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

Division M1 session on March 6, 2016

Instructor:Mr. Isa Hafalir, Mr. Zia Hydari
Attendance:AbdulRafay, Adeel, Bilal, Remy, Sohaib, Areej
Problems Solved in Class:MOEMS Volume 3 p. 73: 3C, 3D, and 3E
MOEMS Volume 3 p. 74: 4D, 4E
From the contest on Feb 28th:  1, 2, 4, 5, and 6.
Concepts:Mean, median, mode. Percent change. Area. Congruent shapes.
Student Difficulties:
Homework:MOEMS Volume 3 p. 75 (all problems from Set 10 Olympiad 5). Due date is March 20th.