Л.Н.Шеврин Математика 5-класс. 1989

Foreword

How to use the textbook

Grade 5. Chapter I. Natural numbers and operations on them

§1. Natural numbers

1. What are natural numbers?

2. Numerical expressions and numerical equalities

3. Beginning the study of properties of natural numbers

4. The order of natural numbers

5. How natural numbers are written

6. Why our numeral system is called decimal

7. Place values and classes in numeral notation

8. Comparing natural numbers

9. Numerical inequalities

10. Chains of equalities and inequalities

11. Review exercises for §1

§2. Operations on natural numbers

12. Addition

13. Problems solved by addition

14. Subtraction

15. Problems solved by subtraction

16. The special number 0

17. Multiplication

18. Problems solved by multiplication

19. Powers. Square and cube of a number

20. Why division is the inverse operation of multiplication

21. Dividing one number by another

22. Problems solved by division

23. Санның қасиеттері

24. Learning to reason in problem solving. When speeds are added and when they are subtracted

25. Review exercises for §2

§3. Numerical and algebraic expressions

26. How algebraic expressions arise in problem solving

27. When numbers must be represented by letters

28. Order of operations

29. What is a formula?

30. What is an equation?

31. Learning to reason in problem solving. What reasoning means

32. Review exercises for §3

§4. Properties of operations on natural numbers

33. Commutative and associative properties of addition

34. Properties involving addition and subtraction

35. Commutative and associative properties of multiplication

36. Properties involving multiplication and division

37. Distributive property of multiplication

38. How operation properties help with calculations

39. Using equations to solve mathematical riddles and perform mathematical tricks

40. Learning to reason in problem solving. How equations help solve problems

41. Review exercises for §4

§5. Divisibility of natural numbers

42. What the sequence of natural numbers resembles

43. Even and odd numbers

44. Multiples of a natural number

45. 2-ге, 5-ке және 10-ға бөлінгіштік белгілері

46. 9-ға және 3-ке бөлінгіштік белгілері

47. Playing mathematical games

48. Division with remainder

49. Learning to reason in problem solving. When division with remainder is useful

50. Review exercises for §5

Long break I. Roman numerals

Chapter II. Fractional numbers

§6. Fractions and operations on them

51. Dividing a unit into parts

52. How fractions are formed from parts

53. Fractions and whole natural numbers

54. Comparing fractions. Proper and improper fractions

55. Extracting the whole part from a fraction

56. Why the whole part of a fraction matters

57. Arithmetic mean of natural numbers

58. Addition and subtraction of fractions

59. Finding an improper fraction from its whole and fractional parts

60. Multiplying and dividing a fraction by a natural number

61. Fundamental property of fractions

62. Review exercises for §6

§7. Decimal fractions and operations on them

63. What is a decimal fraction?

64. When decimal fractions are equal

65. Comparing decimal fractions

66. Addition and subtraction

67. Онға және онның дәрежелеріне көбейту

68. Multiplication by a decimal fraction

69. Division by a natural number

70. Division by a decimal fraction

71. Practising operations with decimals

72. Learning to reason in problem solving. How to find the answer

73. Review exercises for §7

§8. Decimals in practical calculations

74. Approximate value of a number

75. Rounding natural numbers

76. Learning to round numbers quickly

77. How decimals arise in practical calculations

78. What is 1%?

79. Solving percentage problems

80. Learning to reason in problem solving. Sometimes patience is needed

81. Review exercises for §8

Long break II. A conversation about mathematical words

Chapter III. Measuring geometric quantities

§9. Geometric figures

82. What is studied about polygons

83. The sides of a rectangle. Perimeter formula

84. What measurement means. Comparing segments

85. Line and ray

86. Circle. Formula for circumference

87. Four types of angles

88. Types of triangles

89. Measuring angles

90. How degrees help compare angles

91. A circle is also divided into degrees

92. Review exercises for §9

§10. Measuring areas and volumes

93. Units of area. Formula for the area of a rectangle

94. Calculating areas of figures

95. Disk. Formula for the area of a disk

96. Pie charts

97. Introduction to the rectangular parallelepiped

98. Units of volume

99. Formula for the volume of a rectangular parallelepiped

100. Review exercises for §10

answers