Venn Diagrams

Shodor > Interactivate > Lessons > Venn Diagrams


Students learn how to classify items and numbers on Venn Diagrams using computer applets.


Upon completion of this lesson, students will:

  • understand how Venn diagrams are used
  • have practiced sorting shapes by their characteristics into Venn diagrams.

Standards Addressed:

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag.
    • use a web browser.

Teacher Preparation

  • An opaque bag.
  • Objects in a variety of different shapes, sizes, textures, etc. Objects should have some characteristics in common, consider the following list for an example:
    • a large, soft, red ball
    • a small, hard, yellow ball
    • a large, hard, green ball
    • a small, soft, green ball

Key Terms

Venn DiagramA diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures

Lesson Outline

  1. Focus and Review

    • Have a student reach into opaque bag, touch an item, and describe the item.
    • Have another student write down describing words on the board under a heading of "object 1". Encourage students to use single attributes such as large, small, soft, hard, green, yellow, red, etc. to describe the objects.
    • Repeat process until all the objects in the bag are gone.

  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 learning about Venn diagrams. Venn diagrams are a way of organizing objects, numbers, or even ideas.
    • We are going to use the computers to learn about Venn diagrams and to practice organizing things using Venn diagrams.

  3. Teacher Input

    • If space allows, using two large hula hoops or making circles on the floor using masking tape would be ideal for this activity. If not, see the Alternate Outline for other options.
    • Place the hula hoops on the ground so that they overlap somewhat. Choose two recurring characteristics among the items in the bag. Assign each characteristic to a particular hula hoop. For example: soft and blue.
      • Note: Be sure to choose two categories that will allow some objects to fall into the overlapping areas of the Venn diagram. This will, therefore, exclude characteristics that are opposites of each other.
    • Have students place items into the correct hula hoop, showing them what they're supposed to do when an item has both characteristics.
    • After the students have finished placing all the items in the correct areas of the Venn Diagram, re-label the circles, and rearrange the items into the appropriate sections of the new Venn Diagram.
    • Explain that this method of categorization is done using interconnected circles called Venn Diagrams.

  4. Guided Practice

    • Have the students open their browsers to the Venn Diagram Shape sorter applet.
    • Walk the students through the use of the applet, asking students where each shape should go.
    • Be sure to show students the process they should use for Guess the Rule mode.

  5. Independent Practice

    • Have the students work with the Venn Diagram Shape Sorter applet. Wander around the room to ensure that everyone is on task and understands how to use the applet.
    • You might want to have students begin in Make the Rule mode and switch to Guess the Rule mode as they are ready.

  6. Closure

    Lead the students in a discussion about the lesson. Ask guiding questions such as the following:

    • When did you find it most difficult to use the Venn diagrams? Why?
    • Can you think of other things you could sort using Venn diagrams?
    • How can Venn diagrams help you in other areas besides math?

Alternate Outline

If space in the classroom is limited, the lesson can be organized in either of the following ways:

  • Draw two large interconnecting circles on the board. Have students write the names of the objects into the circles according to the class's classification system.
  • Draw two large interconnecting circles on the board. Use pictures of the objects with magnets on the backs of the pictures to classify the objects. Tape could also be used, if you don't have magnets.

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