TABLE1.3:
Symbolic Form Example
Conditional p⇒q
Inverse :p⇒:q
Converse q⇒p
Contrapositive :q⇒:pSpend time reviewing example one on page 85 as a class. Stress the importance of counterexamples.
Interactive Lesson! Use the same setup as the opening activity when discussing biconditionals. Begin with a
definition, such as example one on page 86. Set up your magnetic phrases in if and only if form, then illustrate
to students how the biconditional can be separated into its conditional and converse.
Deductive Reasoning
Pacing:This lesson should take one class period
Goal:This lesson introduces deductive reasoning. Different than inductive reasoning, deductive reasoning begins
with a generalized statement, and assuming the hypothesis is true, specific examples are deduced.
Differentiate between deductive and inductive reasoning to students by linking to the previous lessons. Deductive
reasoning begins with a conjecture (hypothesis) and infers specific examples.
Stress example 5 with your students. Students can get confused with the inverse and contrapositive from the previous
lesson that they make the mistake of using faulty reasoning.
When determining the truth value ofp∧q, students may be confused as to why the value is false if the hypothesis is
false. Offer students a real life example. “If it is snowing, then it is cold.” If the hypothesis is already false, stress
that it doesn’t matter the conclusion; the statement is not applicable.
Be sure the students understand the difference between∧(exclusive)∨and (inclusive) before filling out the truth
tables.
Real World Application!Show a portion of an episode of a courtroom drama scene. Ask students to apply the ideas
of deductive and inductive reasoning to the lawyers. Determine which reasoning the prosecuting attorney is using.
Is it different reasoning than what the defending attorney uses?
Algebraic Properties
Pacing:This lesson should take one class period
Goal: Students should have some familiarity with these properties. Here we can extend algebraic properties to
geometric logic.
Fun Tip!Construct “I have, who has” cards for your class. Using the properties from this lesson (and other lessons
if you have a large class), create as many cards as students in your class. The first card should read, “I have Reflexive
Property of Equality. Who has the property that states ifa=b, thenb=a?” The next card should state, “I have
the Symmetric Property of Equality. Who has...? Continue this process until the last card. The “Who has” of this
card should state, “Who has the property that a equals a?” Shuffle the cards and give one to each student. Because
the cards are all connected, it doesn’t matter who starts. Time the class and then challenge the students to beat
their previous time. Not only does this increase listening in the classroom, but it also reinforces the properties and
encourages active participation.
Chapter 1. Geometry TE - Teaching Tips