Sets and the Venn Diagram

Abstract

This lesson is designed to introduce students to the idea of a set and what it means to be contained in a set. Students will experiment with sets in conjunction with the Venn Diagram.

Objectives

Upon completion of this lesson, students will:

• understand the ideas surrounding sets and Venn diagrams.
• be familiar with the terminology used with sets and Venn diagrams.
• understand how to determine the placement of an element in a Venn Diagram.

Student Prerequisites

• Arithmetic: Students must be able to:
  • prime numbers
  • whole numbers/integers/natural numbers
  • constant vs. variable
  • rational/irrational numbers
  • even/odd numbers
  • palindromes
  • square/cubes
• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser for experimenting with activities

Teacher Preparation

Students will need:

• Access to a browser
• Pencil and paper

Lesson Outline

1. Focus and Review

   Introduce students to the concept of sets. Consider leading students in discussions on the topic:

   • The sets discussion introduces the idea of sets and containment in sets.

   If students are already familiar with the concept, consider asking guiding questions to activate prior knowledge:

   • What is an example of a set? [Answers will vary]
   • Let's use whole numbers as an example. What do we call the number 5? [an element of the set of whole numbers]
   • Let's think of another set that will have some (but not all) elements in common with whole numbers. What do we call the elements they have in common? [intersection]

   If students are unable to answer any of the questions, tell them that they will learn more about that in this lesson. Be sure to ask those questions again in the closure.

2. Objectives

   Let the students know what it is they will be doing and learning today. Say something like this:

   • Today, class, we will be talking more about sets and what it means to be an element in a set.
   • We are going to use the computers to learn about sets and Venn diagrams, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about sets and Venn diagrams first.

3. Teacher Input

   You should first lead the students in a short discussion about Venn Diagrams.

   Ask students how sets and Venn Diagrams are interrelated.

   • Show the students the Venn Diagram Shape Sorter applet.
   • Ask students if these Venn Diagrams are dealing with sets as well.
   • Explain to the class (or have students explain to each other) that all Venn Diagrams display different sets, even if the sets do not contain numbers.

4. Guided Practice

   • Open your browser to Venn Diagrams in order to demonstrate this activity to the students.
   • Begin to explain the applet to the students by showing them the first example on the page. Ask the class if they know what the answer is.
   • When a student has responded correctly, show the class that by clicking in the appropriate section of the diagram, the circles representing the sets will change color.
   • Show the students the location of the "Check Answer" button and check the students' answer together.

   Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone describe the steps you will take for this assignment?"

   • If your class seems to understand the process for doing this assignment, simply ask, "Can anyone tell me what you will do now?"
   • If your class seems to be having a little trouble with this process, do another example together, but let the students direct your actions:
     • On the second example (which appears when the first answer is checked), ask the students which section of the Venn diagram the element belongs in.
     • Check the answer with the class and, in the event it is incorrect, have the students suggest reasons for why the answer might be different from the one guessed.

5. Independent Practice

   • Allow the students to work on their own. Monitor the room for questions to be sure that the students are on the correct web site.
   • Since many of the questions are not strictly math-related, explain to the students that they may not know the answers to some of the questions. If this should happen, they should do their best and move on.

6. Closure

   Lead the class in a discussion using the following guiding questions. If students do not give the correct answer the first time, guide the discussion so that they can discover what the correct answer is.

   • Which questions were more difficult? [The ones with words they didn't understand.]
   • Why do you suppose that is? [Answers will vary]
   • What information do you need to be able to answer these questions? [You need to understand how each set is defined in order to know which elements go where in a venn diagram.]

Alternate Outline

This lesson can be rearranged in several ways if only one computer is available for the classroom:

• The teacher may do this activity as a demonstration.
  • As each new Venn diagram is displayed, allow the students an opportunity to decide individually, or in groups, the solution to the question.
  • After an appropriate time, try an answer from a group or individual and discuss why the answer was or was not correct.