수학 1:1 개인 튜터링

Learners are welcome to share their work/homework from other Mathematics classes that they may be taking, either at a regular school or in another online program if they require help with it so that Pamela can explain it to them in another way that helps them to understand what is required to complete said task.

The content being taught each week will be learner-driven.

In the places around the world where I have had experience with homeschooling, the average amount of hours required where there are stipulated requirements is approximately 800 hours per year. This is usually recommended to be divided up over 180 days, which equates to approximately 4 to 5 hours per day. However, there are 365 usable days per year, which equates to just 2.5 hours per day. Personally, we aim for 2.5 hours per day of structured learning, and at least 1 hour per day of unstructured learning over 6 days per week. This equates to 15 hours of structured learning per week.

This course on Outschool provides 60 minutes towards this weekly total of structured learning, and completing related tasks outside of this course for this course should equate to approximately the same amount of hours again, providing that learners follow-up with their work. Therefore, a further 13.25 hours may need to be accounted for if you are in a jurisdiction that require a minimum amount of hours. You may need to schedule more than one section of this class to work towards this total if required. 

Even if your jurisdiction does not require set hours, this schedule is still useful as a guide to ensure that your learner is reaching their full potential. My jurisdiction does not require any minimum amount of hours of homeschooling, just set levels of achievement in skills and knowledge to be met. This guide to scheduling approximately 800 hours per year helps us to achieve said levels of achievement. 

In my homeschool, these circa 800 hours are divided in the following way:

English Language Arts: 200 hours, which includes c. 30 hours of LOTE, which helps learners practice English through comparing and contrasting languages, without realising that they are practicing English!

Mathematics: 200 hours

Science: 160 hours 
   - Biology: 40 hours
   - Chemistry: 40 hours
   - Physics: 40 hours
   - Earth and Space Science: 40 hours

Social Science: 160 hours
   - Geography: 40 hours
   - History: 40 hours
   - Civics and Citizenship: 40 hours
   - Economics and Business: 40 hours

Music: 10 hours + recreation
Visual Arts: 10 hours + recreation
Media Arts: 10 hours + recreation
Dance: 10 hours + recreation
Drama: 10 hours + recreation
Design Technology: 10 hours + recreation
Digital Technology: 10 hours + recreation
Health and Physical Education: 10 hours + recreation


The areas of skill and knowledge being taught and practiced in this class include but are not limited to:

General:
- Number and place value
- Money and  financial mathematics
- Patterns and algebra
- Using units of measurement
- Shape
- Geometric reasoning
- Location and transformation 
- Data representation  and interpretation 
- Chance

As an example, a learner in high-school might be studying:

Precalculus:
- Functions
- Linear Functions
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- Trigonometric Functions
- Periodic Functions
- Trigonometric Identities and Equations
- Further Applications of Trigonometry
- Systems of Equations and Inequalities
- Analytic Geometry
- Sequences, Probability, and Counting Theory
-  Introduction to Calculus

Calculus:
- Functions and Graphs
- Limits
- Derivatives
- Applications of Derivatives
- Integration - Part 1
- Applications of Integration - Part 1
- Integration - Part 2
- Applications of Integration - Part 2
- Techniques of Integration
- Introduction to Differential Equations
- Sequences and Series
- Power Series
- Parametric Equations and Polar Coordinates - Part 1
- Parametric Equations and Polar Coordinates - Part 2
- Vectors in Space
- Vector-Valued Functions
- Differentiation of Functions of Several Variables
- Multiple Integration
- Vector Calculus 
- Second-Order Differential Equations

If your learner is in middle-school / high-school, then they might be studying:

Pre-Algebra:
- Whole Numbers
- The Language of Algebra
- Integers
- Fractions
- Decimals
- Percents
- The Properties of Real Numbers
- Solving Linear Equations and Inequalities
- Models and Geometry
- Polynomials
- Graphs

