.77.............. 6.15

28.3) 0.008 ........... 0.0008 28.4) 41.39 ........... 41.378

28.5) 8.8152 ......... 8.8189

29. Add the following decimal fractions

Ex: 2.356 + 3.234 + 4.123 = 9.713

29.1) 9.73 + 26.3 + 5.08 = 29.2) 35.17 + 9.24 + 26.03 =

29.3) 0.05 + 12.3 + 5.74 = 29.4) 3.20 + 15.67 + 0.08 =

29.5) 3.74 + 1.05 + 10.463 =

Ex:

Ex:

CI

30. Subtract the following decimal fractions.

Ex : 14.367 - 12.564 = 1.803

30.1) 32.84 - 17.56 = 30.2) 42.13 - 19.76 =

30.3) 1.006 - 0.0897 = 30.4) 0.005 - 0.00489 =

30.5) 15.463 - 9.897 =

31. Work out the following multiplications.

Ex : 3.45 x 2.3

1035

690__

7.935

31.1) 4.69 x 10 31.2) 3.682 x 100 3) 12.86 x 3.4

31.4) 7.85 x 6.2 31.5) 8.5 x 2.3

32. Work out the following Divisions. ?

Ex : 15.54 ÷ 3 = 3) 15.54 (5.18 15__ 05 __03_ 24 __24_ 0

32.1) 6.41 ÷ 10 32.2) 0.253 ÷ 100

32.3) 10.6 ÷ 7 32.4) 16.48 ÷ 16

32.5) 34.65 ÷ 11

33. Convert the following meters into centimeters.

Ex : 5 meters = 5 x 1000 = 5000 centimeters

33.1) 7.5 meters

33.2) 24 meters

33.3) 3.25 meters

33.4) 15 meters

33.5) 18 meters

CII

34. Convert the following liters into milliliters. ?

Ex : 2 liters = 2 x 1000 milliliters

34.1) 12 liters = 34.2) 3 liters = 34.3) 1.6 liters = 34.4) 28 liters = 34.5) 6.9 liters =

35. Convert the following Kilograms into grams.

Ex:- 3 Kilograms = 3 x 1000 = 3000 grams

35.1) 36 Kilograms = 35.2) 25.7 Kilograms = 35.3) 8 Kilograms = 35.4) 7.5 Kilograms = 35.5) 86 Kilograms =


Ex:-: Find the average of 1, 2, 3, 4, 5.

Sum of scores 1 + 2 + 3 + 4 + 5 15 Average = = = = 3 Number of scores 5 5

36.1) 1, 3, 5, 7, 9

36.2) 4, 6, 8, 10, 12

36.3) 18, 4, 7, 11, 15

36.4) 6, 10, 9, 7

36.5) 7, 10, 4, 3

37. Convert the following common fractions into a percentage? 1 Ex:- Converting into percentage. 2

CIII

38. Convert the following percentages into common fractions ?

Ex:-25% = 25/100 = 1/4

38.1) 75% 38.2) 40%

38.3) 12 38.4) 35%

38.5) 33 1/3%

39. Express the first number as a percentage of the second Ex:-2, 5 (2/5) x 100 = 200/5 = 40%

39.1) 3, 8 39.2) 15, 60 39.3) 30, 48 39.4) 36, 60 39.5) 39, 45

40. Find the value of a given percentage of a quantity ?

Ex:- What is the value of 24 ÷ 25% ? 24 x (25/100) = 24/4 = 6

40.1) 50 ÷ 12% 40.2) 25 ÷ 12% 40.3) 32 ÷ 75% 40.4) 625 ÷ 24% 40.5) 575 ÷ 50%


Ex:-28 : 35 = 28/35 = 4 : 5

41.1) 15 : 75 41.2) 12 : 48

41.3) 25 : 100 41.4) 15 : 21

41.5) 22 : 55 42. In each of the following problems a number and a ratio are given. Divide the number in the given ratio

Ex:-120, 5 : 3

42.1) 315, 4: 3

42.2) 245, 3: 4

42.3) 750, 3 : 2

42.4) 112, 4: 3

42.5) 5250, 2 : 5

CIV

43. Write the time using 12 hour clock times?

Ex :

44. Using scale find the length of the line segment ?

Ex :-A B = 3 Cms.

44.1) C D = 44.2) . . =

M N 44.3) S T = 44.4) = S T 44.5)

X Y = 45. Name the following Geometrical figures.

