Teaching Module: Countability

Target

Time spent

Brief Description

Content

Teachers’ Guide

Form 4-7 students who are interested in mathematics.

1.5 hours for each lesson.

In this module we attempt to guide students to explore the infinite by first introducing to them the notions of sets and mappings. This is followed by the concept of countability and some related applications.

The module consists of a total of 8 lessons. In lesson 1 the notion of sets is introduced and vast amounts of examples are given. In lessons 2 and 3 students are guided to compare the “size” of sets, along which the notions of one-to-one correspondence and mappings are introduced. After that we put forward the concept of countability in lessons 4 and 5 as a first step to deal with the infinite, where students will be guided to appreciate how infinite sets differ considerably from finite ones. Some further applications and explorations of countability will be dealt with in lessons 6 to 8. In particular, we will show that there can be no set with “maximum size” .

The teachers’ guide of this teaching module is avaliable here.