Division M2 Session 5/8/2016

Instructor:	Mr. Ahmed Hefny
Attendance:	Adan, Omar, Areej
Handout:	Pre-Algebra Chp 2
Problems Solved in Class:	Chosen exercises from chapter 2
Concepts:	* 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.
Homework:	· 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
Notes:

Division M1 session on April 17, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Sohaib, Abiha, Abdul Qadir, Adeel, Rami, Kamal
Handout:	Pre-Algebra http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf
Problems Solved in Class:	Problems illustrating the distributive property
Concepts:	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.
Homework:	·         Read Section 1.1, 1.2, and 1.3 ·         Watch all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra ·         If you need more help, please watch the following videos and work through the online exercises at: o    https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/commutative-law-of-addition o    https://www.khanacademy.org/math/pre-algebra/order-of-operations/ditributive_property/v/the-distributive-property ·         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)
Notes:

Division M1 session on April 10, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Sohaib, Abiha (Abdul Qadir?, Adeel?, Rami?, Kamal?)
Classwork:	Problems illustrating the distributive property
Homework:	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

Instructor:	Mr. Isa Hafalir
Attendance:	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.

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.
Homework:	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: https://www.artofproblemsolving.com/videos/prealgebra 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)
Handout:	Pre-Algebra http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf
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.
Homework:	Read Section 1.1 and 1.2. Watch all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra Solve all of the exercises and problems from Section 1.1 and 1.2
Notes:	You can download the handout for Section 1.1 and 1.2 from http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf

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
Handout:
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.
Notes:

Division M1 session on Feb 21, 2016

Instructor:	Mr. Isa Hafalir, Mr. Zia Hydari
Attendance:	AbdulRafay, Adeel, Bilal, Ramy, Sohaib, Areej
Handout:	MOEMS Vol 3, pp. 72–85 (please bring this handout to every class)
Problems Solved in Class:	MOEMS Volume 3 handout: All problems on p. 72 From Geometry Chapter 2 handout: 2.44, 2.45, 2.53, 2.54,
Concepts:	Angles, parallel lines, triangles (esp. exterior angle), counting, greatest common divisor
Student Difficulties:	Not counting systematically. Proofs.
Homework:	Finish all problems from Geometry Chapter 2 handout If you face any difficulties, please make sure that you complete the old homework on Khan Academy missions: Lines, Angles, Shapes
Notes:	CONTEST on Sunday Feb 28th. To prepare for the contest, please make sure that you have solved all problems in Geometry Chapter 2 handout. There will be additional problems similar to the ones in the MOEMS handout.