檢視 KhanAcademy 的原始碼

*本站提供一些英文輔助教材，主要是單字練習和單句練習，幫助台灣的小學4,5,6年級的學生更有效地使用英文版的 [https://www.khanacademy.org/math KhanAcademy 數學內容]，作為學習英文的另一種途徑。本站用 [https://quizlet.com/ Quizlet] 幫助學生[[自主學習]]英文單字和單句，並且用 [https://kahoot.com/ Kahoot] 的趣味競賽或合作方式幫助學生[[團隊學習|共學]]英文單字和單句。
*小學4,5,6年級的學生，用英文版的 KhanAcademy [https://www.khanacademy.org/math/cc-kindergarten-math 幼教和小學低年級的數學內容]來學習英文時，不會有數學及英文的雙重困難；因為那些數學觀念在學校的小學低年級的數學課中早已熟悉，或中高年級正在學習，且幾乎天天在數學學習的環境中不斷使用。
*這些簡單又每天都繼續在學習中使用的數學觀念，成為英文初學者入門學習英文的大好基礎和機會。
*當學生日復一日地熟悉本站所提供的輔助教材時，就可以漸近地理解英文版 [https://www.khanacademy.org/math/cc-kindergarten-math/cc-kindergarten-counting/modal/v/counting-with-small-numbers KhanAcademy 的教學影片]所要教導的數學觀念的英文表達方式。
*接下來，學生從做英文版的 [https://www.khanacademy.org/math/cc-kindergarten-math/cc-kindergarten-counting/modal/e/counting-out-1-20-objects KhanAcademy 練習題]的解題過程中，反覆應用所學到的英文來回答類似題型的許多題目，並且即時獲得電腦的回饋，立刻得知自己是否能够用英文來理解題意。
*這樣，讓學生能體驗到剛剛所學到的英文單字可以立刻學以致用解決問題，以利觸發並支持學習英文的動機和興趣。
*此外，藉著不斷的在解題中應用所學到的英文，在來達到深刻理解英文和長期記憶的效果。
__TOC__
== Khan Academy 的數學內容的結構和結構的名稱==
* 主題(subject)：例如： [https://www.khanacademy.org/math/trigonometry Trigonometry]
** 條目：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles Trigonometry with right triangles]
*** 單元：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles Introduction to the trigonometric ratios]
**** 影片/文件：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/a/opposite-adjacent-hypotenuse Hypotenuse, opposite, and adjacent]
**** 測驗：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/modal/e/trigonometry_1 Trigonometric ratios in right triangles]
* 1-8年級(grade)：例如： 
** 條目：例如：
*** 單元：例如：
**** 影片/文件：例如：
**** 測驗：例如：
* 9-12年級(High School)：[https://www.khanacademy.org/math/math-1-2-3 High school math]
** 主題(subject)：例如： [https://www.khanacademy.org/math/trigonometry Trigonometry]
*** 條目：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles Trigonometry with right triangles]
**** 單元：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles Introduction to the trigonometric ratios]
***** 影片/文件：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/a/opposite-adjacent-hypotenuse Hypotenuse, opposite, and adjacent]
***** 測驗：例如：[https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/modal/e/trigonometry_1 Trigonometric ratios in right triangles]

==單字的課程目錄==
===Kindergarten===
====Counting and place value====
=====Counting small numbers=====
*Learn
**Counting with small numbers
**Counting in order
*Practice
**Count with small numbers
**Count in order
**Find 1 more or 1 less than a number
=====Numbers 0 to 100=====
*Learn
**Number grid
**Missing numbers between 0 and 120
*Practice
**Missing numbers
**Numbers to 100
**Count tens
=====Counting objects=====
*Learn
**Counting in pictures
**Counting objects 1
**Counting objects 2
*Practice
**Count in pictures
**Count objects 1
**Count objects 2
=====Quiz 1=====
=====Comparing small numbers=====
*Learn
**Comparing numbers of objects
**Comparing numbers on the number line
**Counting by category
*Practice
**Compare numbers of objects 1
**Comparing numbers to 10
**Compare numbers of objects 2
=====Quiz 2=====
=====Teens=====
*Learn
**Teens as sums with 10
**Teen numbers: monkeys
*Practice
**Teen numbers
=====Unit test=====

