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# Warm UP PowerPoint PPT Presentation

Warm UP. On your paper write a story that connects the following streams of pictures. (1 sentence per picture). What is a Proof?. A proof is a convincing argument that something is true. A proof is simply stating how you found your answer.

Warm UP

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### Warm UP

On your paper write a story that connects the following streams of pictures. (1 sentence per picture)

### What is a Proof?

• A proof is a convincing argument that something is true.

• 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.

• In math, a proof starts with things that are agreed on.

• Properties

• Theorems

• Postulates

• Logic is used to reach a conclusion

• Proof = Your Story (pic + sent.). Were your stories convincing argument for why those pictures are connected?

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 2-Column Proof

Picture (Statement)

Sentences (Reasons)

• Timmy and his mom get in the car and start driving.

• Timmy’s mom takes him to the zoo where they see the elephants.

• 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

• 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

• Each statement on the left is given a justification in the column on the right.