View
217
Download
0
Category
Preview:
Citation preview
Please fill out your student information
sheet.
Informal Geometry AMr. L. Lawson
Agenda Session 1
• Call Roll & Info Sheets (take up course verification forms)
• Introductions• Class policies & procedures
– Syllabus– Pacing guide
• Assignment #1• Notes (1.1 & 1.2)• Assign HW
Worksheet1.1 & 1.2
• Make sure you put your name on your paper.
• Work quietly by yourself.• Complete all that you can• Hang on to it if you finish before
we begin notes
Informal Geometry A
Session 1
(notes)
Inductive Reasoning
Making a conclusion based on a pattern of examples or past events.
We will look at patterns with
numbers and shapes.
Goal 1: Find and describe patterns
Example 1: Find the next 3 terms of the sequence.
33, 39, 45, … I’ll look at adding or
subtracting the
numbers 1st.
Answer: 51, 57, 63 (add 6)
Example 2: Find the next figure in the pattern.
Look at the colors and that
dot.
Answer:
* Look for a Pattern* Make a Conjecture based on your observations* Verify the Conjecture using
logical reasoning
Goal 2: Use Inductive Reasoning
Conjecture
A conclusion that you reach based on observations (a pattern).Conjecture is like an educated guess.
For example, if a number ofdark clouds cover the skyand the wind picks up, onemight conjecture that …
It might rain
Conjecture
Example 3: Complete the Conjecture:
The sum of the first n odd positive integers is ___________.
First odd positive integer: 1
Sum first two odd pos int: 1 + 3 = 4
Sum first three odd pos int: 1 + 3 + 5 = 9
Sum first four odd pos int: 1 + 3 + 5 + 7 = 16
Look for a pattern
Conjecture
Example 3: Complete the Conjecture:
The sum of the first n odd positive integers is ___________.
First odd positive integer: 1
Sum first two odd pos int: 1+3 = 4
Sum first three odd pos int: 1+3+5=9
Sum first four odd pos int: 1+3+5+7=16
=12
=22
=32
=42
n
two
three
four
n2
Conjecture
An important part of a conjecture is that they are NOT always correct.
For example, after losing a lot of money in the slot machines, a person is likely to say, "I will win the next time" .... unfortunately this conjecture is usually wrong.
Counterexample
It only takes 1 false example to show that a conjecture is not true.
Example 4: Find a counterexample for these statements…
All dogs have spots.
All prime numbers are odd.
Point•Has no size, no dimension• Is represented by a dot•Named by using a capital letter
We would call this one “point E.”
• Has one dimension• Is made up of infinite number of points
and is straight• Arrows show that the line extends
without end in both directions• Can be named with a single lowercase
cursive letter OR by any 2 points on the line
• Symbol
Line
Names of these lines:
COLLINEAR Pointslie on the same line
NONCOLLINEAR Points
do NOT lie on the same line
Example
• Points D, B, & C are in a straight line so they are _______________
• Points A, B, & C are ________________
AB
C
D E
• 2 dimensions• Extends without end
in all directions• Takes at least 3
noncollinear pts. to make a plane
• Named with a single uppercase script letter or by 3 noncollinear pts.
Plane
Names of these planes:
M
COPLANAR Pointslie in the same plane
NONCOPLANAR Points
do NOT lie in the same plane
• Is straight and made up of points• Has a definite beginning and definite
end• Name a line segment by using the
endpoints only• You will always use two letters to
name a segment• Symbol
Line Segment
Name of these segments:
-2 -1 0 1 2 3 4 5A
B C
D E
F G H
Name of segment from 3 to 0.
• Is straight and made up of points• Has a beginning but no end• Starting pt. of a ray is called the endpoint• Name a ray by using the endpt. 1st and
another point on the ray• You will always use two letters to name a
ray• Symbol
Ray
Names of these rays:
Homework
Finish the Worksheet!
Journal (session 1)
• Think of a teacher you have had in the past that was a very good teacher.
• Describe your ideal math teacher.
• Do not turn this in today. Keep it with you and put it in your notebook.
Recommended