====Addition and subtraction====
=====What is addition? What is subtraction?=====
*Learn
**Intro to addition
**Intro to subtraction
*Practice
**Add within 5
**Subtract within 5
=====Making 10=====
*Learn
**Getting to 10 by filling boxes
**Adding to 10
*Practice
**Make 10 (grids and number bonds)
**Make 10
=====Making small numbers=====
*Learn
**Making 5
*Practice
**Making 5
**Making small numbers in different ways
=====Quiz 1=====
=====Put together, take apart=====
*Learn
**Add and subtract: pieces of fruit
**Addition and subtraction within 10
*Practice
**Add within 10
**Subtract within 10
=====Addition and subtraction word problems=====
*Learn
**Addition word problems within 10
**Subtraction word problems within 10
*Practice
**Addition word problems within 10
**Subtraction word problems within 10
=====Quiz 2=====
=====Unit test=====

====Measurement and geometry====
=====Comparing size: Measurement and geometry=====
*Learn
**No videos or articles available in this lesson
*Practice
**Compare size
=====Basic shapes: Measurement and geometry=====
*Learn
**Cousin Fal's shape collection
**Recognizing shapes
*Practice
**Name shapes 1
**Name shapes 2
=====Quiz 1=====
=====Comparing shapes: Measurement and geometry=====
*Learn
**No videos or articles available in this lesson
*Practice
**Relative position
*Practice
**Compare shapes
=====Composing shapes=====
*Learn
**Composing shapes
*Practice
**Compose shapes
=====Quiz 2=====
=====Unit test=====
===Arithmetic===
====Addition and subtraction====
* Basic addition and subtraction
* Addition and subtraction within 20
* Strategies for adding and subtracting within 100
* Addition within 100
* Subtraction within 100
* Word problems within 100
* Multi-digit addition with regrouping
* Multi-digit subtraction with regrouping

====Multiplication and division====
* Multiplication intro
* Multiplication by 10s, 100s, and 1000s
* Multiplication: place value and area models
* Multi-digit multiplication 
* Division intro
* Division: place value and area
* Multi-digit division (no remainders)
* Remainders
* Multi-digit division (remainders)
* Multiplication and division word problems

====Negative numbers====
* Intro to negative numbers
* Order negative numbers
* Number opposites
* Absolute value
* Intro to adding negative numbers
* Intro to subtracting negative numbers
* Adding & subtracting negative numbers
* Multiplying & dividing negative numbers

====Fractions====
* Fractions intro
* Fractions on the number line
* Equivalent fractions
* Comparing fractions
* Common denominators
* Decomposing fractions
* Adding and subtracting fractions with like denominators
* Mixed numbers
* Adding and subtracting fractions with unlike denominators
* Adding and subtracting mixed number with unlike denominators
* Adding and subtracting fractions word problems
* Multiplying whole numbers and fractions
* Multiplication as scaling
* Multiplying fractions
* Multiplying mixed numbers
* Multiplying fractions word problems
* Fractions as division
* Dividing unit fractions and whole numbers
* Dividing fractions by fractions
* Dividing fractions word problems

====Decimals====
* Intro to decimals
* Decimals on the number line
* Rounding decimals
* Comparing decimals
* Rewriting decimals as fractions
* Adding decimals
* Subtracting decimals
* Adding and subtracting decimals word problems
* Multiplying decimals
* Dividing decimals

