Journey to Excellence

Constructivist Lesson Plan Sample 1


Teacher: J. Hagele Date: 16 June 2004
Subject: Math Grade: 4
Topic: Identifying Prime Numbers

Introduction:

Numbers have fascinating relationships between one another. Many mathematicians, such as Pythagoras or Aristotle, have been plagued to define these relationships. They have dedicated many years to studying these numbers. Amazing patterns exist in math such as relationships between lengths of right triangles, adding the digits of any number to determine if it is divisible by three, finding area and volume formulas, and determining derivatives. Grouping numbers and analyzing those groupings help us recognize these relationships.

Objectives:

  • Objective 1: Recognize and define a prime number.
  • Objective 2: Collect and record data.
  • Objective 3: Make conclusions based the data.

Materials:

  • 20 counters per student (perhaps beans or pennies)
  • 1 cup or container for each student
  • Paper and pencil for each student
  • Clear desktop/surface for working
  • Overhead to project example (or draw on chalkboard)

Invitation:

There are many ways that we can categorize numbers. What types of numbers do we know? (Students may list odd/even, positive/negative, counting numbers, fractions, integers, whole numbers . . . )

Exploration:

All numbers can be grouped. Some will have more than one correct way to group them. (Do the first number grouping together. Remember to explore the multiple groupings using a composite number!)

  1. Students place 20 counters in a cup on their workspace.
  2. Students are given a number to practice grouping. (Teacher selects a composite number and writes the number on the board. Try a prime number after students have grasped the grouping concept.)
  3. Students count out the correct number of counters and place them on their workspace. Leave remainders in the cup.
  4. Students then determine a grouping by placing them into even rows.
  5. Students chart the information: Number Value, Number of Possible Groupings.

Explanation:

What did you find out about numbers and groupings? (Students should discover that the size of a number does not correlate with the amount of possible groupings.)

Taking Action:

Explain the concept of prime numbers and composite numbers without using the grouping explanation. Have students re-explain prime and composite numbers using the grouping terminology.

Conclusion:

You have seen that numbers have patterns. You may have noticed prime numbers exist as big numbers and small numbers. The smallest prime number is two. The largest prime number is at infinity. Composite numbers exist both as large and small numbers. The smallest composite number is four. The largest composite number is at infinity. Grouping is the key to determine if a number is prime or composite. These groupings are also known as factors. You are now explorative mathematicians.

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