The activities 4 and 5 were designed to
-
begin the exploration of the cardinality of the rational
numbers,
-
provide the surprising experience of making a one-to-one
correspondence between the natural numbers and the set of all pairs of natural
numbers (i.e., the proper fractions without reduction to minimal form), and
-
expose the children to a set which cannot be enumerated in
ascending order,
-
challenge the students by guiding them to construct the
rational numbers greater than 1 while simultaneously operationalising a
one-to-one mapping with the rational numbers less than 1, and
-
encourage the students to reflect on the relative size of these
two sets.
A simpler and more modular enumeration of
the rational number than Cantor's.
Live Demo
title | why | what |
why toontalk |
activities |
rationale 1 | activity 1 | findings 1 | rationale
4/5
| activity 4 |
activity 5 | findings 4/5 | rationale 8 |
activity 8 |
findings 8 | conclusions
