5.2 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.ProblemSolvingActivity-Pascal’sTriangle
- Students are going to work with a diagram of Pascal’s Triangle for this activity.
- Pascal’s Triangle is Figure02.01.01
- http://en.wikipedia.org/wiki/Pascal%27s_triangle
- Student are going to problem solve to find a rule to Pascal’s Triangle.
- Have students work in small groups.
- They can use color on the triangle to point out different patterns.
- Allow a lot of time for the students to explore the patterns of the triangle.
- Ask them to use the Wikipedia pattern to write the rule for the triangle.
- Once they have the rule, they need to write the next two rows of the triangle.
- Then demonstrate two ways that you know that your rule is accurate.
- Finally, write a conjecture and a counterexample for the rule.
- Allow time for student sharing.
III.MeetingObjectives
- Students will recognize visual patterns and number patterns.
- Students will be required to extend and generalize patterns in Pascal’s Triangle.
- Students will write conjectures and counterexamples of their rule.
IV.NotesonAssessment
- Do some independent study on Pascal’s Triangle prior to completing this activity.
- Ask leading questions if students are stuck, but refrain from offering solutions.
- Encourage students to help each other with the patterns if they are having difficulties.
Conditional Statements
I.SectionObjectives
- Recognize if- then statements.
- Identify the hypothesis and conclusion of an if- then statement.
5.2. Reasoning and Proof