Download Calculus Fall 2010 Lesson 01

1
Lesson Plan #001
Class: Geometry
Date: Friday September 7th, 2012
Topic: Points, lines, and planes
Aim: What are points, lines and planes?
Objectives:
1) Students will be able to describe what is a point, a line, and a plane
HW# 1:
Answer the questions on the attached sheet on page 4.
Do Now: Test your skills on the following problems:
1) x  9  9  x is an example of which property?
A) associative property of addition
C) commutative property of addition
B) additive identity
D) additive inverse
2) 2( x  3)  2 x  6 is an example of which property?
A) associative property of multiplication
C) commutative property of multiplication
B) distributive property
D) multiplicative inverse property
3) x  ( y  3)  ( x  3)  y is an example of which property?
A) associative property of addition
B) distributive property
C) additive identity
D) commutative property of addition
4) (5 y )  (1)  5 y is an example of which property?
A) multiplicative identity property
C) commutative property of multiplication
B) multiplicative inverse property
D) associative property of multiplication
5) ( xy) z  x( yz ) is an example of which property?
A) commutative property of multiplication
C) distributive property
B) associative property of multiplication
D) multiplicative inverse property
6) ( x  5)(7  x)  ( x  5)  7  ( x  5)  x is an example of which property?
A) associative property of addition
B) commutative property of multiplication
C) associative property of multiplication
D) distributive property
7) ( y  2)  ( y  2)  0 is an example of which property?
A) multiplicative identity property
B) additive identity property
C) multiplicative inverse property
D) additive inverse property
 1 
  1 is an example of which property?
 2x 
8) 2 x  
A) multiplicative identity property
C) commutative property of multiplication
B) multiplicative inverse property
D) associative property of multiplication
9) Determine which equation illustrates the commutative property.
A) a  0  a
B) a  (b  c)  (a  b)  c
C)
ab  ba
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Go over the Do Now
D) a (b  c)  ab  ac
2
A point represents a location, often denoted with a dot, although it has no length, width or thickness. Usually represented with a
capital letter, for example point P or  P
A line is an infinite set of points that extend endlessly in opposite directions. The line has no
thickness. Its length is infinite. A line is named by listing two points that are on the line. For
example, consider the line shown with the indicated points.
How can this line be named?
A
B
C
A line is also sometimes named using a lower case letter
A plane is a set of points that forms a complete flat surface and extends in all
directions indefinitely. It has no thickness. Although it has no edges, we
usually denote it with a 4-sided figure often labeled with a capital letter or 3
letters on the plane representing points on the plane not on the same line.
Although we have described a point, line, and a plane, they are considered to be undefined terms. These undefined terms are then
used in the definition of other terms.
A definition is a statement of precise meaning of a term. We must define a word or term in words that have been defined or
accepted as undefined terms such as a point, line, or plane.
Definition: A collinear set of points is a set of points all of which lie on the same straight line.
Definition: A non-collinear set of points is a set of 3 or more points that do not all lie on the same
straight line.
Definition: A coplanar set of points is a set of points all of which lie on
the same plane.
Sample Test Question:
Choose the correct statement/statements.
1. Points F, A, L, I, C, G, E, O, and B are coplanar.
2. Points G, E, F, and A are coplanar.
3. O, A, and B are coplanar.
4. Points F, A, L, I, C are coplanar.
Choices:
A. 1 and 2 only
C. 4 only
B. 3 and 4 only
D. 1 only
3
4