"KhanAcademy" 修訂間的差異

於 2018年9月5日 (三) 07:02 的修訂

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。

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

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

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

@@ 行 573： / 行 573： @@
 * 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
+====////====
 ===Precalculus===