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.

Standards Addressed:

Grade 10

Process Skills

The student demonstrates an ability to problem solve.

The student demonstrates an ability to use logic and reason.

Grade 3

Process Skills

The student demonstrates an ability to problem solve.

The student communicates his or her mathematical thinking.

The student demonstrates an ability to use logic and reason.

Grade 4

Process Skills

The student demonstrates an ability to problem solve.

The student communicates his or her mathematical thinking.

The student demonstrates an ability to use logic and reason.

Grade 5

Functions and Relationships

The student demonstrates an ability to use logic and reason.

Process Skills

The student demonstrates an ability to problem solve.

The student communicates his or her mathematical thinking.

The student demonstrates an ability to use logic and reason.

Grade 6

Process Skills

The student demonstrates an ability to problem solve.

The student demonstrates an ability to use logic and reason.

Grade 7

Process Skills

The student demonstrates an ability to problem solve.

The student demonstrates an ability to use logic and reason.

Grade 8

Process Skills

The student demonstrates an ability to problem solve.

The student demonstrates an ability to use logic and reason.

Grade 9

Process Skills

The student demonstrates an ability to problem solve.

The student demonstrates an ability to use logic and reason.

Fifth Grade

Operations and Algebraic Thinking

Analyze patterns and relationships.

Fourth Grade

Operations and Algebraic Thinking

Generate and analyze patterns.

Grades 6-8

Algebra

Understand patterns, relations, and functions

Use mathematical models to represent and understand quantitative relationships

Grades 9-12

Algebra

Understand patterns, relations, and functions

Use mathematical models to represent and understand quantitative relationships

Technical Mathematics I

Number and Operations

Competency Goal 1: The learner will apply various strategies to solve problems.

Reason for Alignment: This lesson brings all the Venn diagram activities together with some thorough discussions on sets and Venn diagrams specifically. There is a good worksheet as well. The discussions in the lesson do get to the main points of the textbook better than the activities would alone.

Student Prerequisites

Arithmetic: Students must be familiar with the following concepts:

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

Key Terms

element

A member of or an object in a set

set

A set is a collection of things, without regard to their order

Venn Diagram

A 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

Focus and Review

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

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.

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.

Teacher Input

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

Ask students how sets and Venn Diagrams are interrelated.

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.

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.

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.

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.