Wednesday, December 14, 2016

Math Resources, Competitions, and Curriculum Suggestions


Math Problems:

AMC 8, AMC 10/12, AIME:
AMC 10/12
AMC 8 Registration Form
AMC 8 Problems and Solutions
American Invitational Mathematics Exam

Interactive MATHCOUNTS Platform
How to Write MathCounts Competition Answers

MathCounts Topics (JHU MathCounts Syllabus):
  1. Fundamentals: Arithmetic
  2. Proportional Reasoning
  3. Radicals and Exponents
  4. Algebra A: Polynomials, Linear Equations and Functions
  5. Algebra B: Applications, Nonlinear Equations, Inequalities, Functions.
  6. Plane Geometry
  7. Coordinate Geometry
  8. Solid Geometry (addresses also transformational geometry)
  9. Statistics and Probability
  10. Sequences and Series
  11. Problem Solving

Art of Problem Solving Videos
Khan Academy Mathematics Videos

Math Typesetting Tool
SAGE Math Cloud
Geometry Sketching Tool

Math Curriculum Suggestions from AOPS
Curriculum Inspirations by James Tanton, PhD (videos)

Thinking and G'Day Mathematics (resources for students and teachers):

Book of Proof (Free PDF available under Creative Commons License)

Other Competitions:

Sunday, May 8, 2016

Division M2 Session 5/8/2016

Mr. Ahmed Hefny
Adan, Omar, Areej
Pre-Algebra Chp 2
Problems Solved in Class:
Chosen exercises from chapter 2
* Definition of exponent
* Properties of exponent:
    - Not commutative
    - Not associative (default order is top to bottom)
    - Does not distribute over addition
    - Distributes over base multiplication (ab)^c = a^c * b^c
    - 1 is a "right identity" element.
 * (a+b)^2 = a^2 + b^2 + 2ab. It can be proven using distributive property.
 * Negative powers.
 * 0th Power.
* Powers of 0.
Student Difficulties:
. Students still have difficulties using variables to prove general statements.
. A problem that took un expected long time is showing that:
(2a+2b)^m = 2^m (a+b)^m
Students had trouble figuring out that this is a simple application of distributive properties.
· Chapter 2: Please watch teh videos and make sure you can solve example problems.
. Solve exercises: 2.1.2, 2.1.5, 2.1.9, 2.2.6, 2.2.10, 2.2.11, 2.4.6
. Solve review exercises: 2.45, 2.50. 2.76

Monday, April 18, 2016

Division M1 session on April 17, 2016

Mr. Zia Hydari
AbdulRafay, Sohaib, Abiha, Abdul Qadir, Adeel, Rami, Kamal
Problems Solved in Class:
Problems illustrating the distributive property
Operators, distributive property
Student Difficulties:
Using variables to prove properties e.g. if the operator “@” is defined as:
a @ b = 2a + 2b
and I asked students to prove that “@” is commutative, the students used specific numbers to create examples but did not use variables to construct a general proof.
·         Read Section 1.1, 1.2, and 1.3
·         Watch all of the videos for Section 1.1, 1.2, and 1.3 from
·         If you need more help, please watch the following videos and work through the online exercises at:

·         Solve all of the exercises and problems from Section 1.1, 1.2, and 1.3
·         Solve problem 1.71 on page 51. Then solve these additional items:
1.     Does multiplication distribute over “@”?
2.     Does addition distribute over “@”?
3.     Does “@” distribute over addition?
4.     Does “@” distribute over multiplication?
HINT: First, try to solve on your own; then use the hint below. Recall that problem 1.71 in the book defines the operator “@” as:
 a @ b = 2a + 2b
Part 1 asks if the following is true: a ( b @ c) = ab @ ac
Part 2 asks if the following is true:  a + (b @ c) = (a + b) @ (a + c)
Part 3 asks if the following is true: a @ (b + c) = (a @ b) + (a @ c)
Part 4 asks if the following is true: a @ bc = (a @ b) (a @ c)

Division M1 session on April 10, 2016

Mr. Zia Hydari
AbdulRafay, Sohaib, Abiha
(Abdul Qadir?, Adeel?, Rami?, Kamal?)
Problems illustrating the distributive property
All problems from Section 1.3

April 3, 2016—CONTEST for All Levels (E, M1, M2)

March 27, 2016—NO AKCMP sessions

AKCMP closed as MCCGP Sunday School was closed.

