Book

Mathematics for Children

272 pages · 7 chapters

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Chapter 1

Natural numbers

18 pages

  1. Elementary I (1st to 5th year)
    1. Introduction
    2. The number zero
    3. Sum
    4. Subtraction
    5. Multiplication
    6. Division
    7. Even and odd numbers
    8. Introduction to Geometry
    9. Quadrilateral
  2. Elementary II (6th to 9th year)
    1. Prime numbers
    2. Greatest Common Divisor
    3. Least Common Multiple
    4. Geometry with sequences of numbers
    5. Triangles
  3. High School
    1. Introduction to Arithmetic Progression
    2. Arithmetic Progression
  4. Solved exercises (all levels)
    1. Natural Number Subtraction Exercises
    2. Exercises for Adding Natural Numbers

Chapter 2

Whole Numbers

13 pages

  1. Elementary I (1st to 5th year)
    1. Above and below zero
    2. Measure
  2. Elementary II (6th to 9th year)
    1. Introduction to Integers
    2. Straight and operations
    3. Signal rule
    4. Potentiation of integers
    5. Angles and Geometry
      1. Angles in basic planes
      2. Property of Angles in Planes
  3. High School (1st to 3rd grade)
    1. Pascal's triangle
    2. Function Basics
      1. Function Discovery
      2. Cartesian Plane
      3. Classification in mathematics
      4. Graphs for integers

Chapter 3

Rational Numbers

15 pages

  1. Elementary I (1st to 5th year)
    1. Equal parts and fractions
    2. Decimals in everyday life
  2. Elementary II (6th to 9th year)
    1. Introduction to Rational Numbers
    2. Operations with Rational Numbers
    3. Percentage Basics
    4. Proportions
    5. Rule of 3
    6. Fees
    7. Quantity Analysis
    8. Proportions and Geometry
    9. Algebraic Expressions
    10. First Degree Equations
  3. High School (1st to 3rd grade)
    1. Power with Negative Exponent
    2. Nth Root
    3. Models and restrictions

Chapter 4

Irrational Numbers

17 pages

  1. Elementary I (1st to 5th year)
    1. Measure and discover
  2. Elementary II (6th to 9th year)
    1. Operation with Radicals
      1. Introduction to Irrational Numbers
      2. Introduction to Radiciation
    2. Approaches on the straight
    3. Geometry - Irrational Numbers
      1. Circumferences
      2. Pi Number
      3. Circle Area
      4. Angles and Circumferences
      5. Triangles and Circles
      6. Pythagorean Suits
  3. High School (1st to 3rd grade)
    1. Arguments and operations
    2. Logarithm
      1. Introduction to Logarithm Table
      2. Logarithm Properties
    3. Rectangle Triangles
    4. Basic Finance
      1. Increases and Discounts
      2. Simple Interest
      3. Compound interest and Euler's number

Chapter 5

Real Numbers

27 pages

  1. Elementary I (1st to 5th year)
    1. Measures between integers
    2. Everyday data
  2. Elementary II (6th to 9th year)
    1. Introduction to Real Numbers
    2. Rational, irrational and approximations
    3. Inequalities of real numbers
    4. 2° degree equation
    5. Bhaskara
    6. Notions of Probability
      1. Introduction to Probability
      2. Fundamentals
      3. Equiprobable Events
  3. High School (1st to 3rd grade)
    1. Notions of Sets
      1. Introduction to Sets
      2. Equivalence between Sets
      3. Venn-Euler Diagrams
      4. Diagram Operations
    2. Intervals and infinity
      1. Notion of Infinity
      2. Ranges in real numbers
      3. Interval Operations
    3. Functions
      1. Introduction to Function Theory
      2. Understanding Relationships
      3. Correspondence law
      4. Function Concept
      5. First Degree Functions
      6. Domain and Image
    4. Statistics Notions
      1. Introduction to Statistics
      2. Basic Concepts of Statistics
      3. Descriptive Statistics
        1. Position Measurements
        2. Dispersion Measures

