**
Lessons on Sets** |
**Description** |

Introduction |
Students learn that a set is a collection of objects (elements) that
have something in common. We define a set by
listing or describing its elements. |

Basic Set Notation |
Basic notation is used to
indicate whether or not an element belongs to a set. Connections are
made to language arts, science and social studies. |

Types of Sets |
Students learn about finite and
infinite sets, as well as the empty or null set. Roster notation is
used. Connections are made to art, science, and language arts. |

Set Equality |
Students
learn how to determine if two sets are equal. The order in
which the elements appear in the set is not important. Real-world
connections are made with sets. |

Venn Diagrams |
Venn diagrams are used to
represent sets pictorially, and to show relationships and
logical relationships between sets. Intersection and union of overlapping sets
are introduced. |

Subsets |
Venn diagrams are used to show
subsets, with one set contained within the other. The distinction
between subsets and proper subsets is made. The relationship between
equal sets and subsets is presented, as well as how to determine the number of subsets
a given set can have. |

Universal Set |
The Universal set is presented
as the set of all elements under consideration. Complete Venn diagrams are used to represent sets which are disjoint,
overlapping, or one contained within another. Real-world connections
are made. |

Set-Builder Notation |
Set-builder notation is
introduced as a shorthand for writing sets, including formulas, notation and restrictions. Common types of numbers
are defined, including
natural numbers, integers, and real and imaginary numbers. Students are shown why they need set-builder notation. |

Complement |
The complement of a set is
defined and shown through numerous examples. Alternate
notations for complement are presented. Set-builder notation and
Venn diagrams are included. Connections are made to the real world. |

Intersection |
The intersection of two sets is
defined and shown through examples with Venn diagrams. Examples include
overlapping sets, disjoint sets, and subsets. Procedures for drawing
intersections are provided. Real-world connections are made. |

Union |
The union of two sets is
defined and shown through examples with Venn diagrams. Examples include
overlapping sets and subsets. Intersection and union of sets are
compared and contrasted. Connections are made to the real world. |

Practice Exercises |
Students
complete 10 additional exercises as practice, and assess
their understanding of all
concepts learned in this unit. |

Challenge Exercises |
Students solve 10 problems that challenge
their
understanding of sets and set theory. They hone their
problem-solving skills as well. |

Solutions |
Complete
solutions are provided for all exercises presented in this unit. The problem,
step-by-step solutions, and final answer for each exercise are
provided. |