Day 39: Adding and Subtracting Fractions

6th Grade Math Standards: 4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 .
(In general, a/b + c/d = (ad + bc)

5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to
represent the problem. Use benchmark fractions and number sense of fractions to estimate
mentally and assess the reasonableness of answers. For example, recognize an incorrect result
2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2 .

The Learning Objective: Add and subtract fractions.

Quote of the Day: “It starts with control of your emotions, but it also extends to having the resolve to resist the easy choice, the expedient solution, and, at times, temptation in its various and alluring forms...Self-Control in little things leads to control of bigger things. For example, the reason I prohibited profanity - a small issue - during practices was because it was usually caused by frustration or anger. A player that can’t control her language when she got upset during a drill or scrimmage would be more likely to lose control in more damaging ways during the heart of a competition - fouling, fighting or making other poor decisions that would almost certainly hurt the team.” - John Wooden

Agenda:

1. Jumpstart: Stop & Shop sells Coca Cola in packs of 9 cans for $7 and Richdale sells Coca Cola in packs of 12 cans for $10. Which store offers the better deal? Show your work at least two ways.
2. Weekly Quiz passed back to all students while they worked on the jumpstart
3. We reviewed the jumpstart
4. Like denominators notes
5. Like denominator practice and tickets to leave
6. Unlike denominators notes
7. Unlike denominators practice

The Assessment: I collected the students work on like denominators at the end of the first class and had time to grade and return to one of my classes a few hours later. I did not have the opportunity to return it to another class as I ran out of time, but will give it back tomorrow. The main concern I had for students in terms of the feedback I gave them had nothing to do with the fractions. It was their lack of circling the key parts in a word problem. In my six years of teaching, this as much as any calculation issue has proven problematic again and again. The student below did not execute in the second biggest mistake I saw. She tried to mentally subtract 3 and 2/4 from 8. She got 5 and 1/2. Even for students that wrote 8 minus 3 and 2/4 (or 3 and 1/2), they still struggled to arrive at the difference. I think part of the reason for the struggle is what I would call "problem fatigue." In other words, they had to add (do one step) before getting to the next step.

Another assessment I did was check off students as they worked on the homework. In one class I had much more time to do this than another (more on that in things I'd do differently). 

A third assessment was reviewing again the rates issue that we are having as a class. I am confident that we are now turning the corner on this type of problem, but the students will see a similar problem in the near future. The students that are successful seem to be gravitating more and more toward making a chart and finding the least common multiple. 

Homework: Students did eight problems finding the sum or difference for of unlike fractions and also two to three word problems. They were given time to start this in class.

My Glass Half-Full Take: One thing that I don't plan for (although in a perfect world I really should) is having students get out of their seats. Today as we were doing the notes, I was constantly asking students to get out of their seats and explain to someone in the class how to do the work or simply to check the problem. It's amazing how beneficial this is for everyone in the class. It shrinks the ratio of student to teacher for me and also gives the students who "get it" a more developed idea of how to solve the problems as they view their classmates who might solve it correctly in a different way or are solving it incorrectly and they try to search for the mistake.

One Thing to Do Differently: Everyday there are many more than one. It's just a matter of whether I share it or not. Here's what comes to mind:

1. The reason my notes aren't linked here are because I ditched them after the first class. I instead handed out a worksheet and just picked out problems I sensed we could struggle with. It worked much better. I then used the word problems from that sheet as the ticket to leave. 
2. These are fourth grade standards and I'm a sixth grade teacher. Just five years ago these exact standards were sixth grade standards, so guess if the students struggled? "The idea that 4 is 32/8 is crazy. It doesn't make any sense." - Student. I wish I knew that before teaching this lesson. I also noticed that more students got 8 minus (1 and 3/8 + 1 and 1/8) wrong than those that did not get it correct. Fractions are tough. It doesn't matter that "they were already taught this." I probably assumed too much going in and could have relied on a pre-assessment better to guide the lesson. 
3. There is a small pack of students that are struggling converting a mixed number to an improper fraction. Since we are moving toward the sixth grade standards in the coming days (multiplying and dividing fractions), I think it's going to be essential to continue to hammer this skill home perhaps in a formative nature. 
4. Notes practice, notes practice. I tried my best with my energy to liven things up, but I feel like there's something that can be done differently here. I am doing a kinesthetic/visual/notes/partner activity in two days so that will be a nice change for everyone. 
5. I gave out two sheets that are essentially the same sheet, but one says unlike fractions and one says like fractions. The one that says unlike fractions is homework. What are the odds that everyone does that assignment tonight and nobody does the other one? 

Link of the Day: What works better? Drilling a concept repeatedly in a day or trying to several different concepts in the same day - for several days? According to research, spreading out the concepts works better. The technical term is interleaving. Only the youngest of children benefit more by drilling initially.