Transcript geo 1.1 & 1.2 session 1

Informal Geometry A
Mr. L. Lawson
Please fill out your student
information sheet.
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
Worksheet
1.1 & 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)
Goal 1: Find and describe patterns
Inductive Reasoning
Making a conclusion based on a
pattern of examples or past events.
We will look at
patterns with
numbers and shapes.
Example 1: Find the next 3 terms of the
sequence.
33, 39, 45, …
Answer: 51, 57, 63
I’ll look at
adding or
subtracting the
(add 6)
numbers 1st.
Example 2: Find the next figure in the
pattern.
Look at the
colors and
that dot.
Answer:
Goal 2: Use Inductive Reasoning
* Look for a Pattern
* Make a Conjecture based on
your observations
* Verify the Conjecture using
logical reasoning
Conjecture
A conclusion that you reach based on
observations (a pattern).
Conjecture is like an educated guess.
For example, if a number of
dark clouds cover the sky
and the wind picks up, one
might 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
posfor
int:a1 + 3 = 4
Look
pattern
Sum first three odd
pos int: 1 + 3 + 5 = 9
Sum first four odd pos int: 1 + 3 + 5 + 7 = 16
Conjecture
Example 3: Complete the Conjecture:
The sum of the first n
n odd positive
n2
integers is ___________.
2
=1
First odd positive integer: 1
Sum first two odd pos int: 1+3 = 4 =22
Sum first three odd pos int: 1+3+5=9 =32
Sum first four odd pos int: 1+3+5+7=16 =42
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.”
Line
• 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
Names of these lines:
COLLINEAR Points
lie on the same line
NONCOLLINEAR Points
do NOT lie on the same line
Example
A
D
• Points D, B, & C
are in a straight
line so they are
_______________
C
B
E
• Points A, B, & C
are
________________
Plane
• 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.
Names of these
planes:
M
COPLANAR Points
lie in the same plane
NONCOPLANAR Points
do NOT lie in the same plane
Line
Segment
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
Name of these segments:
Name of segment
from 3 to 0.
Ray
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
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.