## Reflection: Exit Tickets Finding Greatest Common Factors (GCF) Using Prime Factorization - Section 5: Closing and Exit Ticket

After this lesson, I scored student exit tickets and the homework I'd assigned at the end of this class.  One trend that I saw - my students are able to find the prime factorization of a number, but they aren't sure how to then list the prime factors.  The factor trees looked great, the list of prime factors did not (which then meant students were incorrectly determining the GCF for a pair of numbers, based on faulty prime factors).

The most common mistake was to not repeat a prime factor when needed.  For example, students would use a factor tree to get 12 down to the prime factors of 2, 2, and 3, but they'd only write 2 x 3 as the prime factorization.

I'm going to fix this misconception during the cumulative review portion of my block early next week (beyond my 60 minutes for the core lesson, I have 10-15 minutes of class time during which I can re-teach a concept as needed).  I'm going to:

• name the mistake I saw - for some students, hearing me articulate this will be enough
• have students check their prime factorization by multiplying the factors to get back to the starting number (in my example above, students would then see that 2 x 3 is only 6, not 12)
• have students count the number of prime factors circled and cross-reference that with the number of prime factors they've listed out (in my example above, students would have had 3 prime factors in the tree, but only 2 prime factors listed)
• give students quick practice in class to find the prime factorization of numbers, outside of a real-world context (find the prime factorization of 48)
• give students more practice with prime factorization on homework (I'm putting it on my HW calendar, so that it comes up periodically throughout this unit)

Responding to Data
Exit Tickets: Responding to Data

# Finding Greatest Common Factors (GCF) Using Prime Factorization

Unit 1: Number Sense
Lesson 4 of 19

## Big Idea: Every positive integer (except the number 1) can be represented as a product of one or more prime numbers.

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Standards:
Subject(s):
Math, Number Sense and Operations, division of Korea, factoring polynomial expressions, Decimals, prime factorization, factors, greatest common factor, prime, composite, GCF, factor tree, multiples, distributive property, least common multiple, multiplying
55 minutes

### Carla Seeger

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