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Outline of math knowledge for kids

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<2020-10-28 Wed>

This page will not be updated any more. The reason is that I found my kid learns too quickly, and I must see him as a fellow but not a kid any more. Now we follow the "Mathematics Trench" outline to learn. You can search it on Google if you are interested.

My 5 years old kid, Josh, likes math pretty much, he always actively askes me to teach him math knowledge from when he was three. So I picked some topics I thought which are suitable for him as listed below. It turns out he enjoys them very much, if your kid likes math as well, this list may give you a roadmap for reference.

[D] Numbers

  • Integer, Fraction, Decimal, Per cent
  • Odd, Even
  • Prime, Composite
  • Positive, Negative, Zero
  • Rational, Irrational
  • Real, Imaginary, Complex

[D] Calculations

  • Addition, Subtraction, Multiplication, Division
  • Power, Extracting, Logarithm
  • Reciprocal, Absolute Value, Opposite
  • GCD (greatest common divisor), LCM (least common multiple)
  • Modulo
  • Decomposition of prime factors
  • Factorial
  • Law of commutation, Law of association, Law of distribution
  • Precedence and parenthesis

[D] Sequences

  • Arithmetic Sequences
  • Geometric Sequences
  • Fibonacci Sequence

[D] Permutations and Combinations

  • Permutations
  • Combinations
  • Cartesian Product

[P] Algebra

  • [D] linear equation with one unknown
  • [D] linear equation with two unknowns
  • [D] quadratic equation
  • [D] binomials, binomials expansion
  • [D] polynomials
  • [P] factorization of polynomials
  • [D] functions

[P] Geometry

[D] Analytic Geometry

  • number axis
  • plane-coordinate system
  • space-coordinate system

[P] Linear Algebra

  • [D] Matrix
  • [P] Matrix Addition, Matrix Multiplication

[P] Trigonometric functions

  • [D] sine/cosine/tangent/cotangent
  • [P] Trigonometric functions on the unit circle


  • [D] means DONE, items with this indicator are well learned by my kid;
  • [P] means PARTIALLY DONE, I have taught my kid about these items, he understands the concepts, but can't apply them well;
  • [T] means TODO, I haven't taught my kid about the items marked with this indicator.
  • Last updated: 2020.12.14.

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Have few questions or feedback? Feel free to send me(killian.zhuo📧 an email!


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