Class on 1/15/2017

Instructor:	Mr. Ahmed Hefny
Attendance:	Ayaan, Aiden, Omar
Material Covered:	Pre-Algebra Chapter 10
Problems Solved in Class:	Chosen exercises from chapters 9 and 10
Concepts:	* Review on square roots. * Angles:      - Plane Geometry as an example of axiomatic method.      - Difference between a definition, an axiom and a theorem.      - Points, line segments, rays, lines, angles.      - Highly composite numbers and why we use 60 minutes and 360 degrees.      - Complementary angles, supplementary angles and vertical angles.      - Angles and parallel lines. Remember these 3 patterns:      - Interior angles of convex polygons.          -- Sum of interior angles of a polygon with n vertices.
Student Difficulties:
Homework:	Chapter 10: Please watch the videos and make sure you can solve example problems. Chapter 9: . Solve exercises: 9.2.8,9.3.9. . Solve review exercises: 9.43,9.63 Chapter 10: . Solve review exercises: 10.24, 10.28, 10.37, 10.38, 10.39
Notes:	If you are curious, this website provides a nice exposition of Euclid's Elements. As you can see, everything is based on 10 axioms (called postulates or common notions) from which theorems (called propositions) are derived. The parallel line axiom we discussed today is postulate 5 but is stated a bit differently. Can you see how postulate 5 implies what we said in class ?

Tentative Syllabus

Overview:
This course develops creative problem solving skills for middle school students. For instance, consider the following math problems: 
(i) I have 120 blocks. Each block is one of 2 different materials, 3 different colors, 4 different sizes, and 5 different shapes. No two blocks have exactly the same of all four properties. I take two blocks at random. What is the probability the two blocks have exactly two of these four properties the same? (Source: AIME)
(ii) Prove that √2 (square root of 2) is irrational.

In this course, students will practice solving problems such as those listed above. By the end of this course, students should be able to approach challenging problems (using elementary techniques) and write simple proofs.

Instructors:
Professor Isa Hafalir (http://www.andrew.cmu.edu/user/isaemin/)
Mr. Ahmed Hefny (http://www.cs.cmu.edu/~ahefny/)
Mr. Rameel Rizvi (http://ri.cmu.edu/person.html?person_id=4563)


Location, Dates, Time:
MCCGP 233 Seaman Ln, Monroeville, PA 15146
Jan 8, 2017 to May 14, 2017
Sunday 2:30 pm to 4:30 pm

Text & Topics (tentative)
Prealgebra by Richard Rusczyk, David Patrick, Ravi Boppana

Review & Problem-Solving Strategies
Percents
Square Roots
Angles
Perimeter and Area
Right Triangles and Quadrilaterals
Data and Statistics
Counting

Competition Preparation (time permitting):
AMC 8
MATHCOUNTS
Purple Comet