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. A proof is simply stating how you found your answer.

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Warm UP

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Warm up

Warm UP

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


What is a proof

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

    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 proof1

    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?

    Properties/Theorems/Postulates = Your Sentences. Would someone reading your story agree that your sentences successfully connected the pictures to one another?

    Did you use logic to connect your pictures or did you make up crazy fanciful stories?


    Types of proofs

    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

    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.’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

    Example Formal 2-column Proof

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


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