Chapter 6

Plane Geometry

88 pages

  1. Elementary I (1st to 5th year)
    1. Flat shapes
    2. Lines, parallel and perpendicular
    3. Angles: turns and corners
    4. Polygons
    5. Symmetry
    6. Perimeter and area in the mesh
    7. Enlargement and reduction
  2. Elementary II (6th to 9th year)
    1. 1. Primitive notions and propositions
      1. A little history
      2. I. Primitive notions
      3. II. Primitive propositions
      4. III. Competing straights
      5. Exercises
    2. 2. straight segment
      1. I. The notion of "being between"
      2. II. Segment and ray
      3. III. Positions of two segments
      4. IV. Segment congruence
      5. V. Midpoint
      6. VI. Measurement of a segment
      7. VII. Distance between two points
      8. Segments and straight lines in everyday life
      9. Exercises
    3. 3. Angles
      1. I. Introduction: convexity and half-planes
      2. II. Angle: definitions
      3. III. Congruence and comparison
      4. IV. Right, acute and obtuse angles — measurement
      5. Exercises
    4. 4. Triangles
      1. I. Concept, elements and classification
      2. II. Congruence of triangles
      3. III. Inequalities in triangles
      4. Exercises
      5. Reading: Euclid and deductive geometry
    5. 5. Parallelism
      1. I. Parallel lines
      2. II. Existence and uniqueness of parallel
      3. III. Consequences in the triangle
      4. Exercises
      5. Reading: The fifth postulate
    6. 6. Perpendicularity
      1. I. Definitions — right angle
      2. II. Existence and uniqueness of the perpendicular
      3. III. Projections and distance
      4. Exercises
    7. Constructions with ruler and compass
    8. 7. Notable quadrilaterals
      1. I. Quadrilateral — definition and elements
      2. II. Notable quadrilaterals — definitions
      3. III. Properties of trapezoids
      4. IV. Properties of parallelograms
      5. V. Rectangle, rhombus and square
      6. VI. Consequences — medium bases
      7. Exercises
    9. 9. Polygons
      1. I. Definitions and elements
      2. II. Diagonals, interior angles and exterior angles
      3. Exercises
    10. Areas of flat figures
    11. 10. Circumference and circle
      1. I. Definitions and elements
      2. II. Relative positions of straight line and circle
      3. III. Relative positions of two circles
      4. IV. Tangent segments — circumscribable quadrilaterals
      5. Exercises
    12. Circumference length
    13. Pythagoras Theorem
  3. High School
    1. 8. Notable points of the triangle
      1. I. centroid — medians
      2. II. incenter — angle bisectors internal
      3. III. circumcenter — perpendicular bisectors
      4. IV. orthocenter — heights
      5. Exercises
      6. Reading: Papus: the epilogue of Greek geometry
    2. 11. Angles on the circumference
      1. I. Congruence, addition and inequality of arcs
      2. II. Central angle
      3. III. Inscribed angle
      4. IV. Segment angle (semi-inscribed)
      5. V. Eccentric angles
      6. Exercises
    3. 12. Thales' theorem
      1. I. Thales' Theorem
      2. II. angle bisectors Theorems
      3. Exercises
      4. Reading: Legendre: towards a rigorous and didactic geometry
    4. 13. Similarity of triangles and power of point
      1. I. Similarity of triangles
      2. II. Cases (criteria) of similarity
      3. III. Point power
      4. Exercises
    5. 14. Right triangles
      1. I. Metric relationships
      2. II. Applications of the Pythagorean theorem
      3. Exercises
    6. 15. Any triangles
      1. I. Sines theorem
      2. II. Metric relations and cosine theorem
      3. III. Calculation of notable lines
      4. Exercises
    7. Regular Polygons
    8. Circumference ratio in regular polygons

