Converses and Inverses

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Objective

SWBAT write the converse and inverse of a conditional statement and engage in mathematical practice discourse and precision standards

Big Idea

Students need to understand mathematical logic in order to write formal proofs. This lesson provides an introduction to logic through the context of Alice's Adventures in Wonderland by Lewis Carroll.

Do Now

10 minutes

As the students walk in the room, I hand them a page from the book Alice’s Adventures in Wonderland by Lewis Carroll to read:

Converses and Inverses Do Now

During my unit on transformations, students used examples from Alice... to illustrate transformations. This time, I use the book to show students examples of logical reasoning.  In addition to writing children’s books, Lewis Carroll was a mathematician who specialized in mathematical logic and examples of logical reasoning can be shown throughout the book.

 

 

Mini-Lesson

15 minutes

To begin the Mini-Lesson, we discuss the definition of logical reasoning. Students are able to come up with a basic definition, but are often unaware that logic is a branch of mathematics.  It is helpful to point out how logic relates to MP3 construct viable arguments and critique the reasoning of others. We also discuss how logic is needed to write formal proofs.

The next part of the Mini-Lesson is to go over descriptions of following terms:

  • conditional statement
  • hypothesis
  • conclusion
  • converse
  • inverse

In mathematics these words have different meanings than in some other contexts where students might use them. For example, a scientific hypothesis is a different thing than a mathematical hypotheses. For many of my students, this is the first time using the words in math class. So, I take time here to discuss how the meanings shift between contexts. How are they similar? How do they differ?

Before I ask students work on their own, we will:

  1. Go over some examples of identifying the hypothesis and conclusions of conditional statements
  2. Write the converse and inverse of these conditional statements

Activity

15 minutes

In this activity, students will be work alone to write the hypothesis, conclusion, converse and inverse of conditional statements from the reading in the Do Now.  After 10 minutes, we go over the answers and discuss how the conditionals relate to the reading from the Do Now. 

Summary

5 minutes

For today's Exit Ticket, I ask students to write the converse of the following statement: 

If two sides of a triangle are congruent, then the angles opposite from those sides are congruent.

This introduces students to the Isosceles Triangle Theorem and its converse, which will be further investigated in a later lesson.

Students are given a homework sheet to practice writing more converses and inverses of conditional statements.