

Objectives
of the Unit

Sample
Overview
Unit 8 Lesson 3
develops the Principle of Mathematical Induction. In this lesson, students
learn how to do proofs by mathematical induction in a precise, yet sensemaking
way. They also consider the Least Number Principle, how it is used in
indirect proofs, and how this proof method compares to proofs by mathematical
induction.
The sample below is Investigation 1, "Infinity,
Recursion, and Mathematical Induction." In this investigation, students
will carry out and develop an understanding of induction proofs. Sometimes,
before the proof begins, students need to decide what to prove. This
is often done by experimenting and looking for a pattern. There are typically
two relevant patterns—a recursive pattern (sometimes expressed
as a recursive formula) and a closedform pattern (sometimes expressed
as a function rule). It is the closedform pattern that is proven with
mathematical induction. The recursive pattern is essential for the induction
step in the induction proof. It is important to note that the recursive
pattern must also be proven, often by reasoning about the context, and
it must be done before using the recursive relationship in the induction
proof.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a fourphase cycle of classroom activities—Launch,
Explore, Share and Summarize, and Apply. This instructional model is
elaborated under Instructional Design.
View the
Unit Table of Contents and Sample Lesson Material
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