Н.Я.Виленкин, К.И.Нешков Математика 5-класс, 1971

1.1. Distance formula

1.2. Percentage formula

2.1. Moving right or left, up or down

2.2. Number line

2.3. Coordinate of a point on a line

2.4. Opposite numbers

2.5. Subset

2.6. Absolute value of a number

2.7. Comparing numbers

2.8. Coordinate plane

3.1. How quantities change

3.2. Addition of positive numbers

3.3. Addition of negative numbers

3.4. Addition of numbers with different signs

3.5. Laws of addition

4.1. Subtraction rule

4.2. Expanding and introducing parentheses

4.3. Solving equations

5.1. Multiplication rules

5.2. Commutative and associative laws of multiplication

5.3. Coefficient

5.4. Distributive law of multiplication

5.5. Factoring out a common factor

5.6. Combining like terms

5.7. Raising a number to a power

6.1. Division rules

6.2. Solving equations

6.3. Solving problems using equations

7.1. Bar charts

7.2. Graphs

8.1. Divisor

8.2. Common divisor. Intersection and union of sets

8.3. Greatest common divisor. Coprime numbers

8.4. Multiple

8.5. Formula for a multiple of a given number

8.6. Common multiple. Least common multiple

9.1. Divisibility of a sum

9.2. Divisibility of a product

9.3. 2-ге және 5-ке бөлінгіштік белгілері

9.4. 3-ке бөлінгіштік белгісі

10.1. Prime and composite numbers

10.2. How to factor a number into prime factors

10.3. Finding the greatest common divisor using prime factorization

10.4. Finding the least common multiple using prime factorization

11.1. Representing fractions

11.2. Comparing fractions with like denominators

11.3. Addition and subtraction of fractions

11.4. Addition and subtraction of mixed numbers

12.1. Reducing fractions

12.2. Converting fractions to a new denominator

12.3. Converting fractions to a common denominator

12.4. Addition and subtraction of fractions with unlike denominators

12.5. Addition and subtraction of mixed numbers

12.6. Regrouping one whole as a fraction in subtraction

13.1. Multiplying a fraction by a fraction

13.2. Writing a mixed number as an improper fraction. Multiplying mixed numbers

13.3. Reciprocal numbers

13.4. Division of fractions

13.5. Multiplying a mixed number by a natural number

13.6. Finding a fraction of a number and a number from its fraction

13.7. Solving problems

14.1. Writing a common fraction as a decimal

14.2. Infinite decimals

14.3. Addition and subtraction

14.4. Multiplication and division

14.5. Expression written as a fraction

15.1. Area of a triangle

15.2. Circumference of a circle

15.3. Area of a circle

16.1. Tools for geometric constructions

16.2. Relative position of a line and a circle

16.3. Constructing congruent figures

16.4. Sum of the angles of a triangle

16.5. Parallel lines

16.6. Translation of a figure

17.1. Figures symmetric with respect to a line

17.2. Constructing the axis of symmetry of two points

17.3. Dividing a line segment into two equal parts

17.4. Constructing a perpendicular to a line

17.5. Bisecting an angle

17.6. Figures with an axis of symmetry

18.1. Isosceles and equilateral triangles

18.2. Constructing a triangle from three sides

18.3. Constructing a triangle from one side and its two adjacent angles

18.4. Constructing a triangle from two sides and the included angle

18.5. Rotating a figure about a point

From the history of arithmetic and algebra

Advanced problems

Қосымша. Жай сандар кестесі (997-ге дейін)