45.1) 45.2) 45.3)

45.4) 45.5)

46. Draw the following Geometrical figures.

46.1) Circle 46.2) Rectangle

46.3) Rhombus 46.4) Triangle

46.5) Trapezium

= 9’O Clock

CV

47. Write the names of the given angles?

48.

_____________1) In a certain village there are 3,472 men, 3,556 women and 715 children. What is the population of the village?

_____________2) Chaitu deposited Rs. 12,756, in Gramina Bank : Kaushal deposited Rs 13,456,Yamini deposited Rs.4205; Silpa deposited Rs 3703. Find the total of their deposits in the Bank.

_____________3) Ravi has a coconut grove with 75266 trees. 7529, trees fell in cyclone. How many trees remain.

_____________4) Chaithanya buys a plot of land for Rs. 3,75,865 and constructions a house spending Rs 2,72,872. He sells it for Rs 9,00,000. what amount does he get more than what he spent.

_____________5) An employee’s monthly salary is Rs. 4850. How much does he get in 6 months?

_____________6) There are 224 high schools in a district a T.V. costs Rs 4,435. Find the total amount requires if all the schools are to be supplied T.V. at the rate of one for each school.

_____________7) There are 48 pupils in a class how many benches are required if three can sit on a bench?

_____________8) A cycle merchant bought 25 cycles and paid 20,000 and promised to pay the remaining amount of Rs. 1,250. If so, find the cost price of one cycle.

_____________9) What is the least number of children who may be arranged in rows of 12, 16 or 18 in each row?

47.1) 47.2)

47.3)47.4)

47.5)

CVI

_____________10) There are three bells. First bell rings once in 8 seconds, the second once in 10 seconds and the third once in 12 seconds. If all the three bells ring at the same time, whom do all the three bells ring to gather again?

_____________11) 240 students of a school wrote X class public examinations. If 2/3 of them pass, how many students failed?

_____________12) The cost of Mathematics test books is Rs. 4 1/2½. What is the required to provide the test books to a class of 35 children?

_____________13) Radha scored 64, 6, 65, 35, 75 and 37 marks in Mathematics in 6 examinations. What if her average marks in Mathematics?

_____________14) 327,512,450,615 people attended a film show on four consecutive days. On an average how many people per day attended the film show?

____________15) Ryot got an income of Rs. 15000, from a land of one hectare. The agricultural expenses came to Rs. 9000. What percentage of the income is the expenditure?

_____________16) An employee’s pay is 1200. His house rent allowance is 20% of his pay. What is the house rent allowance?

_____________17) A trader purchased 300 books at the rate of Rs. 12 each. He sold them for a profit of 15 % what is the selling price of each book.

_____________18) There are 25 boys and 20 girls in a class. Find the ratio of the number of boys to the number of girls in the class.

_____________19) In paddy, weights rice and husk are in the ratio of 11:5 If 2240 Kg of paddy are milled find the weight of rice got.

CVII

ANNEXURE XXI

CXVIII

CXXIII

CXXV

ANNEXURE XXII

STUDENTS ACHIEVEMENT KEY – FIRST DRAFT

Sl. No.

Answer Sl. No.

Answer Sl. No.

Answer

1.1 74 thousand 3 hundred and fifty nine

1.2 98 thousand 6 hundred and twelve

1.3 59 thousand 3 hundred and seventy four

1.4 81 thousand and thirty five

1.5 67 thousand 5 hundred and forty one

2.1 60000+4000+500+20+7

2.2 80000+7000+300+40+1

2.3 90000+6000+300+40+1 2.4 70000+2000+300+90+6

2.5 30000+6000+400+50+8

3.1 13274, 25084, 42561, 65248

3.2 23670, 53624, 67325, 75324

3.3 23684, 81383, 84615, 96353

3.4 31600, 52695, 55340, 77670

3.5 17975, 27356, 46795, 78123

4.1 5000 4.2 90000 4.3 600 4.4 60000 4.5 300 5.1 43547 5.2 110457 5.3 169892 5.4 154532 5.5 103521 6.1 51212 6.2 32413 6.3 21212 6.4 22451 6.5 32111 7.1 3 7.2 5 7.3 6 7.4 4 7.5 5 8.1 3 8.2 13 8.3 9 8.4 7 8.5 7 9.1 24 9.2 61 9.3 53 9.4 33 9.5 42 10.1 2 x 4 10.2 8 x 9 10.3 6 x 5 10.4 8 x 7 10.5 3 x 6 11.1 4+4+4+4+4+4+4 11.2 10+10+10+10+10+10+

