1:1 수학 튜터링 및 강화(K-12학년)

Teaching Overview
I truly believe every child is a genius and is capable of mastering mathematics concepts. This class is individualized for each student to provide the optimal support, guidance, and enrichment to help students to feel confident, have the skills and understanding of concepts, and develop a curiosity and love of mathematics. 

I believe social-emotional well-being is essential for academic curiosity and success. I make the learning fun, relevant, and engaging by creating lessons and activities that are the appropriately challenging and teaching with patience and aloha! 

Teaching Style
My teaching style is "I Do. We Do. You Do." First, I typically demonstrate how to approach and solve problems, by using examples and reviewing mathematical concepts. Next, I encourage the students to solve the problems with me by giving me suggestions and directions along the way. When students are comfortable, they will attempt to solve problems independently. I will continue to offer help and guidance when needed, and will check for accuracy. 

I believe it's important to teach where students "are" and also give opportunities for enrichment so students can "reach."  I make the class welcoming and am approachable. I like to connect the learning to the world and engage with student's interests. I employ a mix of styles (lecture, problem-based, project-based, inquiry, interactive, game-play, constructivist) that best work for each individual student. I believe it's important for students to have agency and a say in how they learn. In this 1-on-1 session, students are encouraged to say what they like and don't like. Ultimately, the goal is to help the students feel more confident and to learn math in the way that suits them the best. 

Class Structure
5 minutes: Introduction
We will have an opportunity to discuss and share updates. Students may ask questions about homework problems or around a topic of interest. The session is personalized for the student and we will set goals for the session. 

5 minutes: Warm-up/Pre-Assessment
Student will work on a problem of their choice or a challenge that I have selected based around the topics we have discussed. 

40 minutes: Lesson/Activity
I will go over the concepts with strategy, story-telling, and additional examples to create a deeper understanding of the concepts. We will complete similar exercises together, and explore the concepts further with a variety of online resources, including Desmos, Mathematics Virtual Manipulatives, and multimedia. We will review homework problems and prepare for upcoming assessments with additional practice. The focus will be on understanding the concepts and developing strategy for solving the math problems with step-by-step directions. Ultimately, students will be able to complete and solve problems independently by utilizing the strategies discussed.

5 minutes: Wrap-up/Reflection/Assessment
We will review the goals, challenges, and progress from the session. With reflection, I will help the student to identify areas of strength and areas for improvement. Together, we will create a personalized learning plan going forward, and assess overall learning.

Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.

Math Topics by Grade Level/Course
Elementary (K - 5th)
Counting & Cardinality
Operations & Algebraic Thinking
Number & Operations in Base Ten
Measurement & Data
Geometry
Number & Operations—Fractions

Middle School (6th - 8th)
Ratios & Proportional Relationships
The Number System
Expressions & Equations
Geometry
Statistics & Probability
Functions

Middle & High School Level Courses
Pre-Algebra
Algebra I & II
Geometry
Trigonometry
Integrated Math 1/2/3
Pre-Calculus
Statistics
Economics
AP Calculus
AP Statistics

Specific Concepts
Counting and Cardinality
• One to One Correspondence
• Number recognition
• Count sequence
• Compare numbers- More or Less than or
Equal
• Skip counting
• Odd and Even
• Number sequence
• Sets and Classifying objects
Operations and Algebraic Thinking
• Patterns
• Addition- Putting together / Adding to
• Subtraction- Taking apart / Taking From
• Addition and Subtraction
• Foundation of Multiplication
• Multiplication and Division
• Relationship of multiplication and Division
• Word Problems - Multiple steps
• Property of Operations
• Order of Operations
• Understanding Addition, Subtraction,
Multiplication, and Division
• Equations
• Numerical Expression
• Functions
• Number Theory - Factors, Multiples, Primes,
Divisibility
• Ratios, Rates, Proportions, Percent, Square
Roots
Number Operations Base Ten and Fractions
• Parts and Wholes
• Base Ten
• Place Value
• Whole Numbers
• Fractions- Compare and Order
• Fractions - Read, Write, Model
• Decimal notation
• Decimals - Read, Write, Compare
• Equivalent Numbers - Decimals and
Fractions
• Integers
• Divide Fraction by Fraction
• Build Fractions
• Money- Count bill coins, and Collection of
Money
• Measurement and Data
• Describe and Compare measurable
attributes
• Sort and Classify Objects
• Time - Tell and write with both analog and
digital
• Represent and Interpret Data
• Measurements - Compare Objects, Measure
with Different objects
• Estimates
• Units and Tools
• Probability
• Geometric Measurement
• Conversion of Measurements and units
• Money
• Measurements of Angles
• Volume
• Graphing data points
Geometry
• Spatial Sense - Position of Objects
• Two Dimensional Shapes- Identify, Compare,
Sort
• Composite and Real-World Shapes
• Composes Shapes
• Three Dimensional Shapes- Identify,
Compare, Sort
• Identify Lines and Angles
• Perimeter, Area, Volume
• Coordinates
• Similar, Congruent, Symmetric Shapes
• Sorting and Classifying- by shape attributes
• Graph Coordinates
Additional Topics
• The number system
• Exponents
• Equations and Inequalities
• Dependent and Independent Variables
• Variability
• Summarize and Describe distributions 

