Day 11: Factors

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 solution of problems.

The Learning Objective: List the factors for a two digit number.

Quote of the Day: "Americans spend twice as much time on Facebook as they do exercising. And the younger the age, the worse the effects. The average college student spends three hours a day checking social sites. According to a USA Today report, the grade point of average of college students who regularly use Facebook is a full point lower than their peers who do not...American workers are interrupted once every 10.5 minutes by things like emails, texts, and tweets. Once interrupted, it takes an average of 23 minutes for them to get back on task." - Rick Pitino

Assessment: After we review the notes I gave students a problem to try on their own. Typically this problem took place right at the end of the first block we met, so when we met again at the start of block two I gave the class an index card and gave them another number.

The results were mediocre, but got better after I gave students feedback on the first index card problem and gave them a second index card problem. The feedback I gave students was to list factors in numerical order by starting with the factors that are always there (1 and the number itself). What I was noticing was that students were leaving a factor or a pair of factors out.

Agenda:

1. Jumpstart with divisibility rules, prime number, and composite number definitions
2. Review the jumpstart by asking three different students to give each rule of divisibility (so we repeated each other) through cold calling
3. Reviewed the homework by letting six students come to the board and try the six example problems from the homework. As students were at the board, I played a quick round of pepper with the remaining students.
4. We gave thumbs up and thumbs down to students work at the board. It led to great discussion.
5. Factor Notes (Defining factor and two examples where we list all factors in order using the divisibility rules)
6. Exit ticket where we use a two digit composite number and list the factors
7. Starting the next class with listing the factors on an index card
8. Fabulous factors 
9. The Factor Game
10. Pass out the factor homework and put homework in the agenda book

Glass Half-Full Take: Today was a jam packed day, so there's a lot to pick from both in terms of regrets and victories as a class.

I told one student in the middle of class that he was having a great math class. He asked a question skeptically at one point about why 564 was not divisible by since the sum of the digits was 15. He also went up to the board and got one of the homework questions wrong. And he slipped in one more wrong response. He was engaged and when I would cold call him after he had originally got a question he came back with logical understanding. He was pushing himself today and I praised him for it publicly. Tomorrow I'm going to include a slide about him as "Student of the Day" after we do the Quote of the Day. It was growth mindset personified.

One Regret: In the first class, I was a little all over the place in how Fabulous Factors was organized. In the second class, I fixed the situation. Here's what I did.

First, I explained the factor game which is what they would do after finishing Fabulous Factors. This proved effective because students would finish at different times.

I then had students pass out the construction paper, the factors cut outs, a set of markers (one set per two students), and the white paper which they would use the markers on. I distributed scissors to the students. Then I explained the first step in the task which was to cut out a number of their choosing and recycle the scrap paper.

After students had chosen their number, I told them to list the factors in their notebook and have either a neighboring or student or myself check to verify all factors were listed.

Once their "rough draft" was complete, I had them fold the white paper in half (the hamburger way) and then write the factors using markers.

Lastly I passed a slice of masking tape to every student to put the white sheet onto the construction paper.

All the while I was going around the room stapling the numbers to the construction paper and collecting scissors. By the end of the last class, the room was actually clean.

Homework: This factor worksheet

Link of the Day: Cool problem that I intend to tweak a little and then implement for my Math Academy kids. Try it without the answer given to you first cheater!