Division M1 session on March 20, 2016

Mr. Isa Hafalir
AbdulRafay, Abiha, Rami
Classwork and Homework
In the first half, we did Pre-Algebra book Section 1.3 and exercises 1.3.5 to 1.3.11 were assigned as homework.

In the second half, we went over Set 10 Olympiad 5 and Set 11 Olympiad 1.

5 questions in Set 11 Olympiad 2 were assigned as homework.

Sunday, March 13, 2016

Division M2 session on March 13, 2016

Instructor:Mr. Ahmed Hefny
Attendance:Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar
Handout:Pre-Algebra Chapter 1
Problems Solved in Class:* Probability problems: throwing a die and drawing from a deck of cards.
* Disproving false statements about properties of operators: commutative and associative properties of subtraction, addition distributes over multiplication.
Concepts:[Session 1] A brief introduction to probability:* Probability and statistics are two opposite inference paths; probability tells us, given knowledge about a random process, how to answer questions related to samples from that process. [Ex: what is the probability of getting 3 heads in a row if I throw a fair coin three times ?]. Statistics tells us, given a sample from the random process, how to gain knowledge about that process. [Ex: Given a sample of 10000 voters, how much is the American community biased towards Republicans ?]

* Basic probability laws and the conditions for their correctness: Let A and B be two conditions (usually called events)
- P(A) = # of outcomes that satisfy A / # of all possible outcomes      [Assuming all outcomes are equally likely]
- P(A and B) = P(A)P(B)              [iff A and B are independent]
- P(A and B) = P(A)P(B|A)          [P(B|A) is the probability of B happening given that A happened. P(B|A) = P(B) iff A and B are independent]- P(A or B) = P(A) + P(B)             [iff A and B are disjoint i.e. A and B cannot happen together]
- P(A or B) = P(A) + P(B) - P(A and B)      [This is the same inclusion-exclusion principle for counting the union of two sets]    

[Session 2] Pre-algebra:
Commutative property- Associative property
- Distributive property
- Disproving a property by a counter-example
- Negation vs subtraction. Negation is a unary operator (takes one number) and gives its negative. Subtraction is a binary operator (takes two numbers) and returns the difference. They happen to use the same symbol '-' but they are different things.
Student Difficulties:
  • Thinking in terms of equations
  • Generalizing distributive property to arbitrary operators.
  • Download PDF
  • Note: There are some hints in the end of the file. Try to solve first without looking at them.
Notes:You can access video resources at:
Videos related to today's session are the first four videos of chapter 1.

Division M1 session on March 13, 2016

Instructor:Mr. Zia Hydari
Attendance:AbdulRafay, Sohaib, Abiha, Abdul Qadir
(not present: Adeel, Rami, Kamal) 
Problems Solved in Class:All exercises from section 1.2.
Concepts:Commutative, associative, and identity for addition operator
Student Difficulties:
  • Avoiding unnecessary computations. 
  • Working out the problems step-by-step.
  • Using mathematical vocabulary e.g. commutative property in explaining solution.
  • Identity for addition.
Notes:You can download the handout for Section 1.1 and 1.2 from

Thursday, March 10, 2016

Feb 28, 2016—Math Contest

No classes—students participated in Math Contest. The winners were announced on March 6th:

M2: Basir, Omar
M1: Bilal M, Abdur-Rafay
E:   Abiha