Converse, Inverse, Contrapostive Exploration

Converse, Inverse, Contrapostive Activity from Sam Shah and PCMI

I wanted to introduce Converse, Inverse, and Contrapositive in a way that had students discover what they were before I introduced them to any new vocab.  This activity is aweome!!!

I started out by letting students pick their own  partner. Each group had two small charts, an “if-then” sheet, 1 manilla folder (my Ss actually thought I misprounounced vanilla), two markers, and one directions sheet.  I next walked around and handed each group three cards. Once card had the conditional statement writen in black sharpee. The next card had a hypothesis written on one side in green and the negation of the hypothesis on the other side in purple. The last card had the conclusion written on one side in green and the negation of the conclusion on the other side in purple. I glued together two index cards to create these cards because the sharpee markers bled through the card. I reccomend telling your students NOT to tear the cards or you should lamenate your cards together. Even with this warning I had students trying to seperate the card.

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Next I had students following directions on the sheet. They had to identify the conclusion and hypothesis for the original statement and correctly order their green cards on the if-then chart. They had to identitfy if the statement was true or false. I then had them switch the order and record what they saw on their small chart (hypothesis, conclusion, what happened compared to conditional, truth value). I then had them put the cards back to where they started and had them turn them over to the purple sides. I had them move them around so they discovered Converse, Inverse, and Contrapositive. I then had them copy their four statements and truth values onto their manilla folder. I also had them make a row for the “name” but told them to leave it blank.

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I gave them 25 minutes to do this. When they finished we came together and filled out a chart together and I introduced them to the names of the things they were doing. I also gave them ways to

Students then passed around their folders to other groups so they could see other examples. I LOVED this activity. I think that it was a great engaging way to introduce Converse, Inverse, and Contrapositive.

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