Day 21: Prime Factorization & Greatest Common Factor

6th Grade Math Standards: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example express 36 + 8 as 4(9 + 2).
MA.4.a Apply number theory concepts, including prime factorization and relatively prime numbers, to the solutions of problems.
The Learning Objective: Use prime factorization to find a greatest common factor

Quote of the Day: “Many people believe that a person is born either smart, average, or dumb - and stays that way for life. But new research shows that the brain is more like a muscle - it changes and gets stronger when you use it.” - Carol Dweck

Agenda:

1. Jumpstart with visual patterns number in which the students were asked to find the value of the 10th step (which they did quite well with)
2. We reviewed the homework most notably the first five prime numbers and the prime factors of 1001
3. We did notes on the objective
4. We did pepper with the terms prime and composite as well as testing which numbers were prime and which were composite as part of giving them an idea of what was on the study guide
5. Students were given the opportunity to start their homework in class
6. If students finished they could work on the weekly quiz
7. If students finished this, I let them use their cell phone to play 2048 or decorate our ceiling (only three students finished step six all day).

The Assessment: Starting the homework was the assessment today as many students were able to finish it.

Homework: This worksheet which was created by a colleague and I actually really liked better than anything a book or publishing company has offered over the last six years that I've seen.

My Glass Half-Full Take: Sometimes when you expect outright confusion, you don't get it. I'm not one hundred percent convinced my students will master prime factorization with greatest common factor on their quiz tomorrow particularly given that they do struggle with number sense. That being said, they did ok. My favorite part of today was that a student explained the visual pattern by stating that she knew there were 13 squares in step 3 and 7 steps between that step and step 10. Noticing that there was a difference in each step of 4 squares, she took the 7 steps that had a different of 4 each time and multiplied to get 28. She then added the 13 steps that were already in step 3 to get 41. I had never thought of the pattern in that way before.

One Thing to Do Differently: The idea of calling the method of prime factorization "birthday cake" or "factor trees" has caused students to lose site of what prime factorization is. I only had one student in a class tell me that writing a product of prime numbers is the same concept as prime factorization. For now, the students are not struggling with this material because it's what we are currently doing in class. When we mesh this topic with decimals, statistics, ratios, etc. it could be a whole different story. I've got to eliminate the use of the term "birthday cake" and call it prime factorization instead.

Link of the Day: Similar to get to 10, here is get to 24. This would probably an easier one to make into worksheets for someone like me who does not have technology as readily available as some school systems might (although the use of cell phones is a game-changer as I got to experience for the first time with one student).