Day 22: Greatest Common Factor Via Prime Factorization

6th Grade Math Standards: 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 solution of problems.

Objective: Find the greatest common factor of two numbers using prime factorization

Question of the Day: "Are all numbers less than one negative?"

Agenda:

1. Open Middle Largest Product
2. QSSQ
3. Review the homework problems on prime factorization
4. Pepper
5. GCF with prime factorization notes
6. GCF with prime factorization marker board practice
7. GCF with prime factorization homework

Assessment: Reviewing the homework, pepper, making students stand up when they were done a problem on the notes.

Glass Half-Full: I had to rush through the notes because Open Middle got us off on a tangent and took longer than I had anticipated for the students to recognize what strategy made the most sense. In rushing through the notes, when I went to assess the students formatively at the end of the block it was pretty apparent that in many instances they just were not ready for the homework. Thus, I had the students skip four out of six of the problems where they had to find the greatest common factor using prime factorization. The sections on the homework that they had to list prime and composite numbers was still relevant, quick, and informative (for me not them) review so that part was done. And the students were basically given the go ahead to get the other two problems wrong by me if need be so that they could at least be curious to see how it should be done in class the next day.

Regrets: Open Middle was awesome. To me. The students missed the point to some extent because they got hung up on multiplying the wrong numbers and then assuming that they were right. Perhaps if they had a calculator, they would have tried more numbers and been better able to explain the theory behind why the product was biggest when the tens place had a 9 and the smaller tens place had the larger ones place. This also would have allowed for more opportunities to get practice on greatest common factor with prime factorization. There's a time and a place for fluency of course, but I also have not let students use calculators all year and I do believe the standards ask us to use tools appropriately (MP.5) and look for and make use of structure (MP.7).

Link of the Day: Apparently prime factorization is part of the cryptographic method behind electronic bank transfers. I read that in this post about how prime numbers are being calculated much faster with computers thanks to a new algorithm.