Illuminations: The Factor Game

# The Factor Game

 The Factor Game Board 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.

The Factor Game is a two-person game in which players find factors of numbers on a game board. To play, one person selects a number and colors it. The second person colors all the proper factors of the first person's number. The roles are switched and the play continues till there are no numbers remaining with uncolored factors. Each person adds up the numbers they've colored. The winner is the person with the largest total.

The purpose of this investigation is twofold: to help students determine whether a given number has many or only a few factors and to show how this property of numbers is useful for problem solving. Part I, Playing the Factor Game, engages students in a friendly contest in which winning strategies involve recognizing the difference between prime numbers and composite numbers. Part II, Playing to Win the Factor Game, guides students through an analysis of Factor Game strategies and introduces the definitions of prime and composite numbers. Part III provides questions that are rich in connections to situations in which factors, multiples, divisors, products, and prime numbers are significant.

This investigation is based on the Factor Game from the Prime Time unit of the Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications, (1996) pp.1-16.

### Learning Objectives

 Students will be able to: classify numbers as prime or composite recognize that some numbers are rich in factors, while others have few factors To recognize that factors come in pairs and that once one factor is found, another can also be found To discover the connection between dividing and finding factors of a number

### Materials

 • Colored pencils and Factor Game Boards (optional)• Overheads of Factor Game Board if being done as a classroom activity• Recording Sheets (optional)

### NCTM Standards and Expectations

 Number & Operations 6-8Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

3 periods

### NCTM Resources

Principles and Standards for School Mathematics

### Web Sites

 More and Better Mathematics for All Students
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