Day 49: 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 to find a quotient

Quote of the Day: “Exercise improves mood. Recent studies have found that a regular workout regimen is an even more powerful mood elevator than prescription anti-depressants. What’s less well known, however, is the profound impact exercise has on learning, memory, and creativity…Neurological studies show that when we exert ourselves physically, we produce a protein called brain-derived neurotrophic factor (BDNF) that promotes the growth of neurons, especially in the memory regions of the brain…Learning and memory evolved in concert with motor functions that allowed our ancestors to track down food, so as far as our brain is concerned, if we’re not moving, there’s no real need to learn anything.” – Ron Friedman

Question from Yesterday (as always from a student): "Is zero considered a whole number?" "How can you tell if 3/4 or 7/9 is bigger?"

Assessment: Marker boards, circumventing the room

A couple things of note with these pictures. First of all, the objective is centered around the word division and this is of course multiplication. The reason for that is that in order for students to master division they should know not to take the reciprocal for multiplication problems. Students need to transfer between all four operations in order to truly master all of fraction operations. Not just do them in isolated situations.

Second of all, the pictures here show the value of cross reducing. Great to hear students using words like factor after we reviewed what was happening in these problems. 

Agenda:

1. Estimation 180 (one class only) and marker boards to review multiplying and adding fractions in other classes 
2. Homework review and weekly quiz feedback
3. QSSQ
4. Division of fractions activator. How do we split one full pizza [8 slices]among four people? How do we split 7/8 of a pizza among four people?
5. Division of fraction notes
6. Division of fractions practice (marker boards)
7. Division of fractions homework practice

Glass-Half Full: Marker boards have changed the way I teach. I can't believe I ever taught without them. It is wonderful for students to understand how to divide fractions and see evidence of it. That said, so many are memorizing a process. One student in my last class asked the magical question: "Why do we not take the reciprocal of the first fraction?" Another student in a different class asked, "Is there another way to solve these?" It's thinking. I am very pleased by it.

Regrets: I just need to make sure all classes hear these questions and have time to reflect on them. It's easy to memorize "keep, change, reciprocal" but understanding a little of the why it works is of much higher importance.

Link of the Day: Fawn Nguyen is the best teacher I've never met.