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# 6-N-1-5

last edited by 4 years, 4 months ago

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 students are introduced to the vocabulary for prime and composite numbers and exponents.  All numbers are a product of factors.  Prime numbers are the product of only one and itself. Composite numbers have more than one set of factors.  Factor trees can be used to find factors of any given number.  Factor the number  until all factors are prime. The product of these prime factors will equal the original given number. This is called prime factorization.  If the prime factors are repeated, it can then be written with exponents. Exponents are a way of representing repeated multiplication.  For example, the prime factorization for 24 which is 2 x 2 x 2 x 3 can be written in exponential form, 2³ x 3.

## Teacher Actions

• Develop strategies for finding prime factors of any number. (Ex: Model factoring a whole number using a factor tree. Continue factoring each individual factor until all remaining numbers are prime numbers.)

• Develop a deep understanding of the meaning of factoring.  Compare prime factorizations of differing factors to discover that each positive integer has a unique prime factorization. (Ex: The numbers 12 and 18 will have different prime factorizations.)

• Develop procedural fluency of factoring whole numbers by analyzing patterns in prime factorizations, then writing them in exponential forms.

• Implement tasks that promote reasoning by asking students to compare prime factorizations of many numbers, including both prime and composite numbers.

• Pose purposeful questions that help students identify patterns between repeated multiplication and exponential form. (Ex: How can exponents be used to show patterns between these numbers?  Why is 2 x 2 x 2 x 3 written as 2³ x 3?)

## Misconceptions

• Know that prime numbers have 2 and only 2 distinct factors (1 and itself).

• Know that composite numbers have more than 2 distinct factors.
• Able to identify the prime factors of any positive whole number.

• Know how to express prime factorization using exponents and understand that an exponent tells how many times a number is used as a factor.

• Know that each number has a unique prime factorization composed of positive whole numbers.

• Believe 1 is a prime number because its only factor is “1 and itself.”

• Believe that all odd numbers are prime.

• Believe that 2 is a composite number because it is even.

• 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.

OKMath Framework Introduction