Elementary Algebra:
- Systems of Linear Equations
- Factoring
- Rational Expressions and Equations
- Roots and Radicals
- Quadratic Equations

Intermediate Algebra:
- Graphs and Functions
- Polynomials and Polynomial Functions
- Rational Expressions and Functions
- Quadratic Equations and Functions
- Exponential and Logarithmic Functions
- Conics
- Sequences, Series, and Binomial Theorem

Algebra and Geometry:
- Polynomial and Rational Functions
- Analytic Geometry
- Sequences, Probability, and Counting Theory

Algebra and Trigonometry:
- The Unit Circle - Sine and Cosine Functions
- Periodic Functions
- Trigonometric Identities and Equations
- Further Applications of Trigonometry
- Systems of Equations and Inequalities


As an example, a 2nd-Grade learner might be studying:
• Addition and subtraction word problems
• Place value for multi-digit arithmetic
• Addition of two and three-digit numbers with carrying
• Subtraction of two and three-digit numbers with borrowing
• Very basic place value
• Working with the currency of their current physical location (money - coins and bills)
• Geometric shapes and fractions of shapes
•	Count Aloud Through 500
•	Read Whole Numbers Through 500
•	Write Numerals Through 500
•	Identify Place Value
•	Use Expanded Form: Numbers Through 500
•	Model Addition Problems
•	Place Value and Regrouping
•	Compare Numbers Through 500
•	Comparing and Ordering
•	Order Whole Numbers Through 500
•	Read Number Words Through 500
•	Time to the Nearest Quarter Hour
•	Time Relationships
•	Elapsed Time
•	Find the Value of Coins or Bills
•	Dollar and Cent Symbols for Money
•	Decimal Notation for Money
•	Fewest Bills and Coins
•	How Much Money?
•	Addition and Subtraction
•	Addition Computation Through 500
•	Finding the Difference
•	Subtraction and the Equals Symbol
•	Decompose Numbers
•	Make and Break Numbers
•	Break Up Numbers
•	Breaking Numbers to Subtract
•	Decompose to Subtract
•	Choose Friendly Numbers
•	Opposite Operations: + and -
•	Mental Math: Addition and Subtraction
•	Strategies to Add and Subtract Through 500
•	Subtraction Strategies Up Through 500
•	Addition and Subtraction Are Related
•	Centimeters
•	Estimate Length
•	Compare Measurements
•	Capacity
•	Addition Problem-Solving Strategies
•	Subtraction Problem Solving
•	Modeling Story Problems
•	Problem Solving
•	Problem Solving with Combining
•	Problem Solving with Change
•	Solve Change Story Problems
•	Compare to Solve Story Problems
•	Compare Amounts to Solve Problems
•	Make Equal Amounts to Solve Problems
•	Equalize Story Problems
•	Story Problems
•	More Story Problems
•	Problem Solving: Answer Check
•	Explain Problem Solutions
•	Justify Procedures Selected
•	Justify Solutions
•	Create Story Problems
•	Make Your Own Story Problems
•	Similar Story Problems
•	Classify Story Problems
•	Different Kinds of Problems
•	Count Aloud Through 1,000
•	Read Numbers Through 1,000
•	Write Number Words Through 1,000
•	Represent Numbers Through 1,000
•	Work With Numbers Through 1,000
•	Model Numbers Through 1,000
•	Place Value Through 1,000
•	Standard to Expanded Form
•	Expanded to Standard Form
•	Compare and Order Numbers
•	Plane Figures
•	Solid Figures
•	Build and Take Apart Shapes
•	Sums and Differences
•	Story Problems Through 1,000
•	Compare and Equalise Story Problems
•	Write Sentences for Story Problems
•	Identify Similarities and Differences
•	Check Story Problem Solutions
•	Explain Operations to Solve Problems
•	Which is the Addition/Subtraction Problem?
•	Model Multiplication with Arrays
•	Repeated Addition and Grouping
•	Different Types of Problems
•	Linear Patterns
•	Number Patterns
•	Represent Multiplication
•	Multiply By 2
•	Multiplication: 2s Facts
•	Multiply By 10
•	Multiplication: 10s Facts
•	Multiply By 5
•	Multiplication: 5s Facts
•	Multiplication Order and Rules
•	The Commutative Property
•	The Associative Property
•	Use Properties
•	Division as Repeated Subtraction
•	Division with Repeated Subtraction
•	Division with Equal Sharing
•	Equal Share Division
•	Represent Division
•	Remainders in Division
•	Represent Data
•	Data Questions
•	Use Data to Solve Problems
•	Range and Mode of Data Sets
•	Fractional Parts of a Whole
•	Fractional Parts of a Group
•	Fractional Relationships
•	Fractional Parts and One Whole
•	Fractions and Whole Numbers
•	Fractions and Mixed Numbers
•	Fractions
•	Equivalent Fractions

