50节免费课程，从学前到三角学
用你的方式学数学
面向儿童、青少年和成人的免费通俗数学课程——现已覆盖从数数到三角学的完整弧线。每节课都有自动评分的练习题和交互式图表。
按年级浏览
低年级 (K–2)
- 加减法
- 位值
- 从数数到乘法
- 乘法表与除法
- 分数与小数
- 周长与面积
- 因数与质数
- 负数与运算顺序
- 变量与方程
- 比与百分比
- 角、三角形与圆
- 统计基础
- 图像、方程组与二次方程
- 多项式与因式分解
- 勾股定理与三角学
- 概率与计数
- 双向口算
- 估算与应用题
- 二进制、浮点与模运算
算术 — 两个方向
Addition — carry right
The classic column method: ones first, carry to the left.
Addition — biggest first
Left-to-right addition: hundreds, then tens, then ones.
Subtraction — borrow right
The standard borrowing method, step by step.
Subtraction — left to right
Count down by chunks, or biggest column first.
Multiplication — standard way
Right-to-left multiplying with carrying.
Multiplication — biggest first
Partial products left to right — the mental-math way.
Division
Long division, short division, and chunking.
代数
Variables & expressions
Letters that hold numbers — evaluate and translate.
One-step equations
Undo one thing: the balance rule that starts algebra.
Two-step equations
Undo in reverse order — with step-by-step checking.
Inequalities
<, >, ≤, ≥ — and the one rule that flips the sign.
Exponents & powers
Repeated multiplication, the three rules, x⁰ and x⁻ⁿ.
Square roots
Perfect squares, estimating, and simplifying √12.
Polynomials
Terms, degrees, like terms, and distributing.
Factoring
GCF, x²+bx+c, and difference of squares.
Graphing lines
y = mx + b — slope and intercept on the plane.
Systems of equations
Substitution, elimination, and where lines meet.
Quadratic equations
Parabolas, zero-product, and the formula that always works.
几何
Angles & lines
Acute to straight, complements, parallel lines.
Triangles
The 180° rule, families, and why bridges trust them.
Quadrilaterals
The four-sided family tree and the 360° rule.
Circles
Radius, diameter, π — C = πd and A = πr².
Perimeter & area
Around vs inside — with unit-square grids.
Surface area & volume
Wrapping vs filling — boxes, cylinders, unit³.
The coordinate plane
(x, y) addresses, quadrants, distance.
Transformations
Slide, flip, spin, scale on the grid.
Pythagorean theorem
a² + b² = c², triples, and the distance formula.
Similarity & congruence
Same shape, different size — scale factors.
数与结构
Place value & bases
Why 467 means 400 + 60 + 7 — and how binary works.
Fractions
What numerator & denominator mean, adding, comparing.
Decimals & percents
Place value past the point; everyday percent tricks.
Negative numbers
The number line, and why neg×neg = pos.
Order of operations
PEMDAS honestly — including the ambiguous case.
Factors & primes
Divisibility tricks and prime factorization.
比、数据与概率
Ratios & proportions
Comparing quantities and cross-multiplying.
Unit rates & percents
Per hour, per dollar — and the better-deal test.
Statistics basics
Mean, median, mode, range — and when the mean lies.
Spread & deviation
Variance and standard deviation as 'typical distance.'
Probability basics
0 to 1 — favorable/total, complements, AND/OR rules.
Counting principles
Permutations, combinations, factorials.
三角学
sin, cos, tan
SOH-CAH-TOA on right triangles — sides and angles.
The unit circle
(cos, sin) as a point — and the free identity.
思维能力
Estimation & rounding
Front-end estimating and Fermi problems.
Word problems
Pólya's four-step method for attacking any problem.
Data, averages & graphs
Mean vs median — and how charts can politely lie.
科学与计算中的数学
Scientific notation & SI
Writing the universe's biggest and smallest numbers.
Measurement & error
Accuracy vs precision, significant figures, honest numbers.
Math inside computers
Binary, bits, floating point — and 0.1 + 0.2 ≠ 0.3.
Binary & hexadecimal
How computers count — $FF and 0x10 explained.
Floating point
Why 0.1 + 0.2 ≠ 0.3 — and the integer-cents trick.
Modular arithmetic
Clock math — MOD, parity tests, wrap-around indexing.
两个方向，同一个答案
大多数课本只教从右到左的方法。但熟练的心算者往往相反：先算最大位。没有优劣——只是从不同方向看同一算术。
为什么教两种方法？
研究表明，孩子们自创的从左到右策略很常见，并能加深对位值的理解。 →