10+10+10+10 11.3 11+11+11 11.4 14+14+14+14+14

11.5 16+16+16+16+16+16+16

12.1 10051 12.2 11330

12.3 42009 12.4 56259 12.5 21894 13.1 45 13.2 454 13.3 990 13.4 1404 13.5 1500 14.1 7,14,21,.. 14.2 9,18,27,.. 14.3 12, 24, 36, .. 14.4 5, 10, 15,… 14.5 15, 30, 45,… 15.1 1,2,3,4,6,12 15.2 1,2, 4,11, 22, 44 15.3 1,2,3,6,9,18 15.4 1,2,3,9,12,18,36 15.5 1, 3, 7, 21 16.1 1 16.2 8 16.3 5 16.4 6 16.5 7 17.1 48 17.2 240 17.3 240 17.4 60 17.5 72 18.1 ¼ 18.2 1/3 18.3 ¾ 18.4 4/9 18.5 3/8 19.1 √ 19.2 X 19.3 √ 19.4 X 19.5 √ 20.1 > 20.2 > 20.3 < 20.4 > 20.5 > 21.1 3/9, 4/9, 5/9, 6/9 21.2 6/35, 8/45, 14/45,

15/45 21.3 1/7, ¼, 1/3, 1/2 21.4 1/6, 1/5, 6/8, 3/4 21.5 3/20, 4/20, 7/20, 9/20 22.1 11/15 22.2 5/4 22.3 31/35 22.4 109/88 22.5 7/9 23.1 1/8 23.2 1/8 23.3 5/16 23.4 2/15 23.5 1/18 24.1 3/10 24.2 12/35

CXXVI

Sl. No.

Answer Sl. No.

Answer Sl. No.

Answer

24.3 4/15 24.4 4/7 24.5 15/72 25.1 3/10 25.2 2 25.3 2 25.4 3/13 25.5 3/2 26.1 0.14 26.2 0.0006 26.3 0.135 26.4 0.03 26.5 0.03526 27.1 254/1000 27.2 467/100 27.3 58765/100 27.4 65403/ 1000 27.5 8643/ 10000 28.1 > 28.2 > 28.3 > 28.4 > 28.5 < 29.1 41.11 29.2 70.44 29.3 18.09 29.4 18.95 29.5 15.253 30.1 15.28 30.2 22.37 30.3 0.9163 30.4 0.00011 30.5 5.566 31.1 46.9 31.2 368.2 31.3 43.724 31.4 48.67 31.5 19.55 32.1 0.641 32.2 0.00253 32.3 1.5 32.4 1.3 32.5 31.5 33.1 7500 cm 33.2 24000 cm 33.3 3250 cm 33.4 15000 cm 33.5 18000 cm 34.1 12000 ml 34.2 3000 ml 34.3 1600 ml 34.4 28000 ml 34.5 6900 ml 35.1 36000 gm 35.2 25700 gm 35.3 8000 gm 35.4 7500 gm 35.5 86000 gm 36.1 5 36.2 8 36.3 11 36.4 8 36.5 6 37.1 75% 37.2 62.5% 37.3 31.25% 37.4 70% 37.5 44% 38.1 ¾ 38.2 2/5 38.3 1/8 38.4 7/20 38.5 1/3 39.1 37.5% 39.2 25% 39.3 62.5% 39.4 60% 39.5 86.6% 40.1 6 40.2 3 40.3 24 40.4 150 40.5 287.5 41.1 1:5 41.2 1:4 41.3 1:4 41.4 5:7 41.5 1:5 42.1 180, 135 42.2 105, 140 42.3 450,300 42.4 64, 48 42.5 3000,2250 43.1 7 hours 43.2 5 hours 43.3 8 hours 43.4 3 hours 43.5 5.05 hours 44.1 2 cm 44.2 3 cm 44.3 1.5 cm 44.4 2 cm 44.5 3.5 cm 45.1 Line 45.2 Triangle 45.3 Rectangle 45.4 Ray 45.5 Parallelogram 46.1 46.2

46.3

46.4

46.5

47.1 Acute angle

47.2 Obtuse angle 47.3 Right angle 47.4 Reflexive angle 47.5 Straight angle 48.1 774 48.2 34120 48.3 67737 48.4 362263 48.5 29100 48.6 995440 48.7 18 48.8 850 48.9 144 48.10 120 sec 48.11 80 48.12 157.5 48.13 47 48.14 476 48.15 60% 48.16 240 48.17 13.80 48.18 5:4 48.19 1540 kg

