Transcript proof - Greer Middle College

On your paper write a story that connects the following streams of
pictures. (1 sentence per picture)
1)
2)
3)
W
a
r
m
U
P
What is a Proof?
• 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.
• Properties
• Theorems
• Postulates or axioms
• Logic is used to reach a conclusion
How was the warm-up like a proof?
• 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”
What is a Proof?
• 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?
• In math, a proof starts with things that are agreed
on.
Properties/Theorems/Postulates = Your Sentences.
• Properties
Would someone reading your story agree that your
sentences successfully connected the pictures to
• Theorems
one another?
• Postulates
• Logic is used to reach a conclusion
Did you use logic to connect your pictures or did
you make up crazy fanciful stories?
Types of Proofs
• Some proofs follow a prescribed form and are
called formal proofs.
• Two-column Proofs
• Paragraph Proofs
• Flowchart Proofs
• Coordinate proofs
• Table Proofs
Let’s turn our Warm up into a 2Column Proof
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.
P.O.E.’s
• P.O.E. stands for Property of Equality
• There is a P.O.E. for every operation
–
–
–
–
–
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property of Equality
• There are also 4 more P.O.E.’s
–
–
–
–
Substitution Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Example Formal 2-column Proof
Statement
Reason
5x + 4 = 24
Given
5x = 20
Subtraction Property of
Equality
x=4
Division Property of Equality
• Each statement on the left is given a justification in the column
on the right.