Day 51: Multiplying 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?

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.

Question of the Day: Tom Brday throws 8 touchdowns for every three interceptions. What is the ratio of interceptions to touchdowns?
Objective: Multiply fractions by fractions to find a product; multiply fractions by whole numbers to find a product; multiply mixed fractions to find a product

Agenda:

1. Self-Assessment from the addition and subtraction quiz
2. QSSQ
3. Review the Quiz
4. My Favorite No 
5. Pepper
6. Notes
7. Clickers (exit ticket)
8. Homework started in class

Assessment: I had the students multiple 1/3 by 2/5 to see what they already knew about multiplication of fractions. In one of my classes 11 of 18 students answered 2.

During the notes, students were consistently asked to try on their own before I showed them what to do and I circumvented the room at this time. There was a popular answer of 4 and 1/3 times 2/5 being 4 and 2/15. That was such an issue that it is going to become the question of the day for tomorrow. 

The clickers were only used for one class. I had a two step problem that required students to add and subtract fractions as well as multiply them. 

Glass Half-Full: As the 6th grade standards above indicate, there is nothing that is directly saying that students need to multiply fractions. It is a fifth grade standard. They do have to build upon their knowledge of multiplying though in order to find volumes and make sense of dividing fractions. So the novice in me would say let's just go right to division. The novice in me died a few years ago. When 11/18 of students answer a question wrong, there is a fraction problem (pun intended). Today's lesson was necessary, and hopefully impacted the students recognition of how to carry out the algorithm.

Regrets: The notes are designed to show students why a fraction times a fraction cannot equal two or anything greater than one. It was put in there, but once the robots - I mean students - start to multiply the numerator by the numerator and the denominator by the denominator, they lose site of this concept.

Link: Lost at School was a valuable read for me (although it took me two months to finish because I'm a horrible reader at busy times) in terms of classroom discipline. I think it confirmed many things for me and also showed me that repeated disciplinary actions are cause to change the way you see a problem in the classroom.