Day 12: Multiples

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: List the multiples of a given number.

Quote of the Day: "Don’t tell me how tough the situation is; show me how tough you are facing the situation.” - Jay Bilas

Agenda:

1. Weekly Quiz Jumpstart
2. Multiples My Favorite No
3. Multiples Notes
4. 5 Minutes of ?'s - I split the case into a waive of 2 minutes, 2 minutes, and 1 minute. Six to seven students answered questions in each waive. The questions were mostly vocabulary oriented.
5. The Multiples Contest - The other math class and my class went back and forth saying multiples to one another until they sounded shaky. 
6. Multiple vs. Factor Formative Assessment 
7. Marvelous Multiples Designs
8. The Sieve of Eratosthenes
9. Multiples HW

 







The Assessment: The My Favorite No Today asked students to list four multiples of 12. When I collected the students' work, more than half of them listed factors instead of multiples. This was exactly what I expected. At the end of this first class, I played a game I called five minutes of questions. Among the questions I asked the students were: What are the multiples of 4? What are the factors of 4?
In the second part of class, I asked that students list at least two factors of 12 and two multiples of 12. Only three students could not do this task at that point. I did this instead of asking them to list all factors because that would be an obvious give away between the differences in a factor and multiple. Afterwards I mentioned that they could list multiples forever. 



Homework: The students continue to work on their weekly quiz, but the assignment that is due tomorrow is the Multiples Homework

We input the divisibility rules as part of this homework. It was done ahead of time, but in my opinion this is still a skill that students have not mastered and a very good idea for this assignment.

My Glass Half-Full Take: In six years I have never had more confidence that students are able to differentiate between what a factor and multiple are.

One Thing to Do Differently: I think the Sieve of Eratosthenes is an excellent learning experience, but I definitely rushed it and tried to squeeze it in today. The objective of the lesson is to "discover" the prime numbers. Students start by crossing out one, circling two, and then coloring all multiples of 2 from 1 to 100. The Math Forum gives more details here.

I think I would have rather rushed the "Marvelous Multiples" activity and had the students on a clock of spending no more than ten minutes on that activity. The problem was that myself and the co-teachers were passing out tape, staples, etc. I should have put more students to work to make the process more efficient.

Link of the Day: The power of whiteboards and whiteboard space. I can work on this.