KhanAcademy

• 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 KhanAcademy 數學內容，作為學習英文的另一種途徑。本站用 Quizlet 幫助學生自主學習英文單字和單句，並且用 Kahoot 的趣味競賽或合作方式幫助學生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 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 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 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。

Khan Academy 的數學內容的結構和結構的名稱

• 主題(subject)：例如： Trigonometry
  • 條目：例如：Trigonometry with right triangles
    • 單元：例如：Introduction to the trigonometric ratios
      • 影片/文件：例如：Hypotenuse, opposite, and adjacent
      • 測驗：例如：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)：High school math
  • 主題(subject)：例如： Trigonometry
    • 條目：例如：Trigonometry with right triangles
      • 單元：例如：Introduction to the trigonometric ratios
        • 影片/文件：例如：Hypotenuse, opposite, and adjacent
        • 測驗：例如：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

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

Teens

• Learn
  • Teens as sums with 10
  • Teen numbers: monkeys
• Practice
  • Teen numbers

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

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

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

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

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

Geometry foundations

• Intro to Euclidean geometry
• Angles
• Polygons

Transformations

• Introduction to rigid transformations
• Translations
• Rotations
• Reflections
• Rigid transformations overview
• Dilations
• Properties & definitions of transformations
• Symmetry

Congruence

• Transformations & congruence
• Triangle congruence
• Theorems concerning triangle properties
• Working with triangles
• Theorems concerning quadrilateral properties
• Proofs of general theorems that use triangle congruence
• Constructing bisectors of lines & angles

Similarity

• Definitions of similarity
• Introduction to triangle similarity
• Solving similar triangles
• Angle bisector theorem
• Solving problems with similar & congruent triangles
• Solving modeling problems with similar & cong

Right triangles & trigonometry

• Pythagorean theorem
• Pythagorean theorem proofs
• Special 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 & similarity
• Sine & cosine of complementary angles
• Law of sines
• Law of cosines
• Solving general triangles

Solid geometry

• Solid geometry intro
• Density
• 2D vs. 3D objects

Analytic geometry

• Distance and midpoints
• Dividing line segments
• Problem solving with distance on the coordinate plane
• Parallel & perpendicular lines on the coordinate plane
• Equations of parallel & perpendicular lines

Circles

• Circle basics
• Arc measure
• Arc length (degrees)
• Introduction to radians
• Arc length (radians)
• Sectors
• Inscribed angles
• Inscribed shapes problem solving
• Properties of tangents
• Standard equation of a circle
• Expanded equation of a circle
• Constructing regular polygons inscribed in circles
• Constructing circumcircles & incircles
• Constructing a line tangent to a circle

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

Trigonometry

• 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

Conic sections

• Introduction to conic sections
• The features of a circle
• Standard equation of a circle
• Expanded equation of a circle
• Center and radii of an ellipse
• Foci of an ellipse
• Focus and directrix of a parabola
• Introduction to hyperbolas
• Foci of a hyperbola
• Hyperbolas not centered at the origin
• Identifying conic sections from their expanded equations
• Challenging conic section problems (IIT JEE)

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