CXXVII

ANNEXURE XXIII

AN ACHIEVEMENT TEST IN CONTENT OF MATHEMATICS FOR V STANDARD STUDENTS

(FINAL STUDY TOOL) Personal Information 1. Name of the student : 2. Gender : Boy/Girl 3. Age : 4. Caste : OC/BC/SC/ST/Minorities/Christians/Others 5. Father name : 6. Father education : Illiterate/Primary Inter/Education/S.SC/Inter/

Degree/P.G/Others 7. Mother name : 8. Mother education : Illiterate/Primary Education/S.S.C/Inter/Degree/

P.G/Other 9. Income : 10. School address :

11. Mathematics teacher name :

Instructions:

v Teachers are requested fill the above information.

v Students are advised to observed the questions carefully and give the answers.

v Each question gives subjections.

1. Express the following numbers in words

Ex:-25346 twenty five thousand three hundred on forty six

1.1) 743594

1.2) 986125

1.3) 593743

1.4) 810357

2. Write the following numbers in the expand form

Ex :- 12345 = 10000+ 2000+ 300+ 40+ 5

2.1) 464527=

2.2) 687396 =

2.3) 896341 =

2.4) 572396 =

CXXVIII

3. Write the following numbers ascending order.

Ex: - 35490, 24927, 81426, 58974

Ascending order : - 24927, 35490, 58974, 81426.

3.1) 25084, 65248, 42561, 13274.

3.2) 67325, 23670, 75324, 53624.

3.3) 84615, 23684, 96353, 81383.

3.4) 55340, 52695, 31600, 77670.

4. Find the place values of the underlined digits in the following numbers.

Ex :- 37645 How much the 7 place value 7000.

1) 75329 2) 92430 3)87643

4) 67542

5. Do the following Additions.

Ex:- 12345 15682 13212 41239

5.1) 12340+14462+16745=

5.2) 23871+36734+49852=

5.3) 85234+21673+62985=

5.4) 31728 + 51278 + 71526=

6. Do the following Substractions.

Ex: - 56275

(-) 23164

____________

33111__

6.1) 874256 6.2) 787587 6.3) 935689

(-) 362132 (-) 463453 (-) 723564

__________ _______________ ______________

__________ ________________ _______________

6.4) 589768

(-) 365255

____________

____________

CXXIX

7.


Ex :- 1345 ÷ 12

Divisibility 112

8.1) 360 ÷15 8.2) 793 ÷ 13

8.3) 848 ÷16 8.4) 462 ÷14

9. Convert the additions into multiplications form.

Ex :- 5+5+5 = 5x3 9.1) 2+2+2+2+2+2+2 =

9.2) 9+9+9+9+9+9+9+9+9+9+9+9 =

9.3) 6+6+6+6+6+6+6+6+6 =

15:5 =

30:6 =

42:7 =

20:5 =

CXXX

9.4) 8+8+8+8+8+8+8+8+8+8 =

10. Do the following multiplications

Ex :- 356 x 42

712

_1424

14952

10.1) 437 x 23 10.2) 254 x 45

10.3) 627 x 67 10.4) 987 x 57

11. Write multiples of given numbers. Ex :- 4 Multiplies 4, 8, 12, 16................

14.1) 7 14.2) 9 4.3) 12 4.4) 5

12. Write all the factors of given numbers Ex: - 16 factors 1, 2, 4, 8, 16..................

15.1) 12 15.2) 44 15.3) 18 15.4) 36

13. Find the L.C.M. of the following numbers.

EX: 6, 8, 12 L.C.M.

_2 6, 8, 12_ _3 3, 4, 6__ _2 1, 4, 2__ 1, 2, 1

L.C.M.= 2 x 3 x 2 x 2 x 1 x 1 = 24

13.1) 8, 12, 16 13.2) 12, 16, 20

13.3) 16, 20, 24 13.4) 10, 15, 20

14. Write the fractions of the part shaded in the total.

Ex:

14.1) 14.2) 14.3)

14.4)

CXXXI

15. Write each group of fractions in the ascending order?

16. Add the following fractions.

Ex:

17. Subtract the second from the first.

Ex:

Ex:

Ascending order:

15.1) 15.2)

15.3) 15.4

16.1)

16.2)

16.3)

16.4)

17.1)

17.2)

17.3)

