Day 19: Test on Factors and 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 solution of problems.

The Learning Objective: Find the least common multiple of two or more numbers, identify all the factors in a number, find the greatest common factor of two numbers, memorize the divisibility rules

Quote of the Day: "A carpenter was fixing to retire and tells the company he works for he was through building houses. They ask him to build one more before he retires. He agrees and through the process of building this last house he begins to cut corners, uses cheaper materials, doesn’t use the same precision in which he used to and basically built an inferior home. When he’s done he gives the keys to his boss and says here you go I’m done. The boss returns the key and says thanks for all your hard work and dedication to this company. This home is yours and we appreciate you. Obviously, had the carpenter known he was building his own house he would not have cut corners. You are building your house every day and you don’t even know it.”

Question of the Day (as always from the mouth of a student): How do we tell on a word problem whether to find the least common multiple or greatest common factor?

Assessment: The test went well. I really do not care about the average. Thank god for sabremetrics in baseball. I think it can change the way that tests are analyzed. Without looking at the actual mistakes students make, it's really easy to make a quick judgment about the grade, but look at the mistake below. The first student has done several things well on problem number twelve below. First, they seem to know what a factor is. Second, they list every factor in pairs. Third, the student knows to only list 6 once. The red x can be distracting because it does indicates the concept has not been mastered, but this student is very close. My only job left is to make sure the student knows that and this problem isn't a reason to shout how math is hard (which I can live with) or even worse that "I'm not good at math."

The number got caught off, but it's 30. And again the student had to list the factors, and again the vase is three-quarters full. Just need a little flower.

This next mistake on problems 15 and 16 is another example of a student being very close to mastery. The red x has not appeared yet in the picture because I am going to show it to the students without the red x and see if they have a problem with it. That said, the student seems to understand what a multiple is. The math is a little murky as numbers get higher with 15 and the student also fails to list the first multiple for each number, but this is the best way for the student to learn that fact. 

Here, there is a clear indication that a student is well on her way to mastery of listing factors. Getting that 3 x 17 is 51 is especially significant since so many students mistaken that number to be a prime number. That said in the word problem below (which I should really push that we change because of the wording), the student fails to list the number six after listing 2 and 3 as factors. Oddly enough in the same test the student successfully stated that for a number to be divisible by 6, 2 and 3 also must go into that number. The student failed to apply that rule here, but this mistake is correctable. The 3 x 29 math is also an issue, but again if the student knows 2 x 39 is 78 we are on our way to determining what number times 3 will get 78. 

The mistake on number 21 happened a handful of times. Students mixed up greatest common factor and least common multiple. We need to keep drilling for them that factors start with 1 and itself. Factors start with 1 and itself. Factors start with 1 and itself. And then hopefully as the math is being done here and the student sees one is written, they recognize that they are listing factors instead of multiples.

Factors start with 1 and itself. Factors start with 1 and itself. Finkle and Einhorn. Einhorn and Finkle.

Agenda:

1. Agenda Books
2. Collect the Weekly Quizzes
3. Take the test
4. Do the wicked hard and totally unfair bonus
5. Super Bowl Commercials from Yummy Math

Glass Half-Full Take: Much of this test was about memorization. Divisibility rules and definitions of vocabulary specifically. I'm not a fan of teaching students (or myself for that matter) to memorize, but sometimes it is necessary. This overachieving answer to what a factor is brought a smile to my face.

If you can't see it, a student defined factor (which was what the question asked) and then proceeded to define multiple too. 

Another good part of today was the effort that students put forth with the bonus. So many students are starting by writing down what they know and not giving up without a fight. It's nice to see persistence and struggling even though not a single one left that problem thinking they had solved it. 

One Regret: The time after a test is such a land of opportunity for learning, but it's very difficult to manage since some students are done with the test and some are still working. Obviously the priority of the day was the test, but I chose the Super Bowl commercial activity based on where the students had struggled in the fifth grade (numbers and the base 10). I would have loved to be more active in explaining the worksheet, but did not want to take away from the students still working on the test. What I am going to do next year is explain it the sheet at the start of the second lesson.

Link of the Day: The problem that 1,000 math teachers can't solve from Dan Meyer.