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:

• have been introduced to the notion of sets and Venn diagrams.
• have learned the terminology used with sets and Venn diagrams.
• have practiced determining the placement of an element in a Venn Diagram.

Standards

The activities and discussions in this lesson address the following NCTM standards:

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots

• discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots

Student Prerequisites

• Arithmetic: Many of the following sets are used in the Venn Diagram applet:
  • prime numbers
  • whole numbers/integers/natural numbers
  • constant vs. variable
  • rational/irrational numbers
  • even/odd numbers
  • palindromes
  • squares/cubes
• Technological Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser, such as Netscape, for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• pencil and paper
• Copies of supplemental materials for the activities:
  • Worksheet To Accompany "Sets and the Venn Diagram"

Key Terms

• set
• element
• Venn diagram

Lesson Outline

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Prompt students with the question, "Can anyone tell me what an integer is?" Have a student think of an example of an integer and tell the class.

   • Ask the students, "Can anyone tell me what whole numbers are?" After a student gives an answer, ask, "Is [the number given as an example for the first question] a whole number?"

   • Tell the students, "So, this number is an element of the set of integers and it is [or is not] a member of the set of whole numbers. Does anyone know what I mean by that?"

   • Relate the material to the students by entertaining a discussion about sets and containment in sets.

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.

   Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.

   • 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.

   • If you choose to, you may pass out the Worksheet.

4. Guided Practice

   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 and to complete the worksheet, should you choose to provide one. Monitor the room for questions and to be sure that the students are on the correct web site.

   • Students may need help with some of the later questions. Not all of the Venn diagram questions are math related. Some relate to science, and some to common knowledge, in order to allow students to practice Venn diagrams more fully. Help the class talk about what an unknown word could be--chances are good that if one student does not know what a word means, someone else in the class will.

6. Closure

   You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outlines

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.
  • The worksheet may still be completed by individuals or in groups.
• Groups may take turns practicing Venn diagrams with the applet for 10 minutes each, and may complete the worksheet afterward.