Chapter 7

Trigonometry

94 pages

  1. Elementary I (1st to 5th year)
    1. 01. Whole turns, half turns and quarters
    2. 02. Corners, spokes and paths on the wheel
    3. 03. Triangles that grow without changing shape
    4. 12. Triangulation in the field
  2. Elementary II (6th to 9th year)
    1. 01. Arcs, chords, rays and angles
    2. 02. Measurement of angles in degrees, minutes and seconds
    3. 03. Inscribed polygons and the sine of a central half-angle
    4. 04. Demonstrations of the values ​​of 30, 45 and 60 degrees
    5. 05. Pythagoras, height and projections in the right triangle
    6. 06. Trigonometric ratios and solving right triangles
    7. I. Arcs and angles
      1. I. Arcs and measurements
      2. II. Angles and their measurements
      3. III. Trigonometric cycle
      4. Exercises
      5. Reading: Bolzano
    8. V. Notable arcs
      1. I. Theorem and applications
      2. Exercises
    9. IX. Right triangles
      1. I. Metric elements and relationships
      2. II. Trigonometric ratios
      3. III. Solving right-angled triangles
      4. Exercises
    10. 01. Arcs and angles
    11. 05. Notable angles
    12. 09. Right triangles
  3. High School
    1. 01. Radians, arc length and trigonometric cycle
    2. 02. Circular functions and periodicity
    3. 03. Sine function: definition, signs and graph
    4. 04. Cosine function: horizontal coordinate and graph
    5. 05. Tangent function: slope, domain and graph
    6. 06. Cotangent, secant and cosecant
    7. 07. Fundamental relationships demonstrated
    8. 08. Identities and three demonstration paths
    9. 09. Reduction of the second, third and fourth quadrants
    10. 10. Complements, reduction identities, and parity
    11. 11. Arc addition and subtraction formulas
    12. 12. Sine, cosine and tangent of double and triple arc
    13. 13. Arc half division and tangent formulas
    14. 14. Transform sums into products and products into sums
    15. 15. Fundamental equations of sine, cosine and tangent
    16. 16. Intervals and classical trigonometric equations
    17. 17. Arcsine, arccosine and arctangent
    18. 18. Sine, cosine and tangent inequalities
    19. 19. Laws of sines, cosines, projections and areas
    20. 20. Heights, Heron, Medians, angle bisectors and Radii
    21. 21. Solving triangles and discussing the ambiguous case
    22. II. Circular functions
      1. I. General notions and periodicity
      2. II. Sine function
      3. III. Cosine function
      4. IV. Tangent function
      5. V. Cotangent, secant and cosecant
      6. Exercises
      7. Reading: Fourier
    23. III. Fundamental relationships
      1. I. Fundamental relationships
      2. II. Identities
      3. Exercises
    24. IV. Reduction to the 1st quadrant
      1. I. Reduction by quadrants
      2. II. Complementary arches and board
      3. III. Identities and parity
      4. Exercises
    25. VI. Transformations
      1. I. Addition formulas
      2. II. Multiplication, division and half arc
      3. III. Transformation into product
      4. Exercises
      5. Reading: Poncelet
    26. VII. Equations
      1. I. Fundamental equations
      2. II. Intervals and classical equations
      3. III. Inverse circular functions
      4. Exercises
      5. Reading: Euler
    27. VIII. Inequalities
      1. I. Sine inequalities
      2. II. Cosine inequalities
      3. III. Tangent inequalities
      4. Exercises
    28. X. Any triangles
      1. I. Laws of cosines and sines
      2. II. Projections, areas and law of tangents
      3. III. Heights, medians, angle bisectors and radii
      4. IV. Solving any triangles
      5. Exercises
    29. Entrance exams
      1. Circular functions
      2. Fundamental identities
      3. Transformations
      4. Equations
      5. Inverse functions
      6. Inequalities
      7. Triangles
    30. 02. Circular functions
    31. 03. Fundamental relationships
    32. 04. Symmetries
    33. 06. Transformations
    34. 07. Equations
    35. 08. Inequalities
    36. 10. Any triangles
    37. Final review
  4. Map of texts and formulas