17.4)

CXXXII

18. Work the following multiplications write down the production the simplest form.

19. Simplify the following divisions?

20. Change into decimal fraction?

21. Add the following decimal fractions

Ex: 2.356 + 3.234 + 4.123 = 9.713

21.1) 9.73 + 26.3 + 5.08 = 21.2) 35.17 + 9.24 + 26.03 =

21.3) 0.05 + 12.3 + 5.74 = 21.4) 3.20 + 15.67 + 0.08 =

Ex:

Ex:

Ex:

18.1)

18.2)

18.3)

18.4)

19.1)

19.2)

19.3)

19.4)

20.1) 20.2) 20.3)

20.4)

Ex:

CXXXIII

22. Subtract the following decimal fractions.

Ex : 14.367 - 12.564 = 1.803

22.1) 32.84 - 17.56 = 22.2) 42.13 - 19.76 =

22.3) 1.006 - 0.0897 = 22.4) 0.005 - 0.00489 =

23. Work out the following multiplications.

Ex : 3.45 x 2.3

1035

690__

7.935

23.1) 4.69 x 10 23.2) 3.682 x 100 23.3) 12.86 x 3.4

23.4) 7.85 x 6.2

24. Work out the following Divisions. ?

Ex : 15.54 ÷ 3 = 3) 15.54 (5.18 15__ 05 __03_ 24 __24_ 0

24.1) 6.41 ÷ 10 24.2) 0.253 ÷ 100

24.3) 10.6 ÷ 7 24.4) 16.48 ÷ 16

25. Convert the following meters into centimeters.

Ex : 5 meters = 5 x 1000 = 5000 centimeters 25.1) 7.5 meters 25.2) 24 meters 25.3) 3.25 meters 25.4) 15 meters

26. Convert the following liters into milliliters. ?

Ex : 2 liters = 2 x 1000 milliliters

26.1) 12 liters = 26.2) 3 liters = 26.3) 1.6 liters = 26.4) 28 liters =

CXXXIV

27. Convert the following Kilograms into grams.

Ex:- 3 Kilograms = 3 x 1000 = 3000 grams

27.1) 36 Kilograms = 27.2) 25.7 Kilograms = 27.3) 8 Kilograms = 27.4) 7.5 Kilograms =


Ex:-: Find the average of 1, 2, 3, 4, 5.

Sum of scores 1 + 2 + 3 + 4 + 5 15 Average = = = = 3 Number of scores 5 5

28.1) 1, 3, 5, 7, 9

28.2) 4, 6, 8, 10, 12

28.3) 18, 4, 7, 11, 15

28.4) 6, 10, 9, 7

29. Convert the following common fractions into a percentage? 1 Ex:- Converting into percentage. 2

30. Find the value of a given percentage of a quantity ?

Ex:- What is the value of 24 ÷ 25% ? 24 x (25/100) = 24/4 = 6

30.1) 12% of 50 30.2) 12% of 25

30.3) 75% of 32 30.4) 24% of 625


Ex:-28 : 35 = 28/35 = 4 : 5

31.1) 15 : 75 31.2) 12 : 48

29.1) 29.2)

29.3) 29.4)

CXXXV

31.3) 25 : 100 31.4) 15 : 21

32. Write the time using 12 hour clock times?

Ex :

33. Name the following Geometrical figures.

33.1) 33.2) 33.3)

33.4)

34. Draw the following Geometrical figures.

34.1) Circle 34.2) Rectangle

34.3) Rhombus 34.4) Triangle

35. Write the names of the given angles?

= 9’O Clock

32.1)32.2)

32.3) 32.4)

35.1) 35.2)

35.3) 35.4)

CXXXVI

36. Solve the verbal problems

_____________36.1)In a certain village there are 3,472 men, 3,556 women and 715 children. What is the population of the village?

_____________36.2) Ravi has a coconut grove with 75266 trees. 7529, trees fell in cyclone. How many trees remain.

_____________36.3) An employee’s monthly salary is Rs. 4850. How much does he get in 6 months?

_____________36.4) A cycle merchant bought 25 cycles and paid 20,000 and promised to pay the remaining amount of Rs. 1,250. If so, find the cost price of one cycle.

_____________36.5) What is the least number of children who may be arranged in rows of 12, 16 or 18 in each row?

_____________36.6) Radha scored 64, 6, 65, 35, 75 and 37 marks in Mathematics in 6 examinations. What if her average marks in Mathematics?

