Dr. Shen’s Math Classes for Kids
Location: Carmel, Indiana.
Email: ShenMathClass@gmail.com
Wechat:shen_at_iupui
Url: https://sites.google.com/view/mathshen
How to study math:
https://www.youtube.com/watch?v=fgNaIWzBRGY&t=16s
This is a lecture given by me in Chinese. In this lecture, I will tell parents the importance of learning math and how to prepare their kids to learn math in middle and high school.
Instruction for Registration: Please enter your child's full name and any email address you can view it weekly. I will contact parents via the registered email addresses. Please bookmark the classroom room link in the confirmation email so that your child can enter the classroom without entering his name again in the future. Your child can register for a class in advance and feel free to withdraw before the 2nd lesson without any charge. The password to the classroom will be added after the first lesson.
Tuition and Payment Methods: The fee for each course is $300, paid to Z. Shen by Zelle or paypal using the following email address: ShenMathClass@gmail.com. Please mention your child’s full and the class name in the memo. If your child drops the class later, please notify me by email and I will refund the remaining fee.
Elementary Math I (4th-5th graders)
Date/Time: (8/9-12/13, Saturday 5:30-6:30P, ET)
https://iu.zoom.us/meeting/register/fVuDpvhgTleD2WK3DfXIpA
PreAlgebra II (5th-6th graders)
Date/Time: (8/2-12/6, Saturday, 7:00P-8:00P)
https://iu.zoom.us/meeting/register/gSecPxpmShanH2S1OS14Ew
Advanced Math I (for 6th-8th graders)
(Equivalent to AOPS Introduction to Algebra, Geometry and Probability)
Foundation for AMC8 & MATHCOUNTS
Date/Time (8/3-12/7, Sunday, 7:00P-8:00P, ET)
https://iu.zoom.us/meeting/register/y3Ep1UsZRJaj1mRWvzSYAg
AMC 10 (Geometry & Probability) (8th-10th graders)
July 22-Nov 3 (Tuesdays, 7:00P-8:00P, ET)
https://iu.zoom.us/meeting/register/rln1zE8AQ_idO0xHRSA4dA
Elementary Math Class
4th-5th graders
The purpose of this course is to improve student’s critical thinking skill.
By focusing on improving students’ critical thinking skills, I will equip them with a valuable lifelong skill. By training students to study math problems in multiple ways, I encourage creativity and analytical thinking, providing exercises for practice after each lesson helps reinforce their understanding and allows them to apply what they have learned. The inclusion of lecture notes will also be helpful for students to review and refer back to. No textbook is required. The course materials have been thoughtfully prepared and tailored to the needs of the students in a concise manner. Overall, it is a well-structured and engaging course for 4th-5th graders.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Elementary Math I (4th-5th graders)
Date/Time: Saturday 5:30-6:30P, 8/9-12/13, 2025
Registration Link: https://iu.zoom.us/meeting/register/fVuDpvhgTleD2WK3DfXIpA
1. Finding missing numbers
2. Determining patterns
3. Sequences I. https://www.youtube.com/watch?v=2basjDJivcI
4. Sequences II
5. Addition and Subtraction
6. Division and Multiplication
7. Solving Equations I
8. Solving Equations II
9. Word Problems I. https://www.youtube.com/watch?v=YPJ2DQNBexk
10. Word Problems II
11. Word Problems III
12. Word Problems IV
13. Patterns and Counting Problems
14. Counting Problems I
15. Counting Problems II
Elementary Math II
Date/Time: Spring 2026
Registration Link:
16. Average Values
17. Algebraic Operations
18. Rates
19. Speed Problems
20. Age Problems
21. Word Problems V
22. Word Problems VI
23. Word Problems VII
24. Finding the Original Values
25. Finding missing digits I
26. Finding missing digits II
27. Inverse problems
28. Set Theory
29. Basic Geometry https://www.youtube.com/watch?v=zs9XPwhw4a8
30. Logic deduction
Prealgebra
(AoPs series)
5th-6th graders
Course Description: This is a comprehensive course for 5th-6th graders! By covering algebra, number theory, geometry, and probability, students will gain a solid foundation in various mathematical topics. The course being spread over two semesters allows for a more in-depth exploration of these concepts. It’s great to see students being exposed to a diverse range of math disciplines at an early age.
