"KhanAcademy" 修訂間的差異

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*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。
 
*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。
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*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,2,3年級的數學課中早已熟悉，且幾乎天天在數學學習的環境中不斷使用。
+
*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。
 
*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。
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*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 [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。
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*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，重複應用所學到的英文來答題，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。
+
*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，讓學生感受到所學到的英文可以立刻學以致用，以利觸發並支持學習英文的動機。
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*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。
 
*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__
 
__TOC__
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==單字練習==
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== 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===
 
===Kindergarten===
 
====Counting and place value====
 
====Counting and place value====
行 121： 行 139：
 
=====Quiz 2=====
 
=====Quiz 2=====
 
=====Unit test=====
 
=====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===
 +
====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)
 +
====////====
 +
 +
===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

於 2018年9月5日 (三) 07:52 的最新修訂

  • 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。

目錄

Khan Academy 的數學內容的結構和結構的名稱

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

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)

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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
取自 "http://www.limingyu2007.com/index.php?title=KhanAcademy&oldid=9863"