Day 44: Fractions Review

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?

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and
V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.

The Learning Objective: Multiply fractions to find a product. Divide fractions in order to find a quotient. Add fractions to get a sum. Subtract fractions to get a difference. Locate a fraction relative to the position of other fractions on a number line.

Quote of the Day: “Confidence must be monitored so that it does not spoil or rot and turn to arrogance. Arrogance or elitism, is the feeling of superiority that fosters the assumption that past success will be repeated without the same hard effort that brought it about in the first place. Thus, I have never gone into a game assuming victory. In fact the quality of our opponent had nothing to do with my own Confidence. Rather I drew strength, Confidence, from the sure knowledge that I had done all things possible to prepare myself and our team to perform at our highest level in competition. The opponent might perform at a higher level - or not. I didn’t concern myself with the other team’s preparation and potential; I just concentrated on ours." - John Wooden

Agenda:

1. Jumpstart with 5 problems that look at 4 different operations and expose students to mixed fractions, regular fractions and whole numbers. I checked weekly quizzes while students did this jumpstart.
2. We reviewed the jumpstart by having 5 students go to the board.
3. The students did this Frayer Model which served as a reminder of how the operations were different and similar to one another. To simplify things for most students my colleagues and I agreed to tell them to just turn all mixed numbers to improper fractions. It was probably not the best long term decision, but I have no regrets as it simplified a complicated topic as it is. 
4. Stations. Cookie recipe, locating fractions on a number line, using fraction tiles to find equivalent fractions, and word problem tactics. 

The Assessment: Students doing the jumpstart on the board, circumventing from group to group as students worked on the Frayer Model and sitting with the students at the number line station during the stations activities. I also checked students weekly quizzes on the spot for them.

Homework: Study for the quiz, finish and fix the weekly quiz

My Glass Half-Full Take: The morning was stressful, but the afternoon was great. It was the first time I had students work in groups of four this year. It was a very positive result. Behavior issues were still prevalent, but nothing more than I would typically get in a lecture (students talking, losing focus or going off topic). Plus for students that were distracted often times their group could bring them back to task and hold them accountable faster than I could.

One Thing to Do Differently: This was somewhat out of my control, but my computer got upgraded to Windows 8 during the professional day yesterday. As a result, I had difficulty using the projector and reviewing the Frayer Model the way I would have liked. By my third class, I was faster and had adjusted well enough to review the Frayer Model in a better manner.

Another part of the lesson that wasn't as strong was that I was one hundred percent reliant on students helping students for the stations with the fraction tiles and the station with the word problems. I'm not sure how much I could have done things differently to get to these stations. Since I was at the number line station, and every student got to the number line station, I did see every student. I also assessed students ability to apply the four operations to fractions during the Frayer Model, so it's not as if I never assessed that skill - I just didn't assess one task of that skill. Perhaps an alternative way to do this would have been to teach students at the number line station and then have those students go and teach other students. That would allow me to see the other stations, but overall I was very happy the way things went and could live with doing today's lesson exactly as it went again (maybe a Mac upgrade instead of Windows though).

Link of the Day: Great article on estimation from Jessica Marks. It's a skill perhaps more valuable than any we can teach given the availability of calculators today to find precise answers. Estimation forces students to think logically.