Algebra, Patterns and Relationships
• Algebraic Expressions
• Formulas
• Functions
• Graphing Relationships
• Inequalities
• Linear Relationships
• Number and Geometric Patterns
• Solving Equations
• Systems of Equations
• Variables and Substitution
• Represent and Analyze Quantitative Relationships
between Dependent and Independent Variables
• Use Properties of Operations to Generate
Equivalent Expressions
• Work with Radicals and Integer Exponents
• Understand the Connections between Proportional
Relationships, Lines and Linear Equations
• Analyze and Solve Linear Equations and Pairs of
Simultaneous Linear Equations
• Define, Evaluate and Compare Functions
• Use Functions to Model Relationships between
Quantities
Data and Graphs
• Experiments and Data Collection
• Infer, Predict, Evaluate, Compare Data
• Measures of Central Tendency and Variation
• Represent, Read, Interpret Data Displays
Geometry
• Circles and Pi
• Classify Two- and Three-Dimensional Figures
• Coordinate Plane
• Drawing, Modeling, and Constructing Figures and
Describe the Relationships between them
• Formulas for Perimeter, Area, Surface Area, Volume
• Logic and Reasoning
• Points, Lines, and Planes
• Properties of Two-Dimensional Figures
• Understand and Apply the Pythagorean Theorem
• Similarity, Congruence, and Symmetry
• Transformations
Measurement
• Estimate and Measure
• Measurement Systems
• Measurement Tools
• Rates, Indirect Measurements, Proportion
Numbers
• Compare and Order Numbers
• Equivalent Forms of Rational Numbers
• Estimation and Rounding
• Exponents and Roots
• Number Properties
• Number Theory Concepts
• Operations to Solve Problems
• Operations with Integers and Absolute Value
• Operations with Real Numbers
• Order of Operations
• Percents
• Ratios, Rates, Proportions
• Understand Ratio Concepts and Use Ratio
Reasoning to Solve Problems
• Real Number System
Probability
• Develop Understanding of Statistical Variability
• Summarize and Describe Distributions
• Sample Space, Combinations, Permutations
• Theoretical and Experimental Probability
• Use Random Sampling to Draw Inferences about
a Population
• Draw Informal Comparative Inferences about
Two Populations
• Investigate Chance Processes and Develop, Use,
and Evaluate Probability Models
• Understand Patterns of Association in Bivariate
Data

Algebra
Absolute Value Equations and Inequalities
• Graphing Absolute Value Equations
and Inequalities
• Solving Absolute Value Equations
and Inequalities
Algebraic Expressions
• Add, Subtract Expressions
• Multiply, Divide, Factor Expressions
including Exponents
• Variables and Expressions
Linear Equations and Inequalities
• Slope, Intercepts, Points on a Line
• Solving Linear Equations
• Solving Linear Inequalities
• Solving Problems with Equations
and Inequalities
• Systems of Equations and Inequalities
• Writing and Graphing Linear Equations
• Writing and Graphing Linear Inequalities
Numbers
• Exponents and Roots
• Number Properties
• Number Theory Concepts
• Operations with Real Numbers
• Ratios, Proportions, Percents and Rates
Patterns and Functions
• Composition and Operations on Functions
• Graphing Functions and Transformations
• Inverse of Function
• Patterns
• Properties of Functions - Domain and Range
• Properties of Functions –
• Zeros, End Behavior, Turning Points
• Relations and Functions
• Solving Problems with Functions
• Translate Between Forms
Probability
• Counting Principles and Sample
Spaces
• Theoretical and Experimental
Probability
Quadratic Equations, Inequalities, and
Functions
• Factoring Quadratic Equations
• Graphing and Properties of
Quadratic Equations
• Solving Quadratic Equations and
Inequalities
• Systems of Nonlinear Equations
and Inequalities
Radical, Exponential and Logarithmic
Equations and Functions
• Graphing Exponential and
Logarithmic Functions
• Properties of Exponents and
Logarithms
• Radical Expressions, Equations and
Rational Exponents
• Solving Exponential and
Logarithmic Equations and
Inequalities
• Solving Problems with Exponential
and Logarithmic Functions
Statistics
• Data Analysis – Data Collection
• Data Displays – Measures of Data