As an example, a 3rd-Grade learner might be studying:
• Multiplication of one and two-digit numbers
• Division of one and two-digit numbers
• Multiplication and division with algebraic thinking (45 ÷ X =9)
• Find greatest common factors between two numbers
• Commutative properties of multiplication
• Addition and subtraction of large numbers
• Basic introduction to fraction
• Round numbers to the nearest 10th
• Measurements and plotting data on a chart
• Finding the area of a rectangle by multiplication of its sides
•	Numbers Through 10,000
•	Odd and Even Numbers
•	Read and Write Numerals Through 10,000
•	Write Number Words Through 10,000
•	Numbers in Expanded Form
•	Construct Numbers to 10,000 
•	Compare and Order Numbers Through 10,000
•	Compare Numbers Through 500
•	Round Numbers Through 10,000
•	Effects of Addition and Subtraction
•	Addition and Subtraction Answers
•	Combine and Change Problems
•	Compare and Equalize Story Problems
•	Mathematical Expressions
•	Expressions and Number Sentences 
•	Expression Comparison 
•	Missing Symbols
•	Missing Values 
•	Number Patterns
•	Story Problems and Patterns 
•	Model and Explain Multiplication
•	Area Models for Multiplication
•	Understand Multiplication
•	Commutative Property of Multiplication
•	Multiplication Facts
•	Multiplication Facts 
•	Associative Property
•	Multiplication Story Problems
•	Multiply Multidigit by 1-Digit Numbers
•	Multiply Equal Groups 
•	Multiplication with Equal Measures
•	Write Multiplication Stories 
•	Model and Explain Division
•	Applying Division Symbols and Rules
•	Division as Sharing
•	Relating Multiplication and Division
•	Use Inverse Relationships
•	Effects of Division
•	Dividing with Remainders
•	Divide Greater Numbers
•	Story Problems with Equal Groups 
•	Equal Measures with Remainders
•	Divide Money Amounts
•	Write Division Story Problems 
•	The Order of Operations
•	Choose the Correct Operation 
•	Use More Than One Operation
•	Right Angles and Other Angles
•	Identify and Classify Polygons
•	Triangles
•	Parallelograms
•	Identify and Classify Solids
•	Combine Solids to Create New Shapes
•	Decimal Place Values
•	Money in Decimal Notation
•	Money Story Problems 
•	Represent and Name Fractions 
•	Compare and Order Fractions
•	Model Fraction Story Problems
•	Add and Subtract Like Fractions
•	Fractions and Decimals 
•	Probability
•	Identify, Record, and Display Outcomes
•	Use Data to Make Predictions
•	Tools and Units for Measuring Length
•	Estimate and Measure Centimeters
•	Telling Time in Minutes
•	Determine Elapsed Time in Minutes
•	Elapsed Time on a Calendar
•	Capacity
•	Measure to the Nearest Litre
•	English Units of Capacity
•	Measure in English and Metric Units
•	Unit Conversions
•	Unit Conversions 
•	Analyze Story Problems 
•	Understand Multistep Problems
•	Estimate to Predict Solutions
•	Strategies to Solve Complex Problems
•	Story Problem Reasoning 
•	Explain Solutions to Problems
•	Exact and Approximate Solutions
•	Check Accuracy of a Calculation
•	Find the Perimeter of Objects
•	Rectangular Area
•	Surface Area
•	Find the Volume of a Solid
•	Perimeter, Area, and Volume

