M2: https://goo.gl/17XRbN
Postscript: AMC 8 Prep Sessions during Fall 2016
Instructor:

Mr. Ahmed Hefny

Attendance:

Adan, Omar, Areej

Handout:

PreAlgebra 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:

Instructor:

Mr. Zia Hydari

Attendance:

AbdulRafay, Sohaib, Abiha, Abdul
Qadir, Adeel, Rami, Kamal

Handout:


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:
·
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:

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

Instructor:

Mr. Isa Hafalir

Attendance:

AbdulRafay, Abiha, Rami

Classwork and Homework

In the first half, we did PreAlgebra 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.

Instructor:  Mr. Ahmed Hefny 
Attendance:  Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar 
Handout:  PreAlgebra 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(BA) [P(BA) is the probability of B happening given that A happened. P(BA) = 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 inclusionexclusion principle for counting the union of two sets] [Session 2] Prealgebra:  Commutative property Associative property  Distributive property  Disproving a property by a counterexample  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: 

Homework: 

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. 
Instructor:  Mr. Zia Hydari 
Attendance:  AbdulRafay, Sohaib, Abiha, Abdul Qadir (not present: Adeel, Rami, Kamal) 
Handout:  PreAlgebra http://aopscdn.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: 

Homework: 

Notes:  You can download the handout for Section 1.1 and 1.2 from http://aopscdn.artofproblemsolving.com/products/prealgebra/exc1.pdf 