Textbook: Prealgebra
Authors: Richard Rusczyk, David Patrick and Ravi Boppana
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
PreAlgebra I
Date/Time: Saturday 7:00P-8:00P, Spring 2026
Registration Link:
1. Addition and Multiplication
2. Reciprocals and Division
3. Exponents I
4. Exponents II
5. Multiples, Divisibility and Primes. https://www.youtube.com/watch?v=BzMkTh3q_8A
6. Prime Factorization
7. Divisors
8. Fractions I
9. Fractions II
10. Fractions III
11. Linear Equations. https://www.youtube.com/watch?v=8ztcOl9uRYo
12. Word Problems and Inequalities.
13. Decimals
14. Ratios, Conversions, and Rates
15. Proportions and Rates
PreAlgebra II
Date/Time: Saturday 7:00P-8:00P, August 2-December 6, 2025.
Registration Link: https://iu.zoom.us/meeting/register/gSecPxpmShanH2S1OS14Ew
16. Percent Problems I
17. Percent Problem II
18. Square Roots
19. Angles
20. Angles in Polygons
21. Measuring Segments and Regions
22. Areas of Triangles and Circle
23. The Pythagorean Theorem https://www.youtube.com/watch?v=3e_BW6T-AnI
24. The Pythagorean Theorem and Quadrilaterals
25. Basic Statistics
26. Data and Statistics
27. Counting I
28. Counting II
29. Probability I
30. Probability II
Advanced Math Class
6th-8th graders
Course Description: This is a comprehensive math curriculum for 6th-8th graders. I shall teach math systematically by covering each topic thoroughly,. providing exercises and lecture notes after each lesson to help reinforce understanding and allow students to practice independently. Some problems discussed in class and in homework are from math contests and competitions like AMC8. This will push students’ problem-solving skills. The course covers the materials in the AoPs book series: Introduction to Algebra; Introduction to Number Theory; Introduction to Geometry; Introduction to Counting & Probability.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Advanced Math Class I (Algebra & Number Theory) (Equivalent to AOPS Introduction to Algebra, Geometry and Probability)Foundation for AMC8 & MATHCOUNTS
Date/Time: Sunday, 7:00P-8:00P, August 3-December 7, 2025
Registration Link: https://iu.zoom.us/meeting/register/y3Ep1UsZRJaj1mRWvzSYAg
1. Computing Numbers
2. Linear Equations
3. Word Problems I
4. Word Problems II
5. Linear Systems
6. Algebraic Expressions
7. Quadratic Equations
8. Inequalities I
9. Inequalities II https://www.youtube.com/watch?v=oaAfLXV4zKI
10. Problems on Numbers I
11. Problems on Numbers II
12. Problems on Number III
13. Sequences I
14. Extremum Problems
15. Word Problems III
Advanced Math Class II (Geometry & Probability)
Date/Time: Sunday, 7:00P-8:00P, Spring, 2025
Registration Link:
16. Coordinate Geometry
17. Angles in triangles and polygons
18. Similarity of Triangles
19. Areas of rectangles and triangles
20. Area Comparison of Triangles
21. Pythagorean Theorem
22. Application of Pythagorean Theorem
23. Circles I
24. Circles II
25. Solid Geometry I
26. Solid Geometry II
27. Counting Techniques I
