## Teaching Prime and Composite Numbers

Prime and composite numbers are among the first very abstract math concepts taught to upper elementary students. Ideally, the lesson is taught after students have mastery of basic multiplication and division skills. Facility with recognition of prime and composite numbers is invaluable for simplifying fractions and other more complex mathematical tasks. After students have been introduced to the ideas of prime numbers and composite numbers, the game outlined in this lesson plan can be used to help them gain confidence, speed and accuracy. It will also help them to explore related ideas such as the frequency of prime numbers and divisibility rules.

## Learning Objectives

Students will:

- define prime numbers as those numbers with two and only two factors: one and themselves.
- define composite numbers as those numbers with more than two factors.
- apply divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11 to identify prime numbers through 100.
- increase the speed and accuracy with which they identify prime numbers.

## Materials and Preparation

Materials needed:

- Duplicated 100 chart for each pair of students
- File folder for each pair of students
- Rubber cement
- Laminator and film
- Markers, stickers, or other decorations for folders
- Wipe off markers
- Number cards 1 through 100 for each pair of players

Preparation:

- Use the rubber cement to affix a hundreds chart inside of each folder. Use a marker to create a scoring sheet on the opposite side of the inside of each folder. This can be a simple grid with a line for each player's name and a blank column for tallying the score for each player.
- Laminate the folders so that students can write on the game board and score sheet then erase after every game.

## Procedure

- Conduct a brief review of prime and composite numbers. Recall that prime numbers have two and only two factors: one and themselves. Recall that composite numbers have more than two factors.
- Review the divisibility rules: Even numbers divide by 2; if the digits add up to 3, 6 or 9, it divides by 3; numbers that yield an even answer when divided by 2 also divide by 4; numbers ending in 5 or 0 are divisible by 5; even numbers that also divide by 3 are divisible by 6; numbers that are still even after three divisions by 2 are divisible by 8; numbers ending in 0 are divisible by 10; and numbers below 100 that have double digits are divisible by 11.
- Review the procedure to analyze numbers using a factor tree if necessary.
- Give directions for the game: Players pair off and take a folder, set of number cards and an erasable marker. Shuffle the number cards and take turns choosing one. Decide if the number is prime or composite by using divisibility rules or factor trees. If the number is prime, mark a "P" on the digits on the 100 chart in the folder. Score 5 points. If the number is composite, mark a C on the correct square of the 100 chart and score 1 point for each prime factor identified using a factor tree. Tally scores at the end of the playing time to determine a winner.
- Evaluate the work of each pair of students by checking the placement of C's and P's on the 100 chart after the game. If a pair of students has an unacceptable number of errors, review the concepts involved in a small group as needed.