4.2 Reasoning and Proof
Inductive Reasoning
I.SectionObjectives
- Recognize visual patterns and number patterns
- Extend and generalize patterns
- Write a counterexample to a pattern rule
II.MultipleIntelligences
- Include group work in this lesson. Rather than explaining all of the information in the lesson and then assigning
group work, intersperse the group work with the lesson. - Begin by going over visual patterns.
- Then have students work in pairs. Each student draws a visual pattern. Then they exchange papers with their
partner. Our next step is to write a rule for the pattern they have been given, and to extend the pattern two
steps. - Next, go over number patterns.
- Then have the students work in pairs. Each student writes a number pattern. Then they exchange papers with
their partner. Our next step is to write a rule (an equation) for the number pattern and to extend the pattern two
steps. - Finally teach about conjectures and counterexamples.
- Have students work with the patterns that they have previously worked with and write a conjecture and a
counterexample for each pattern. - Multiple Intelligences- linguistic, logical- mathematical, bodily- kinesthetic, spatial- visual, interpersonal,
intrapersonal
III.SpecialNeeds/Modifications
- Write all vocabulary on the board. Request that students copy this information down in their notebooks.
- Vocabulary
- Conjecture
- Counterexample
IV.AlternativeAssessment
- Collect student papers.
- Review each student’s work to assess understanding.
- Use this to review at the beginning of the next class. You can use different student patterns in the beginning
of the next class to review the previously learned material. - This will be especially helpful to special needs students who require a lot of review to recall previously learned
concepts.
4.2. Reasoning and Proof