Day 16: Least Common Multiple Day 2

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: Find the least common multiple of two or more numbers.

Quote of the Day: "Don't worry about whether you're better than somebody else, but never cease trying to be the best you can become. You have control over that; the other you don't. Time spent comparing yourself to others is time wasted." - John Wooden

Agenda:

1. Jumpstart - Mystery Number 
   
2. Review the homework & discovering the least common multiple shortcut
3. Least common multiple of 8 and 12 (formative assessment on an index card)
4. The clickers to decide if a question was asking for greatest common factor or least common multiple
5. Start the least common multiple homework
6. Work with math partners on the rest of the LCM homework

The Assessment: Finding the least common multiple of 8 and 12, utilizing the clickers, checking the current homework (due tomorrow) and the past homework (due today).

 Most students prefer the option below, and I prefer the option above (it demonstrates more mathematical fluency and can be used to tackle much harder cases such as the least common multiple of 22 and 36). In any case, I accept either way as they lead to the same outcome.

Homework: Word problems that include finding common multiples and the least common multiple.

My Glass Half-Full Take: I am seeing evidence in my assessments that students are able to find a least common multiple. In one class, only one student was finding the greatest common factor of 12 and that student recognized the mistake shortly thereafter.

One Thing to Do Differently: I think coming up with a line of questioning ahead of time for the discovering the least common multiple shortcut activity would allow it to go better. Some questions to include are these:

• What do you notice about finding the solution to the least common multiple of...
• 3 and 4
• 2 and 5
• 5 and 9

•  What do you notice about finding the solution to the least common multiple of...
• 10 and 15
• 6 and 8
• 8 and 12

•  If they do not see the pattern after a couple minutes, ask them to find the greatest common factor between the numbers first or even ask if the numbers are prime and composite (which isn't entirely the pattern but one class saw this first and was able to make the connection soon thereafter). 

Link of the Day: Every year after the state testing, I spend some time doing financial lessons with the students. I don't understand why there isn't a financial literacy piece in the standards (even though President Obama has acknowledged financial illiteracy is an issue by signing Executive Order 13530, but anyway the standards are the standards), but this lesson from Yummy Math tackles standards and literacy in my opinion.