Class Summary - 11/6/16

Instructors:	Mr. Rameel Rizvi
Attendance:	Ayyan, Aiden, Omar, Areej, AbdulRafay
Homework:	Read: Chapter 5.6 (this is a review of all main concepts from the chapter--as usual, make sure to do this slowly and thoroughly!); Problems to solve:  5.33 (parts (b) and (d)), 5.34 (parts (b), (d), (f), (h), (j)), 5.36, 5.43, 5.44, 5.51 (all parts), 5.52 (all parts), 5.55, 5.60
Challenge Problem:	Before starting to paint, Bill had 130 ounces of blue paint, 164 ounces of red paint, and 188 ounces of white paint. Bill painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily in equal amounts. When Bill finished, he had equal amounts of blue, red, and white paint left. Find the total number of ounces of paint Bill had left. (Source: AIME II 2009)
Class Activity:	Finished Chapter 5.
Concepts:	Continued where we left off from Chapter 5 in the previous week, reviewing word problems and solving equations of a single variable.  Covered inequalities, which deal with expressions where the left-hand side (LHS) and right-hand side (RHS) are not equivalent. We use "<" (less than) to express the LHS having a value strictly less than the RHS and we use ">" (greater than) to express the LHS having a value strictly greater than the RHS. Sometimes, we may desire a nonstrict inequality, that is, where it's possible for the LHS to be equivalent to the RHS (in addition to being either less than or greater than the RHS, depending on the situation). We denote such a possibility with a horizontal bar immediately underneath the "<" and ">" symbols. We went through various properties of inequalities and showed that a number line can be used to visually represent them: we shade in black the region on the line corresponding to the values that are permitted by the inequality, perhaps stretching out to positive or negative infinity, in which case we draw a shaded arrow in the appropriate direction. For endpoints, strict inequalities require an open circle whereas nonstrict ones require a shaded circle.  We saw that claims about inequalities could be confirmed using number lines. For example, we showed that transitivity holds: if a > b and b > c, then a > c (this works with other inequality variants as well, of course). In addition, if a > b, then a + k > b + k for any k. We also saw that for k > 0, if a > b then ak > bk, whereas if k < 0 and a > b, then ak < bk.
Student Difficulties:	The biggest difficulty seems to be converting word problems to symbolic equations/inequalities to then be solved (rather than actually solving). The best way to deal with this is to think: what variables do I need (often just one), and what constraints am I being given on these variables? Consider constraints step by step and update equations accordingly for every new constraint you read until there are none left. And remember: Always ask yourself, "Does this make sense?"
Notes	Please hand-in your homework solutions, written in a consistent notebook, in the next class.