Day 42: Dividing Fractions

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

The Learning Objective: Divide fractions in order to find a quotient.

Quote of the Day: “One of the most striking things that separates people who sustain their success from those who are only briefly or never successful is their strong sense of responsibility for their own actions. It is easier to move from failure to success than it is from excuses to success. Excuses: Eliminate them.” - John Maxwell

Agenda:

1. I collected Weekly Quiz #6 from all students 
2. Jumpstart question: The ratio of carved to uncarved pumpkins at the Harvest Fest is 11:8. There are 95 total pumpkins. The ratio of carved to uncarved pumpkins at the Haunted House is 11:8. There are 130 total pumpkins. What is the ratio of carved to uncarved pumpkins at both events? See picture below.
3. As the students worked on the jumpstart I assessed the homework which we went over.
4. After going over the homework, I gave the students the Powerpoint on eating pizza. It was very appropriate on this day (Halloween) that I was dressed as Rafael. 
5. Students explained to me how each person in a group of 4 would get two slices.
6. Then I took once slice away and asked students how each of the 4 people would get an equal amount of pizza now. 
7. We did notes on dividing fractions including what a reciprocal is. 
8. The students tried five division problems including the class activator problem about the pizza. 

The Assessment: As students tried reciprocal and division problems on their own I went around to assess them. On the whole, most students had the process down, although it was clear to me that there was rote memory - not mastery of how division works.

Another assessment came from the jumpstart. I promised no homework if anyone correctly answered the jumpstart. Many students knew to draw tape diagrams, but did not know they needed to do two separate tape diagrams. Not a single student solved this.

Likewise not a single student could determine that 7/8 of a pizza divided by 4 was 7/32 before they were instructed on that problem (many could afterwards). That being said I had one student who put 1.75 over 8 which was an answer I had never seen before and could be correct depending on the teacher you ask. The student below did 4 divided by 7/8.

I also assessed the homework. In one class it was apparent that six students did not know how to multiply mixed fractions still and it could have been more than that because a few students were missing the homework. I had to reassess this topic again after going over the homework with these students to make sure that they knew how to multiply before I taught them how to multiply the reciprocal.

Homework: Weekly Quiz #7 was made available online over the weekend.

My Glass Half-Full Take: The enthusiasm with trying to solve the pizza problem was great and the students could not argue the relevancy of being able to divide fractions. I enjoy creating a story off of the word problem rather than simply starting the class by telling students, when you multiply by the reciprocal it's the same thing as dividing. We also attempted to discover this pattern rather than having me directly show the students. Two out of three classes recognized a pattern and used the word reciprocal to describe it when I compared problems of division and multiplication of the reciprocal without telling them what I was doing.

One Thing to Do Differently: We shortened each class by ten minutes today in order to give the students an assembly about making positive choices (it was the end of Red Ribbon Week). If those ten minutes were given back to each class, I think I'd give students five more problems on division and ask that they use common denominators to solve one of them just to expose them more to this way of doing the problem.

My prep block was last today, and even though I had plenty of things to do (including write this post) I decided to take up the offer of one of my colleagues to observe his class. He loves using whiteboards and in my time in his class it was easy to see why. He would ask the class to hold up their whiteboards after they were done a problem and he would individually assess each student much faster than I ever could when the students used their notebooks. I'd like to use marker boards myself and get away from notebooks just a little bit in my room.

Link of the Day: This Washington Post article discusses the relevance of common core instruction as it is perceived by adults. I hear adults say to me all the time, "It isn't solved like I was taught." I know how they feel because I can say the same. My feeling is that first of all I am going to teach the standards that are required of the students.

Secondly, I don't have much issue with trying to teach a "simple" problem with area models, number lines, etc. even if Arne Duncan walked into my classroom tomorrow and said you can teach whatever you want so long as it's math. The reason being is that eventually students having an idea of how number lines and area models work allows them to solve problems that aren't as basic as 326-197.