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6-N-2-1

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Saved by Tracie Raibourn
on October 11, 2016 at 8:53:40 am

6.N.1.5 Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.

In a Nutshell

This is the first time the vocabulary: factors, prime, composite and exponents are introduced. All numbers are a product of factors. Prime numbers are the product only of one and itself. Composite numbers have more than one set of factors. Any composite number can be written as a unique set of prime factors (prime factorization). Exponents are a way of representing the number of times a prime number appears in the factorization.

Student Actions	Teacher Actions
Develop a deep understanding of factoring by discovering that each positive integer has a unique prime factorization Develop accurate and appropriate procedural fluency by writing prime factorizations in exponential forms Develop the ability to make conjectures through discovery of the differences between prime and composite numbers as a function of number of factors.	Implement tasks that promote reasoning by asking students to compare prime factorizations of many numbers. Pose purposeful questions about repeated multiplication model expanded form. Implement tasks that promote reasoning to support students in exploring prime and composite numbers by comparing number of factors using various models (arrays, multiplication facts, etc.
Key Understandings	Misconceptions
Prime numbers have 2 and only 2 distinct factors (1 and itself). Composite numbers have more than 2 distinct factors. Identify the prime factors of any positive whole number. Express prime factorization using exponents. Each number has a unique prime factorization composed of positive whole numbers.	Students may believe “1” is a prime number because it’s only factor is “1 and itself” but it does not have 2 distinct factors. Students may believe that all “odd” numbers are prime. Students may believe that “2” is a composite number because it is “even”. Students may confuse exponents with factors and read “2³” as 2 x 3 rather than 2 x 2 x 2. Multiplying the base by the exponent rather than repeated multiplication of the base. Students may believe that there can be more than one number for each set of prime factors.