Day 53: Dividing Fractions with a Common Denominator

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?

Objective: Divide fractions using a common denominator

Agenda:

1. Visual Pattern #27
2. QSSQ 
3. Division of Fractions Intro. You and three friends get a pizza (I display a pizza on the board). Then I tell kids to look at the back wall to see what's different. When they turn around, I've changed the board to show that one slice is missing and your brother took it. They fell for the oldest trick in the book. Now how are we going to split the pizza with 7 slices (7/8 of a pie) among 4 people?
4. Think, pair, share
5. Review how to divide fractions by finding a common denominator
6. Notes including a number line 
7. Independent practice and homework

Assessment:

Glass Half-Full: I found this helpful link about dividing fractions from Republic of Math about 20 minutes before school and wanted to incorporate it somehow into the lesson. I thought it was a useful of thinking about the problems and technically the standard does use the term visual fraction model. I doubt most students found it helpful, but there were probably a few, and I'm teaching "what I'm supposed to."

I have never taught students by making them find a common denominator first. The thought occurred to me in the moment when students were solving the activator problem with the pizza that most of them were in essence trying to either split the pizza into thirty-seconds or making sure each person got 1.75 slices. I don't think that students were making any connection to multiplying by a reciprocal. That was only brought about as a result of memorization. As the above link does delve into the students could eventually learn about multiplication of the reciprocal through self-discovery, but it's usually not the first maneuver students go to. Plus when we start talking about integrating the other operations, it's less for students to be confused by.
Just find a stupid common denominator. Even if you multiply. I don't care. Do it.

Regrets: I was vague as to whether students needed to find the number of slices per person or the fraction of the whole pizza per person. The two questions are different, so it would be best to ask both on the same slide. More students determined 1.75 slices per person than 7/32 of a pizza per person.

Link: Good way to practice coordinate plane and celebrate Black Friday from Robert Kaplinsky.