As an example, 4th-Grade learners might cover the following:
• Multiplication and divisions word problems
• Long multiplication
• Long division with remainders
• Place value of whole and decimal numbers
• Equivalent fractions
• Compare fractions
• Improper fractions and mixed numbers
• Simplifying or reducing fractions
• Addition and subtraction of fractions and mixed numbers
• Multiply a whole number by a fraction
• Fraction word problems
• Write a decimal as a fraction
• Compare two decimals
• Addition and subtraction of decimals
•	Place Value Through 100,000,000
•	Numbers Through 100,000,000
•	Expanded Form Through 100,000,000
•	Compare And Order Greater Numbers 
•	Using Boundary Numbers for Rounding
•	Estimate Sums and Differences 
•	Add Whole Numbers
•	Subtract Whole Numbers
•	Multiply by 2-Digit Numbers 
•	Different Ways to Divide 
•	Prime Numbers Less Than 100
•	Order of Operations 
•	The Distributive Property 
•	Story Problems: Solve and Check 
•	Rate Story Problems 
•	Line Pairs
•	Types of Angles
•	Angles and Rotation
•	Fractions
•	Sketch Fractions
•	Different Meanings of Fractions 
•	Explain Equivalent Fractions 
•	Determine Equivalent Fractions 
•	Find a Fraction 
•	Estimating Lengths
•	Change Measurement
•	Measurements in Stories 
•	Relating Multiplication and Division
•	Measuring Temperature
•	Everyday Temperatures
•	Add and Subtract Fractions 
•	Unlike Denominators 
•	Different Ways to Write Products
•	Fraction Factors 
•	Fraction and Whole Number Products 
•	Fraction Division 
•	Compare Decimals
•	Order Three Decimal Numbers
•	Decimal Numbers and Rounding
•	Add and Subtract Decimal Numbers
•	Equivalent Decimals and Fractions
•	Halves and Fourths
•	Relate Decimal Numbers to Fractions 
•	Probabilities as Fractions
•	Organise Outcomes
•	Find All Possible Combinations
•	Surveys
•	Graph Data
•	Data Representations
•	Mode, Median, and Outliers
•	Analyse Story Problems 
•	Multistep Problems
•	Estimate to Predict and Verify 
•	Solve Story Problems That Are Alike
•	Use Simpler Problems to Solve Harder Ones
•	Represent and Explain Story Problems
•	State Solutions Clearly 
•	Problem-Solving Strategies
•	Estimated and Exact Answers
•	Define and Sketch Triangles
•	Define and Sketch Quadrilaterals 
•	Identify Diameters and Radii of Circles
•	Congruent Figures
•	Bilateral and Rotational Symmetry
•	Describe Geometric Solids
•	Geometric Nets
•	Negative Numbers on the Number Line
•	Count with Negative Numbers 
•	Negative Numbers in Everyday Math
•	Rational Numbers on a Number Line 
•	Expressions and Equations
•	Addition Property of Equality 
•	Multiply by Equal Quantities 
•	Two-Variable Equations 
•	The Coordinate Plane
•	Line Segments in the Coordinate Plane
•	Linear Relationships 
•	Perimeters of Polygons
•	Formulas for Perimeters 
•	Understand Area
•	Areas of Rectangular Shapes
•	Formulas for Area 
•	Area and Perimeter Story Problems 
•	Perimeter and Area of Rectangles