28. Counting Techniques II
29. Probability I
30. Probability II
Competition Math (AMC10)
8th-10th graders
Course Description: This is a well-structured course for 8th-10th graders interested in challenging math and preparing for the AMC10. By discussing previous contest problems, students will benefit from a practical approach to learning math systematically. Splitting the course into two semesters, with a focus on algebra in the first semester and geometry, number theory, and probability in the second semester, allows students to develop a strong foundation in each topic area. This course design will help students build the necessary skills and knowledge to excel in the AMC10 and beyond.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Part I (Algebra and Number Theory)
Date/Time: Spring 2026
Lesson 1. Algebraic Simplification
Lesson 2. Ratios and Proportions
Lesson 3. Percentage Problems
Lesson 4. Factoring Methods
Lesson 5. Word Problems – Distance and Speed
Lesson 6. Quadratic Equations
Lesson 7. Equation Solving Skills
Lesson 8. System of Equations https://www.youtube.com/watch?v=ry7VndLSPS4
Lesson 9. Sum and Products of Roots
Lesson 10. Character of Digits
Lesson 11. Divisibility
Lesson 12. Primes
Lesson 13. Factors and Divisors
Lesson 14. Exponents
Lesson 15. Arithmetic and Geometric Sequences
Part II (Geometry, Combinations and Probability)
Date/Time: Tuesday 7:00P-8:00P, July 22-Nov 3, 2025
Registration Link: https://iu.zoom.us/meeting/register/rln1zE8AQ_idO0xHRSA4dA
Lesson 1. Pythagorean Theorem I
Leeson 2. Pythagorean Theorem II
Lesson 3. Triangle Area
Lesson 4. Similar Triangles
Lesson 5. Circles
Lesson 6. Angle Bisector and Median
Lesson 7. Solid Geometry
Lesson 8. The mass point method
Lesson 9. Coordinate Geometry I –Lines
Lesson 10. Coordinate Geometry II-Circles
Lesson 11. Mean, Median, Mode and Range
Lesson 12. Counting by Permutations and Combinations
Lesson 13. Counting – Balls and Boxes
Lesson 14. Counting with Geometric Figures
Lesson 15. Probability
PreCalculus I (Algebra 2)
Date/Time: (Monday & Friday 7/21-8/22, 7:30P-8:30P ET)
7/21, 7/25, 7/28. 8/1, 8/4, 8/8, 8/11, 8/15. 8/18, 8/22
Fee: $200
Registration Link: https://iu.zoom.us/meeting/register/VAlLx4u2RBWf9Syybj_aBg
PreCalculus II (Trignometry)
Date/Time: (Monday & Wednesday, 8/25-12/10, Monday & Wednesday 3:00-4:15P)
Fee: Free
Registration Link:
https://iu.zoom.us/meeting/register/eqnaMdcgRBelqjnHF-I2PA
Pre-Recorded Courses
Students have the opportunity to enroll in pre-recorded courses and learn at their own pace. They can access recorded lectures and download homework materials through the Google Classroom platform. To register your child for a pre-recorded course, kindly send an email to ShenMathClass@gmail.com. In the subject line of the email, please write “course title, pre-recorded”. This will help ensure the successful enrollment of your child.
Elementary Math Class
4th-5th grades
The purpose of this course is to improve student’s critical thinking skill.
