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This activity provides an introduction to composite numbers and prime numbers through factorization.
Invitation to Learn
Discovering Mathematics with the TI-73: Activities for Grades 5 and 6, by Melissa Nast; ISBN 1-8886309-22-1
The number one is a unique number because it only has itself as a factor. A prime number is a counting number larger than one that has exactly two factors. The two factors are one and the number itself. A composite number is a counting number that has more than two factors. Each composite number is divisible by three or more whole numbers.
Each composite number can be renamed as a product of prime numbers. This is known as prime factorization. Understanding prime factorization helps students understand the composition and decomposition of numbers.
Prime factorization is a strategy students may employ to find the Greatest Common Factor (GCF) of two or more numbers. Students may also use prime factorization to find the Least Common Multiple (LCM) of two or more numbers. It may be interesting to note that the product of the LCM and the GCF of two numbers is equal to the product of the two numbers themselves.
Invitation to Learn
Pretend you are a detective. What is one piece of evidence that would help you to identify suspects from a crime scene? Fingerprints would be one type of evidence. Every person has a one-of-a-kind fingerprint. Have students make a fingerprint of their right index finger on a Post-it® note. Have students place their Post-it® note on the line plot, matching their fingerprint with one of the nine main patterns pictured on a teacher-made categorical line plot poster. Even though there are nine fingerprint patterns, allow students time to notice that each individual fingerprint is still one-of-a-kind.
Write the following analogy on the board: human is to fingerprint as number is to factorprint. Tell students that just as each human has a one-of-a-kind fingerprint, we will learn that each number has a one-of-a-kind factorprint.
(The activities listed below are intended to be taught sequentially. They will take several lessons/days to complete with students.)
Gerlic, I., & Jausovec, N. Multimedia: Differences in cognitive processes observed with EEG. Educational technology research and development, September 1999, Vol. 47, Number 3, p5-14.
This study investigated the cognitive processes involved in learning information presented in three different methods: with text; with text, sound, and picture; and with text, sound, and video. Students brain activity was measured using an EEG in each format. Less mental activity was found using the text only presentation. The results showed higher mental activity with the video and picture presentations, confirming the assumption that these methods induced visualization strategies on the part of the learners.
Zazkis, R., & Liljedahl, P. Understanding primes: The role of representation. Journal for research in mathematics education, May 2004, Vol. 35 Issue 3, p164-186.
The authors of this article investigated how preservice elementary teachers understood the concept of prime numbers. They attempted to describe the factors that influenced their understanding. The authors suggested that an obstacle to a full conceptual understanding is a lack of a representation for a prime number. The importance of representations in understanding math concepts is examined.