Division with Fraction Word Problems

I've been spending a lot of time lately thinking about how I'm not hitting the skill cap there is for teaching. I am trying to increase my ability in facilitating math discussions.  The students are now working on creating their own division (with fraction) word problems.

Division is a very rough topic, as many students do not understand the concept division and do not know when to apply it when given a word problem. I understand that this is quite challenging, but creating your own division problem means you understand what division is and why it's optimal to use it. Therefore, if a lesson like this is successful, that is a big breakthrough for my class. Some questions that were made:

With a topic like this, there is a lot of discussion that has to surface:

#1 - Does our question make sense?
#2 - Does our question require us to find how many (insert fraction) are in (insert fraction)?
#3 - Is it realistic and does the unit we chose make sense considering the quotient? (e.g. we can't have 1.5 people)
#4 - Working on problems that don't make sense and understanding why, and possibly changing it so that it does make sense.

Some misconceptions some of the kids have had so far when making their own problems:

A) The question does not make sense
B) The question does not require us to divide to solve
C) The question is not clear
D) Divisor and dividend have different units

As a teacher, it's been hard clearing up the misconceptions. You have to get students to understand why their own question doesn't make sense. Lastly, when they are finally successful in creating their own questions (like the ones I posted in the pic above), they tend to stick to the same format or don't change the scenario (I'm still happy though!).

A hands-on activity is far better for something like this, or at least should be done before this lesson (note for the future). While this reminds me much more of a lesson for a science class, I have been thinking about purchasing multiple different cups of different measurements and having students solve these types of division word problems in real life.

A question like "Mr. E has 1/3 (cup, gallon, quart) of milk. He wants to share it equally between 2 students. How much milk will each student get?" or "how many 1/5 cups of milk are in 3 cups of milk? Students will actually take the 1/5 cup and continue to fill the container/measuring cup until they find their quotient. The kids would appreciate this as they did with the last chance lesson.

A lesson like this is also good for teaching conversions i.e. finding how many cups are in a quart, converting quarts to gallons, etc. I'll probably do something like this before this unit is over.

Chance Lesson - Unit Rate & Unit Price

Below are videos of VSC Math's first chance lesson. The students generally worked really well during this lesson and did a great job learning about how to find the unit price.

Task: I set up different fruit stations around the back of the classroom. There were:
Lemons - (3 for $1.50)
Kiwis - (6 for $4.80)
Limes - (8 for $1.60)
Grapefruit (1 for $2.00)
Tangerines (8 for $3.20)
Golden Apples (4 for $5.00)

Groups were to go around to different stations and find the unit rate of each fruit, along with answering a few questions:

Here are some videos of students learning:

Note: You'll see some students gettin' jiggy to Michael Jackson's music in the videos!

This week's topic: Unit Rate & Unit Price

This week, we've been learning how to find the unit rate and unit price of items. I decided that this year, I want to incorporate more movement into my lessons. To the students, they're called "chance lessons". This is a good way for students to work as a team and show that they're able to work collaboratively with their groups.

Students that succeed in these types of lessons generally don't waste much time to get started and are good at working together. Below are a few pictures of the lesson. The next post will showcase videos of the students working together and displaying their learning.