Monday, April 18, 2016

Division M1 session on April 17, 2016

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:



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