===Pre-algebra===
====Arithmetic properties====
* Place value: Arithmetic properties
* Rounding whole numbers: Arithmetic properties
* Regrouping whole numbers: Arithmetic properties
* Order of operations: Arithmetic properties
* Arithmetic properties: Arithmetic properties
* Distributive property: Arithmetic properties
* Rational and irrational numbers
====Factors and multiples====
* Divisibility tests: Factors and multiples
* Factors and multiples: Factors and multiples
* Prime numbers: Factors and multiples
* Prime factorization: Factors and multiples
* Least common multiple: Factors and multiples
* Greatest common factor
====Reading and interpreting data====
* Representing data: Reading and interpreting data
* Stem and leaf plots: Reading and interpreting data
* Picture graphs, bar graphs, and histograms: Reading and interpreting data
* Frequency tables and dot plots: Reading and interpreting data
* Number patterns
====Measurement====
* Area of rectangles: Measurement
* Perimeter: Measurement
* Volume of a rectangular prism
====Fractions====
* Fractions intro: Fractions
* Fractions on the number line: Fractions
* Equivalent fractions: Fractions
* Comparing fractions: Fractions
* Common denominators: Fractions
* Decomposing fractions: Fractions
* Adding and subtracting fractions with like denominators: Fractions
* Mixed numbers: Fractions
* Adding and subtracting fractions with unlike denominators: Fractions
* Adding and subtracting mixed number with unlike denominators: Fractions
* Adding and subtracting fractions word problems: Fractions
* Multiplying whole numbers and fractions: Fractions
* Multiplication as scaling: Fractions
* Multiplying fractions: Fractions
* Multiplying mixed numbers: Fractions
* Multiplying fractions word problems: Fractions
* Fractions as division: Fractions
* Dividing unit fractions and whole numbers: Fractions
* Dividing fractions by fractions: Fractions
* Dividing fractions word problems
====Decimals====
* Intro to decimals
* Decimals on the number line
* Rounding decimals
* Comparing decimals
* Rewriting decimals as fractions
* Adding decimals
* Subtracting decimal
* Adding and subtracting decimals word problems
* Multiplying decimals
* Dividing decimals

====Negative numbers and coordinate plane====
* Intro to negative numbers
* Order negative numbers
* Number opposites
* Absolute value
* Intro to adding negative numbers
* Intro to subtracting negative numbers
* Adding & subtracting negative numbers
* Multiplying & dividing negative numbers
* Coordinate plane

====Ratios, rates, proportions====
* Intro to ratios
* Visualize ratios
* Ratio application
* Intro to rates
* Intro to percents
* Percent, fraction, decimal conversions
* Percent problems
* Percent word problems
* Constant of proportionality 
* Identifying proportional relationships
* Writing & solving proportions

====Equations, expressions, and inequalities====
* Intro to variables
* Substitution & evaluating expressions
* Expression value intuition
* Constructing numeric expressions
* Evaluating expressions word problems
* Writing algebraic expressions introduction
* Writing basic algebraic expressions word problems
* Algebraic equations basics
* One-step equations intuition
* One-step addition & subtraction equations
* One-step multiplication and division equations
* One-step equation word problems
* Inequalities: Greater than and less than basics
* Two-step equations intro
* Dependent and independent variables
====Exponents, radicals, and scientific notation====
* Exponents
* Square roots
* Cube roots
* Exponent properties
* Negative exponents
* Scientific notation
* Orders of magnitude
* Computing with scientific notation

===Algebra 1===
====Algebra foundations====
* Overview and history of algebra
* Introduction to variables
* Substitution and evaluating expressions
* Evaluating expressions word problems
* Writing algebraic expressions introduction
* Dependent & independent variables
* Combining like terms
* Introduction to equivalent algebraic expressions
* Interpreting linear expressions
* Division by zero

====Solving equations====
* Algebraic equations basics
* Why we do the same thing to both sides of an equation
* One-step addition & subtraction equations
* One-step multiplication & division equations
* Two-steps equations intro
* Two-step equation word problems
* Linear equations with variables on both sides
* Linear equations with parentheses
* Analyzing the number of solutions to linear equations
* Linear equations word problems
* Linear equations with unknown coefficients

====Solving inequalities====
* Introduction to inequalities with variables
* One-step inequalities
* Two-step inequalities
* Multi-step inequalities
* Compound inequalities