By focusing on improving students’ critical thinking skills, I will equip them with a valuable lifelong skill. By training students to study math problems in multiple ways, I encourage creativity and analytical thinking, providing exercises for practice after each lesson helps reinforce their understanding and allows them to apply what they have learned. The inclusion of lecture notes will also be helpful for students to review and refer back to. No textbook is required. The course materials have been thoughtfully prepared and tailored to the needs of the students in a concise manner. Overall, it is a well-structured and engaging course for 4th-5th graders.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Elementary Math I
31. Finding missing numbers
32. Determining patterns
33. Sequences I. https://www.youtube.com/watch?v=2basjDJivcI
34. Sequences II
35. Addition and Subtraction
36. Division and Multiplication
37. Solving Equations I
38. Solving Equations II
39. Word Problems I. https://www.youtube.com/watch?v=YPJ2DQNBexk
40. Word Problems II
41. Word Problems III
42. Word Problems IV
43. Patterns and Counting Problems
44. Counting Problems I
45. Counting Problems II
Elementary Math II
46. Average Values
47. Algebraic Operations
48. Rates
49. Speed Problems
50. Age Problems
51. Word Problems V
52. Word Problems VI
53. Word Problems VII
54. Finding the Original Values
55. Finding missing digits I
56. Finding missing digits II
57. Inverse problems
58. Set Theory
59. Basic Geometry https://www.youtube.com/watch?v=zs9XPwhw4a8
60. Logic deduction
Basic Math
Pre-recorded Course
Equivalent to AOPS’ PreAlgebra
Course Description: The course is suitable for 5th-6th graders and runs through two semesters. By introducing new and abstract concepts in mathematics, I shall challenge your students and prepare them for more advanced math topics.
I will provide exercises and lecture notes after each lesson. This will allow students to practice the concepts they’ve learned and refer back to my notes for reinforcement. Enhancing students’ basic math knowledge and abstract thinking during the 5th-6th grade stage will definitely help them build a solid foundation for studying advanced math in middle school and participating in math contests later on.
Topics
1. Fractions I
2. Fraction II
3. Linear Expressions
4. Linear Equations I. https://www.youtube.com/watch?v=t7LPMB73n08
5. Linear Equations II
6. Factors and Divisibility of Numbers
7. Problems on Numbers
8. Percentage Problems I
9. Percentage Problems II
10. Rectangles
11. Triangles https://www.youtube.com/watch?v=kVbu0ALStJ0
12. Circles I
13. Circles II
14. Inequalities
15. Polynomials
16. Fractional Expressions
17. Square Roots
18. Solving Linear Algebraic Equations
19. Coordinate Geometry I
20. Coordinate Geometry II
21. Solid Geometry I
22. Solid Geometry II
23. Counting Techniques I
24. Counting Techniques II
25. Probability I
26. Probability II
27. Mathcounts 1
28. Mathcounts 2
29. Mathcounts 3
30. Mathcounts 4
AMC8 for beginners
Pre-recorded Course
This course is designed for students who have either completed my PreAlgebra Class or will enter 7th grade in the upcoming fall. The lectures will cover various topics including Number theory, Geometry, and Probability, amongst others. The problems to be discussed in class will be specifically selected from previous Mathcounts contests, focusing on the countdown part. Each week, students will receive one set of Mathcounts countdown consisting of 80 problems as their homework. These practice problems will help reinforce the concepts covered in class and further develop the students’ math skills. By the end of the course, students should be well-prepared to proceed to the Advanced Math class. If you have any further questions or would like additional information, please don’t hesitate to ask.
