Class Summary - 9/25/16

Instructors:	Mr. Rameel Rizvi
Attendance:	Aidan, Areej, Ayyan, Omar, AbdulRafie
Homework:	Read: Chapter 1.8 (this is a review of all main concepts covered in Chapter 1); Problems to solve (found at end of Chapter 1, "Review Problems"):  1.42, 1.50, 1.54, 1.56, 1.67, 1.68, 1.69, 1.71
Challenge Problem:	1.75 (please attempt this! good practice for AMC 8)
Class Activity:	Covered chapters 1.6 up to 1.8
Concepts:	More review of arithmetic properties. Highlighted how Gauss' formula for sum of first n positive integers is a result of addition being commutative and associative. Introduced idea of division with the definition of the reciprocal, the number r such that for a given number x, xr = 1. Showed that by definition 0 cannot have a reciprocal (as for any number x we have that 0x = 0), and that for all other numbers x, r = 1/x. Also showed that division is neither associative nor commutative (like subtraction), and performed some calculations step-by-step using the definitions we learned (reciprocals, commutativity, associativity, distributivity, prime factorization) rather than through the more quick, direct approach (for example, by changing division by 7 to multiplying by 1/7, the reciprocal of 7, even though we are all capable of directly dividing by 7).
Student Difficulties:	As can be expected, approaching calculations with definitions rather than through the rote methods taught in elementary/middle school is very new to the students. It will take time to process how all of mathematics is essentially built off a set of axioms, which few students this young comprehend.
Notes	Please hand-in your homework solutions, written in a consistent notebook, in the next class.

Class Summary - 9/18/16

Instructors:	Mr. Ahmed Hefny
Attendance:	Aidan, Areej, Ayyan, Omar, AbdulRafie
Homework:	"Art of problem solving" Exercises:  1.2.1, 1.2.4, 1.3.1, 1.3.7, 1.4.2, 1.4.3, 1.5.10, 1.5.11,
Class Activity:	Covered chapters 1 up to 1.5
Concepts:	Review of arithmetic properties (commutative, associative, distributive, identity element and inverse).
Student Difficulties:	Students are still facing difficulties in abstraction and reasoning with symbols, but they are getting better at it.
Notes	Please hand-in your homework solutions in the next class.