_____________36.7) An employee’s pay is 1200. His house rent allowance is 20% of his pay. What is the house rent allowance?

_____________36.8) There are 25 boys and 20 girls in a class. Find the ratio of the number of boys to the number of girls in the class.

CXXXVII

ANNEXURE XXIV


CXXXVIII

CXXXIX

CXLIII

CXLVII

ANNEXURE XV

STUDENTS ACHIEVEMENT

FINAL DATA KEY

Sl. No.

Answer Sl. No.

Answer Sl. No.

Answer

1.1 7 lakhs 43 thousand 5 hundred ninety four

1.2 9 lakhs 86 thousand 1 hundred and twenty

five

1.3 5 lakhs 93 thousand 7 hundred and forty

three 1.4 8 lacks 10 thousand 3

hundred fifty seven 2.1 400000+60000+4000

+500+20+7 2.2 600000+80000+7000+

300+90+6+ 2.3 800000+90000+6000+

300+40+1 2.4 500000+70000+2000+

300+90+6 3.1 13274,25084,

42561,65248, 3.2 23670,53624, 67325,

75324 3.3 23684, 81383, 84615,

96353 3.4 31600, 52695,55340,

77670 4.1 5000 4.2 90000 4.3 600 4.4 60000 5.1 43547 5.2 110457 5.3 169892 5.4 154532 6.1 512124 6.2 324134 6.3 212125 6.4 224513 7.1 3 7.2 5 7.2 6 7.4 4 8.1 24 8.2 61 8.3 53 8.4 33 9.1 2x7 9.2 9x12 9.3 6x9 9.4 8x10 10.1 20102 10.2 11430 10.3 42009 10.4 56259 11.1 7,14,21,28,… 11.2 9,18,27…. 11.3 12,24,36,.. 11.4 5,10,15,.. 12.1 1,2,3,4,6,12 12.2 1,2,4,11,44, 12.3 1,2,3,6,9,18 12.4 1,2,3,4,6,9 13.1 48 13.2 240 13.3 240 13.4 60 14.1 ¼ 14.2 2/6 14.3 ¾ 14.4 4/9 15.1 3/9, 4/9, 5/9, 6/9 15.2 6/45,8/45,14/45, 15/45 15.3 1/7, ¼, 1/3, 1/2 15.4 1/6, 1/5, 6/8, 3/4 16.1 11/15 16.2 5/4 16.3 31/35 16.4 109/88 17.1 1/8 17.2 1/8 17.3 5/16 17.4 2/15 18.1 3/10 18.2 12/35 18.3 4/15 18.4 4/7 19.1 6/20 19.2 2 19.3 2 19.4 3/13 20.1 0.14 20.2 0.0006 20.3 0.135 20.4 0.03 21.1 41.11 21.2 70.44 21.3 18.09 21.4 18.95 22.1 15.28 22.2 22.37 22.3 0.9163 22.4 0.00011 23.1 46.9 23.2 368.2 23.3 43.724 23.4 48.67 24.1 0.641

CXLVIII

24.2 0.00253 24.3 1.514 24.4 1.03 Sl. No.

Answer Sl. No.

Answer Sl. No.

Answer

25.1 7500 25.2 24000 25.3 3250 25.4 15000 26.1 12000 ml 26.2 3000 ml 26.3 1600 ml 26.4 28000 ml 27.1 36000 gm 27.2 25700 gm 27.3 8000 gm 27.4 7500 gm 28.1 5 28.2 8 28.3 11 28.4 8 29.1 75% 29.2 62.5% 29.3 31.25% 29.4 70% 30.1 6 30.2 3 30.3 24 30.4 150 31.1 1:5 31.2 1:4 31.3 1:4 31.4 5:7 32.1 7 hours 32.2 5 hours 32.3 8 hours 32.4 3 hours 33.1 Straight angle 33.2 Triangle 33.3 Ray 33.4 Rectangle 34.1

34.2

34.3

34.4

35.1 Acute angle 35.2 Obtuse angle

35.3 Right angle 35.4 Straight angle 36.1 7743 36.2 67736 36.3 29100 36.4 850 36.5 144 36.6 47 36.7 240 36.8 5:4

CXLIX

ANNEXURE XVI

THE MEMORIES OF RESEARCH

CL

CONDUCTION OF TEST FOR PRIMARY SCHOOL TEACHERS

CONDUCTION OF TEST FOR V STANDARD STUDENTS

CLII

CLASSROOM TEACHING

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