====Working with units====
* Rate conversion
* Appropriate units
* Word problems with multiple units 
====Linear equations & graphs====
* Two-variable linear equations intro
* x-intercepts and y-intercepts
* Slope
* Horizontal & vertical lines
* Intro to slope-intercept form
* Graphing slope-intercept equations
* Writing slope-intercept equations
* Point-slope form
* Standard form
* Summary: Forms of two-variable linear equations
====Functions====
* Evaluating functions
* Inputs and outputs of a function
* Functions and equations
* Interpreting function notation
* Introduction to the domain and range of a function
* Determining the domain of a function
* Recognizing functions
* Maximum and minimum points
* Intervals where a function is positive, negative, increasing, or decreasing
* Interpreting features of graphs
* Average rate of change
* Average rate of change word problems

====Linear word problems====
* Interpreting linear functions and equations
* Comparing linear functions
* Constructing linear models for real-world relationships
* Linear models word problems
====Sequences====
* Introduction to arithmetic sequences
* Constructing arithmetic sequences
* Introduction to geometric sequences
* Constructing geometric sequences
* Modeling with sequences
* General sequences

====Systems of equations====
* Introduction to systems of equations
* Equivalent systems of equations and the elimination method
* Solving systems of equations with substitution
* Manipulating expressions with unknown variables
* Number of solutions to systems of equations
* Solving any system of linear equations
* Systems of equations word problems
====Inequalities (systems & graphs)====
* Checking solutions of two-variable inequalities
* Graphing two-variable inequalities
* Modeling with linear inequalities
====Absolute value & piecewise functions====
* Graphs of absolute value functions
* Piecewise functions
====Rational exponents & radicals====
* Exponent properties review
* Radicals
* Rational exponents intro
* Properties of exponents (rational exponents)
* Advanced exponent & radical evaluation
* Simplifying square roots
* Simplifying radicals (higher-index roots)
====Exponential growth & decay====
* Exponential vs. linear growth
* Exponential expressions
* Graphs of exponential growth
* Exponential vs. linear growth over time
* Exponential decay
* Exponential functions from tables & graphs

====Polynomials====
* Intro to polynomials
* Adding & subtracting polynomials
* Adding and subtracting polynomials: two variables
* Multiplying monomials
* Multiplying monomials by polynomials
* Multiplying binomials
* Multiplying binomials by polynomials
* Special products of binomials
* Polynomials word problems
====Factorization====
* Introduction to factorization
* Factoring monomials
* Factoring polynomials by taking common factors
* Evaluating expressions with unknown variables
* Factoring quadratics intro
* Factoring quadratics by grouping
* Factoring polynomials with quadratic forms
* Factoring quadratics: Difference of squares
* Factoring quadratics: Perfect squares
* Strategy in factoring quadratics
* Factoring polynomials with special product 
====Quadratics====
* Parabolas intro
* Quadratic factored form
* Solving quadratics by taking square roots
* Quadratic vertex form
* Solving quadratics by factoring
* Completing the square
* The quadratic formula
* Quadratic standard form
* Features & forms of quadratic functions
* Transforming parabolas
====Irrational numbers====
* Irrational numbers
* Sums and products of rational and irrational numbers
* Proofs concerning irrational numbers

===Geometry===
====Transformations====
* Introduction to rigid transformations
* Translations
* Rotations
* Reflections
* Rigid transformations overview
* Dilations
* Properties & definitions of transformations
* Symmetry
====////====