Topics
1. Geometry I
2. Problems on Numbers I https://www.youtube.com/watch?v=7vttmZhDeJg
3. Probability I
4. Algebra I
5. Algebra II
6. Problems on Numbers II
7. Problems on Numbers III
8. Geometry II https://www.youtube.com/watch?v=bCfF7e-Suwo
9. Geometry III
10. Problems on Numbers IV
11. Geometry IV
12. Word Problems
13. Equations
14. Probability II https://www.youtube.com/watch?v=-0uFW8zLjpY
15. Probability III
Advanced Math Class
6th-8th graders
Course Description: This is a comprehensive math curriculum for 6th-8th graders. I shall teach math systematically by covering each topic thoroughly,. providing exercises and lecture notes after each lesson to help reinforce understanding and allow students to practice independently. Some problems discussed in class and in homework are from math contests and competitions like AMC8. This will push students’ problem-solving skills.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Advanced Math Class I (Algebra & Number Theory)
1. Computing Numbers
2. Linear Equations
3. Word Problems I
4. Word Problems II
5. Linear Systems
6. Algebraic Expressions
7. Quadratic Equations
8. Inequalities I
9. Inequalities II https://www.youtube.com/watch?v=oaAfLXV4zKI
10. Problems on Numbers I
11. Problems on Numbers II
12. Problems on Number III
13. Sequences I
14. Extremum Problems
15. Word Problems III
Advanced Math Class II (Geometry & Probability)
16. Coordinate Geometry
17. Angles in triangles and polygons
18. Similarity of Triangles
19. Areas of rectangles and triangles
20. Area Comparison of Triangles
21. Pythagorean Theorem
22. Application of Pythagorean Theorem
23. Circles I
24. Circles II
25. Solid Geometry I
26. Solid Geometry II
27. Counting Techniques I
28. Counting Techniques II
29. Probability I
30. Probability II
Competition Math (AMC8 and MATHCOUNTS)
Geometry and Probability only, 13 Lessons
Course Description: This course offers an intensive focus on geometry and probability, specifically tailored to prepare students for the challenging problems encountered in AMC8/Mathcounts competitions. A strong foundation in pre-algebra is essential for success in this course.
Students will benefit from comprehensive lecture notes and a curated set of exercises following each lesson. These exercises are designed to reinforce understanding and mastery of key concepts in geometry and probability, ensuring students are well-prepared for competition-level problem-solving.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Topics
1. Geometry
1.1 Pythagorean Theorem
1.2 Circles.
1.3 Area
1.4 Similarity
1.5 Three-Dimensional Geometry
1.6 Review on Geometry
2. Probability
2.1 Probability Basics
2.2 Compound Events ad Counting
2.3 Casework and Probability
2.4 Probability and Combinations
2.5 Complementary Counting and Probability
2.6 Geometric Probability
2.7 Expected Values
Competition Math (AMC8 and MATHCOUNTS)
(Complete Course, 40 Lessons)
6th-8th graders
Course Description:
This course is designed for 7th-8th graders who have a strong interest in challenging mathematics. The material covered in this course goes beyond what is typically taught in a standard classroom. It is important for students to have a solid foundation in pre-algebra before enrolling in this course.
Throughout the course, students will be provided with lecture notes and a set of exercises after each lesson. By completing these exercises, students will have the opportunity to reinforce their understanding of the material.
Taking this course will greatly enhance students’ problem-solving skills and enrich their knowledge in elementary math. They will be able to tackle more advanced mathematical concepts and develop a deeper understanding of the subject matter.
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Topics
3. Algebra
3.1 Variables and Equations
3.2 Linear Equations
3.3 Systems of Equations. https://www.youtube.com/watch?v=ritgnN7jqc4
3.4 Ratios., Proportions ad Percents
3.5 Distribution
3.6 Quadratics
3.7 Exponents and Radicals
3.8 Statistics
3.9 Sequences and Series
3.10 More substitution
4. Counting
4.1 Basics
4.2 Venn Diagrams
4.3 Bowling Pins and Handshakes
4.4 Counting Outcomes
4.5 Casework
4.6 Factorials and Permutations
4.7 Combinations
4.8 Sticks and Stones
4.9 Pascal’s Triangle
5. Probability
5.1 Probability Basics
5.2 Compound Events ad Counting
5.3 Casework and Probability
5.4 Probability and Combinations
5.5 Complementary Counting and Probability
5.6 Geometric Probability
5.7 Expected Value
6. Number Theory
6.1 Primes and Divisibility
6.2 Factors
6.3 Factor Tricks
6.4 Different Bases
6.5 The Unit Digit
6.6 Fractions and Decimals
6.7 Modular Arithmetic
7. Geometry
7.1 Geometry Basics
7.2 Circles. https://www.youtube.com/watch?v=H11tukp-g_Q
7.3 Pythagorean Theorem
7.4 Area
7.5 Three-Dimensional Geometry
7.6 Similarity
7.7 Review
Challenge Math for MATHCOUNTS
(7th-8th graders)
Course Description: This course is for 7th-8th graders who have completed my Advanced Math course and need more practice for MATHCOUNTS. I will discuss various problems selected from Mathcounts, mostly focused on Geometry, Number Theory and Probability. This course is geared for students who continue to enhance their problem solving skills. After each lesson, students will receive my lecture notes and a set of previous Mathcounts. No textbook is required.
