Type of Class: Honors Geometry 

Related VA SOL: G.1d

Time Frame: 90-minute block period

Objectives:

  • Students will be able to make a conclusion based on a set of logical arguments.
  • Students will recognize when a set of logical arguments will not reach a valid conclusion.
  • Students will know how to convert logical arguments into its logical equivalency in order to “chain” through the statements.
  • Students will be able to create a set of logical arguments that will consist a valid conclusion.

Materials:

  • Colored chalk
  • Paper and pencil
  • Markers/colored pencils
  • Worksheet

Procedures:

    1. Introduce syllogism by showing a clip from the Monty Python and the Holy Grail.
    2. Introduce the formal definition of syllogism and illustrate, symbolically, how a conclusion can be made from the logical arguments.
      1. For example:

p

q

   If the dog chases the cat,

then the cat will run.

q

r

          If the cat runs,

the mouse will laugh.

p

r

\If the dog chases the cat,

then the mouse will laugh.

 

    1. Talk about how the process is similar to the “transitive” property and how you must build a “chain” through the statements to reach a valid conclusion.
    2. From the movie, write out the major premises and see how the characters concluded that the woman is a witch.
    3. Give two or three examples where no conclusion can be made.

a. For example:

p

q

If the television is on,

then the baby will cry.

r

q

If the radio is on,

then the baby will cry.

\No conclusion

 

 

b. For example:

p

q

If the pants are dirty,

then I will not wear them.

p

r

If the pants are dirty,

then I will throw them away.

\No conclusion

 

 

    1. Give an example of using negation to chain through the statements. Remind students that p ® q is logically equivalent to ~q ® ~p
    2. For example:

p

q

If the soda is flat,

then do not drink it.

q

~q

If you buy it,

then drink it.

p

~r

\If the soda is flat,

then do not buy it.

 

    1. Give examples of three or more major premises and have students find the conclusion by “chaining” through the statements.
    2. In groups of three’s, have students work together to reach a conclusion from a long series of premises. Each student will have two or three premises that he/she will work with and will combine to find out the conclusion.

Assessment:
In the same groups, students will come up with their own syllogism and they will exchange with other groups and figure out the conclusion. This is a great opportunity for students to make creative premises, such as writing the sentences in different order, using negation, etc.

Suggestions/Comments:
Though this lesson is created for Honors Geometry, it can be used in other levels of Geometry.