===Algebra 2===

====Functions====
* Combining functions
* Composing functions
* Modeling situations by combining and composing functions
* Shifting functions
* Stretching functions
* Introduction to inverses of functions
* Finding inverse functions
* Verifying that functions are inverses
* Determining whether a function is invertible
====Complex numbers====
* What are the imaginary numbers?
* What are the complex numbers?
* The complex plane
* Adding and subtracting complex numbers
* Multiplying complex numbers
====Arithmetic with polynomials====
* Adding and subtracting polynomials
* Multiplying polynomials
* Long division of polynomials
* Synthetic division of polynomials
* Practice dividing polynomials with remainders
* Polynomial Remainder Theorem
====Polynomials====
* The binomial theorem
* Understanding the binomial theorem
* Factoring polynomials - Quadratic forms
* Factoring polynomials - Special product forms
* Advanced polynomial factorization methods
* Proving polynomial identities
* Polynomial identities with complex numbers
* Quadratic equations with complex numbers
* The Fundamental Theorem of Algebra
* Finding zeros of polynomials
* Zeros of polynomials and their graphs
* End behavior of polynomial functions
* Graphs of polynomials
* Introduction to symmetry of functions
* Symmetry of polynomial functions
====Radical relationships====
* Solving square-root equations
* Extraneous solutions of radical equations
* Solving cube-root equations
* Domain of radical functions
* Graphs of radical functions
====Rational relationships====
* Simplifying rational expressions
* Multiplying & dividing rational expressions
* Adding & subtracting rational expressions
* Nested fractions
* Solving rational equations
* Direct and inverse variation
* End behavior of rational functions
* Discontinuities of rational functions
* Graphs of rational functions
* Modeling with rational functions
====Exponential growth & decay====
* Equivalent forms of exponential expressions
* Solving exponential equations using properties of exponents
* Interpreting the rate of change of exponential models
* Constructing exponential models according to rate of change
* Advanced interpretation of exponential models
* Distinguishing between linear and exponential growth
====Exponentials & logarithms====
* Introduction to logarithms
* The constant e and the natural logarithm
* Properties of logarithms
* The change of base formula for logarithms
* Solving exponential equations with logarithms
* Solving exponential models
* Graphs of exponential functions
* Graphs of logarithmic functions
* Logarithmic scale (optional)
====Trigonometry====
* Introduction to radians
* The unit circle definition of sine, cosine, and tangent
* The graphs of sine, cosine, and tangent
* Basic trigonometric identities
* Trigonometric values of special angles
* The Pythagorean identity
* Introduction to amplitude, midline, and extrema of sinusoidal functions
* Finding amplitude and midline of sinusoidal functions from their formulas
* Period of sinusoidal functions
* Graphing sinusoidal functions
* Constructing sinusoidal functions
====Advanced equations & functions====
* Solving equations by graphing
* Systems of quadratic equations
* Interpreting the symmetry of algebraic models
* Interpreting the end behavior of algebraic models
* Interpreting the periodicity of algebraic models
* Comparing features of functions

====Series====
* Arithmetic sequences
* Basic sigma notation
* Finite arithmetic series
* Geometric sequences
* Finite geometric series
* Finite geometric series applications

====Modeling====
* Modeling with one-variable equations and inequalities
* Manipulating formulas
====Conic sections====
* Introduction to conic sections
* The features of a circle
* Standard equation of a circle
* Expanded equation of a circle
* Focus and directrix of a parabola
===Trigonometry===
====Trigonometry with right triangles====
* Introduction to the trigonometric ratios
* Solving for a side in a right triangle using the trigonometric ratios
* Solving for an angle in a right triangle using the trigonometric ratios
* Modeling with right triangles
* Trigonometric ratios and similarity
* Sine and cosine of complementary angles
* Trigonometric ratios of special triangles
* Introduction to the Pythagorean trigonometric identity
* The reciprocal trigonometric ratios
====Trigonometry with general triangles====
* The law of sines
* The law of cosines
* Solving general triangles
====The unit circle definition of sine, cosine, and tangent====
* Introduction to radians
* The unit circle definition of sine, cosine, and tangent
* The graphs of sine, cosine, and tangent
* Basic trigonometric identities
* Trigonometric values of special angles
* The Pythagorean identity
* Long live Tau
====Graphs of trigonometric functions====
* The graphs of sine, cosine, and tangent
* Introduction to amplitude, midline, and extrema of sinusoidal functions
* Finding amplitude and midline of sinusoidal functions from their formulas
* Period of sinusoidal functions
* Graphing sinusoidal functions
* Constructing sinusoidal functions
====Trigonometric equations and identities====
* The inverse trigonometric functions
* Solving basic sinusoidal equations
* Solving advanced sinusoidal equations
* Solving sinusoidal models
* Introduction to the trigonometric angle addition identities
* Using trigonometric identities to solve problems
* Challenging trigonometry problems
===Precalculus===
===Statistics and probability===
===AP Calculus AB===
===AP Calculus BC===
===Multivariable calculus===
===Differential equations===
===Linear Algebra===
==[[小學雙語數學]]==
* 和均一教育平台小學數學的內容和進度配合