Saturday, February 4, 2017

Instructor:
Mr. Rameel Rizvi
Attendance:
Aiden, Omar
Material Covered:
Pre-Algebra Chapter 11, 12 (up til and including 12.2)
Problems Solved in Class:
Chosen exercises from chapters 11 and 12
Concepts:
* Covered perimeter of bounded figures. 
  1. For a rectangle, the total perimeter length is given by 2(l + w) where l is the length, w the width
  2. For a circle, this is the circumference, whose length is 2πr with r the radius
* Covered area of bounded figures
  1. For a rectangle, the total area is given by l*w square units, where is the length, the width
  2. For a circle, this is πr^2 with r the radius
  3. For a triangle, this is (1/2)bh where b is the base length and h is the height
* Triangle inequality: For any 3 points A,B,C on a plane, AB + BC >=  AC, and this is only equal for a line
* Pythagorean Theorem: For a right triangle with sides a,b,c we have a^2 + b^2 = c^2
   - Proved this using triangles enclosed in a square
* Special triangles
   - 45-45-90 (side lengths a and a*sqrt(2))
   - 30-60-90 (side lengths a, a*sqrt(3), 2a)
* Briefly covered a quadrilateral known as a rhombus, whose defining property is all sides having equal length. The diagonals of a rhombus bisect the vertex angles (split them in half), and they intersect  perpendicularly (forming right angles). The area of a rhombus can be found by multiplying the lengths of the diagonals and halving the result.
Student Difficulties:
Students seemed familiar to some extent with the shapes covered, but there may have been trouble understanding the proofs that were presented (such as for Pythagoras' Theorem or for the area of a rhombus).
Homework:
Chapter 11: Read chapter summary.
Problems: 11.40, 11.45, 11.47, 11.50

Chapter 12
Problems: 12.1.2, 12.1.5, 12.2.6
Notes:

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