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)
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