Transcript Agenda - Greer Middle College Charter

EQ: What is a proof?
Agenda
 Warm Up/Check Homework/Turn in T.H.T.
 Talk about Parent Portal
 Quiz on Conditionals and POE’s
 Notes on Proofs
Homework
 RELAX
On your paper write a story that connects the following
streams of pictures. (1 sentence per picture)
1)
2)
3)
1.
If an animal is a turtle, then it is a reptile.
2.
Hyp.: an animal is a turtle ; Con: it is a reptile
3.
4.
If an animal is a reptile, then it is a turtle. False,
counterexample: snake, alligator, lizard
5.
If you see bees, then flowers are blooming.
If flowers are blooming, then it is warm.
If it is warm, then it is spring.
6.
Conditional: If I am a high school sophomore, then
I am in the 10th grade. (True)
Converse: If I am in the 10th grade, then I am a
high school sophomore. (True)
7.
Conditional: If an angle measures 130, then it is
an acute angle. (False; 130 is obtuse) Converse:
If an angle is acute, then it measures 130.
(False; 45 is an acute angle)
8.
Division Property of Equality
9.
Symmetric Property of Equality
10.
Transitive Property of Equality
11.
Subtraction Property of Equality
12.
Subtraction Property of Equality
13.
Substitution Property of Equality
14.
15.
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A proof is a convincing argument that
something is true.
A proof is simply stating how you found your
answer.
In math, a proof starts with things that are
agreed on.
• Theorems
• Postulates or axioms
Logic is used to reach a conclusion
 The
pictures are the “benchmarks” of the
story.

In a proof we call these the “statements”
 The
sentences you wrote linked the pictures
together to create a full story.

In a proof we call these the “reasons”
•
A proof is a convincing argument that
something is true. Proof = Your Story (pic + sent.).
Were your stories convincing
argument for why those pictures are
connected?
•
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In math, a proof starts with things that are
agreed on.
Theorems and Postulates = Your Sentences.
Would someone reading your story agree that
• Theorems
your sentences successfully connected the
• Postulates pictures to one another?
Logic is used to reach a conclusion
Did you use logic to connect your pictures or
did you make up crazy fanciful stories?
•
Some proofs follow a prescribed form and are
called formal proofs.
• Two-column Proofs
• Paragraph Proofs
• Flowchart Proofs
• Coordinate proofs
• Table Proofs
Picture (Statement)
Sentences (Reasons)
1.
Timmy and his mom get
in the car and start
driving.
2.
Timmy’s mom takes him
to the zoo where they
see the elephants.
3.
After the zoo Timmy’s
mom takes them to get
ice cream.
Statement
5x + 4 = 24
5x = 20
x=4
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Reason
Given
Straction
Dion
Property of Equality
Property of Equality
Each statement on the left is given a justification in the
column on the right.