Day 15: Least Common Multiple

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: “You can take the best team and the worst team and line them up and you would find very little physical difference. You would find an emotional difference. The winning team has a dedication. It will have a core group of veteran players who set the standards. They will not accept defeat.” - Merlin Olsen, Los Angeles Rams

Agenda:

1. Estimation 180 the smaller stapler
2. Review the homework --> this wasn't great as many students did the first 8 problems in class and then didn't follow up with the 9th problem at home. 
3. Free write regarding how students would handle 8 hot dogs in a package and 12 hot dog buns in a package.
4. A look at how George Banks from Father of the Bride handled the same situation. 
5. Least Common Multiple notes (two word problems)
6. Start the least common multiple homework (I did one, they showed me one, then they were off and running).
7. Form Math Partners for quick grouping (done today because classes are pretty much final in school now)
8. Utilize the TurningPoint clickers to assess six different questions:

• Is 18 a multiple or factor of 9?
• Is 3 a multiple or factor of 9?
• How many multiples does the number 9 have?
• How many factors does the number 9 have?
• What is the greatest common factor of 8 and 10?
• What is the least common multiple of 8 and 10?

After the assessment it was pretty clear that we had some work to do in differentiating what a factor and multiple were.

The Assessment: Turning Point, a fist of five after the two notes problems, the free write exercise, the previous night's homework, the students that passed in their weekly quiz today to be highlighted for potential wrong answers, and the opportunity to start homework in class.

Homework: The students had 16 different least common multiple practice problems (the last five were more challenging as they involved more multiples), the weekly quiz is due in three more days, and we have a quiz on Friday to start studying for.

My Glass Half-Full Take: These are why I teach. Funny. Thoughtful. Creative. Analytical.

One Thing to Do Differently: The homework worksheet has it's boring parts. There are zero word problems. The students are doing the typical drill and kill. Once they get one right, the process of finding the least common multiple is clear. I could have done two things to change the pace on this. The first is sprinkle in a change of directions and give them some greatest common factor problems as well. The second would be to ask if there was an alternative way to find the answers other then simply listing the multiple (which is the only way I showed them). The least common multiple of 3 and 4 is 12, which is simple to arrive at when students see all that needs to be done is simply multiply the two numbers. When 10 and 6 are used instead and they see the answer is actually lower than 60 though it blows that whole theory up.

Link of the Day: Not all of these are great for teaching kids, but the site I pulled the Father of the Bride clip from today is from Harvard and it is called Math in the Movies.