PART I
Lesson 1. Algebra
Lesson 2. Problems on Numbers I
https://www.youtube.com/watch?v=ZlwDNcGymOM
Lesson 3. Geometry I
Lesson 4. Problems on Numbers II
Lesson 5. Problems on Numbers III
Lesson 6. Problems on Numbers VI
Lesson 7. Counting Techniques
Lesson 8. Problems on Numbers IV
Lesson 9. Geometry II
Lesson 10. Probability I
Lesson 11. Algebra II
Lesson 12. Coordinate Geometry
Lesson 13. Problems on Numbers VI
Lesson 14. Geometry III
Lesson 15. Equations on Numbers
PART II
Lecture 1: Sequences
https://www.youtube.com/watch?v=DLOfxsDdUGc
Lecture 2 Problems on Numbers I
Lecture 3. Equations on Numbers I
Lecture 4. Geometry I
Lecture 5. Equations
Lecture 6. Geometry II
Lecture 7. Problems on Numbers II
Lecture 8. Geometry III
Lecture 9. Problems on Numbers III
Lecture 10. Problems on Numbers VI
Lecture 11. Geometry VI
Lecture 12. Counting Geometric Figures
Lecture 13. Probability I
Lecture 14. Probability II
Lecture 15. Probability III
Intermediate Algebra
(AoPs series)
Pre-Recorded Course
For 8th-10th graders
Course Description: The course is suitable for 8th-9th graders. Suppose that you have completed AoPS’ Introduction to Algebra , then much of the first four chapters will be review. I will just skip these four chapters. If you have not completed Introduction to Algebra, then you should have experience factoring quadratic expressions before starting this book. If you have completed a typical algebra 1 course, you may be ready for this text, but the first for chapter might not be review.
Textbook: Intermediate Algebra
Authors: Richard Rusczyk, Mathew Crawford
http://www.AOPS.com
Instructor: Dr. Shen
Email: ShenMathClass@gmail.com
Topics
Parabolas
Problem-solving with parabolas
Maxima and minima of quadratics
Circles
Ellipse
Hyperbolas
Synthetic Division
Introduction to Polynomial Division
Polynomials
The Remainder theorem
The factor theorem
Integer roots
Rational roots
The fundamental theorem and graphing
Bounds
Nonreal roots
Irrational roots
Irrational roots
Vieta’s formula
Using roots to make equation
Factoring multivariable polynomials by grouping
Sums and differences of powers
The factor theorem for multivariable polynomials
Arithmetic sequence
Arithmetic series
Geometric sequences
Geometric series
Sequence, summation and product notations
Nested sums and products
Review
Identities
Ratios
Induction
Binomial theorem
Manipulating inequalities
The trivial inequalities
AM-GM inequality with two variables
AM-GM inequality with more variables
The Cauchy-Schwartz inequality
Maxima and minima
Exponential function basics
Introduction to logarithm
Logarithmic identities
Using logarithm identities
Switching between Logs and exponents
Natural logarithms and exponential decay
Raising radicals to power
Evaluating expressions with radicals
Radical conjugates
Rational functions and their graphs
Rational functions and inequalities
Even and odd functions
Monotonic functions
Piecewise defined Functions
Absolute value
Graphing absolute value
Recursive sequences
Telescoping
Sums of polynomial series
Arithmetico-geometric series I
Arithmetico-geometric series II
HM-GM-AM-QM inequalities