On the day before the lesson, distribute the Find a Cliché activity sheet. Instruct each student as homework to find a cliché or familiar phrase that is familiar, appropriate, and at least 5 words. Preferably, each student's phrase should be different from every other student's phrase, so encourage students to search for a unique cliché. Do not share the purpose of this homework.
As the students enter class, collect the cliché homework exercise. Quickly sort through the clichés to make sure they are appropriate and familiar, and remove any duplicates. Because students will be working in pairs, you will only need half as many clichés as you have students. You also may wish to have a few extra clichés of your own to add to the collection to make sure that each pair gets a unique cliché.
Ask: "What is a proof?" Through discussion, students should recognize that a proof is a group sentences leading to a conclusion. Remind students that those sentences create a chain of logically valid deductions using agreed-upon assumptions, definitions, or previously proven statements. Typically, a proof is used to show that the concluding statement must be true. Clarify that a proof is a presentation tool, not a solution method for a problem. In problem solving, the goal is to carry out appropriate, logical steps to find unknown values or a solution. In a proof, the conclusion is already known. The goal is to assemble supporting statements to make a convincing argument that the conclusion is correct.
A joke can be similar to a proof. Jokes are often a chain of statements called the "setup" that are used to reach an unexpected conclusion called a "punch line." The punch line should be surprising but familiar. In this exercise, you will be writing a joke that has the same structure as a paragraph-style proof. Show the Jokes as Proofs overhead to reinforce this comparison.
Group the students into pairs, allowing them to create their joke collaboratively. Distribute the Jokes as Proofs activity sheet and one cliché to each group. Students should not get their own cliché so they can later find humor in how someone modified it. Have students record their cliché for Question 1.
Explain that just as the conclusion of a proof is usually known before the proof is created, they will begin by creating the punch line of the joke. Warn students not to modify the cliché so much that the resulting sentence is incomprehensible or does not sound like the original cliché. For example, "Don't cry over spilled milk" could become "Don't lie over milled silk." It sounds like the original sentence and has the same number of words and syllables, but is slightly altered to give it an entirely new meaning. The phrase "Phone cry clover filled bilk" should not be used because it doesn't make sense as a sentence. Also, "Don't cry over spoiled mints" wouldn't work either because it doesn't sound similar enough to the original sentence. They also need to be careful to modify the cliché enough to make it interesting. You also may want to remind them to keep their jokes appropriate.
Next have students write the setup to the joke, creating a story in which the modified cliché (the punch line) is the conclusion. Like a proof, in which every premise is necessary to reach the conclusion, every sentence in the setup should lead the reader directly to the punch line. Also like a proof, in which every part of the conclusion is explained, the story should justify every part of the punch line.
Explain that when they are done, students will have successfully written a joke in a form analogous to a paragraph-style proof. While it may be funny to extend the joke when telling it to make it longer and heighten the imagery and suspense, this joke should be succinct like a proof. If done correctly, every sentence in the setup will be required. That is, the omission of any sentence would cause the punch line to make less sense.
Ask groups to exchange and edit each other's jokes to make them more concise. The goal is to have the shortest collection of premises reach the same conclusion, while still justifying every element of the conclusion.
When they have finished, have the students read the jokes to the class. Depending on the size of your class or the amount of time you have, you may want to limit the joke reading to a few volunteer groups. Reiterate that a proof is different from problem solving in that a proof is a presentation tool and that the conclusion is known before the proof is written.