Algebra II
Absolute Value Equations and Inequalities
• Graphing Absolute Value Equations
and Inequalities
• Solving Absolute Value Equations
and Inequalities
Conic Sections
• Properties of Conic Sections
• Solving Problems with Conic Sections
Linear Functions, Equations, and Inequalities
• Slope, Intercepts, Points on a Line
• Solving Linear Equations
• Solving Linear Inequalities
• Solving Problems with Equations
and Inequalities
• Systems of Equations and Inequalities
• Writing and Graphing Linear Equations
• Writing and Graphing Linear Inequalities
Matrices
• Matrices Operations and Problems
Numbers
• Complex Numbers
• Number Properties
• Operations with Real Numbers
Patterns and Functions
• Composition and Operations on Functions
• Graphing Functions and Transformations
• Inverse of Function
• Patterns
• Properties of Functions - Domain and Range
• Properties of FunctionsZeros, End Behavior, Turning Points
• Relations and Functions
• Solving Problems with Functions
• Translate Between Forms
Polynomial, Rational
Expressions, Equations
and Functions
• Solving and Graphing Polynomial Equations
• Solving and Graphing Rational Equations
Probability
• Counting Principles and Sample Spaces
• Theoretical and Experimental Probability
Quadratic Equations, Inequalities,
and Functions
• Complex Solutions to Quadratic Equations
• Factoring Quadratic Equations
• Graphing and Properties of Quadratic
Equations
• Solving Quadratic Equations and Inequalities
• Systems of Nonlinear Equations and
Inequalities
Radical, Exponential and
Logarithmic Equations and
Functions
• Graphing Exponential and Logarithmic
Functions
• Properties of Exponents and Logarithms
• Radical Expressions, Equations and Rational
Exponents
• Solving Exponential and Logarithmic Equations
and inequalities
• Solving Problems with Exponential and
Logarithmic Functions
Sequences and Series
• Properties of Sequences and Series
• Solving Problems with Sequences and Series
Statistics
• Data Analysis
• Data Collection
• Data Displays
• Measures of Data

Geometry
Measurement
• Formulas and Measurement
• Indirect Measurements, Ratios, and Rates
• Units, Unit Conversions, and Error
Points, Lines, Angles, Planes
• Angle Relationships and Problems
• Coordinate Geometry - Slope, Distance, Midpoint
• Geometric Constructions
Proofs and Logic
• Conditional Statements
• Conjectures, Axioms, Theorems, Proofs
• Inductive and Deductive Reasoning
Two- and Three- Dimensional Shapes
• Congruency
• Relationship Between Plane and Solid Figures
• Right Triangles, Including Pythagorean Theorem
• Similarity
• Symmetry and Transformations
• Theorems and Problems with Circles
• Theorems and Problems with Polygons
• Theorems and Problems with Quadrilaterals
• Theorems and Problems with Triangles
• Three-Dimensional Figures
• Trigonometric Ratios in Right Triangles

Trigonometry
Complex Numbers
• Polar Coordinates, DeMoivre’s Theorem
• Trigonometric Form
• z Complex Number
Introduction to Trigonometry:
Linear Relationships and Functions
• Introduction to Trigonometry
• Introduction to Trigonometry: Linear
Relationships and Functions
• Relations, Functions, and Graphs
• Defining and Finding Trigonometric Functions
• Slope, Linear Relations, Scatter Plots, and
Piecewise Functions
• Introduction to Trigonometry: Linear
Relationships and Functions Unit Review
Trigonometric Ratios
• Trigonometric Ratios
• Angles and Angle Measures
• Measuring angles using radian and degree
measures
• Right Triangles and Trigonometric Ratios
• The Unit Circle
• Trigonometric Ratios Unit Review
Graphing Trigonometric Functions
• Introduction to Graphing Trigonometric
Functions
• Graphing Trigonometric and Inverse
Functions
• Inverse Trigonometric Functions
• Transformations of Trigonometric Functions
• Real-world Applications of Trigonometric
Functions
• Vectors
• Graphing Trigonometric Functions Unit
Review
Trigonometric Laws and Identities
• Trigonometric Laws and Identities
• Law of Sines and Law of Cosines
• Trigonometric Identities and Equations
• Area of Triangles
• Angular and Linear Velocities
• Trigonometric Laws and Identities Unit
Review
• Modeling Periodic Phenomenon
Vectors
• Graphing and Operations with Vectors
• Solving problems with Vectors