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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.