First, we have to wrap our heads around what this means in real life. When four children are sharing four, eight, or twelve items, division is easy. But what if we have less items than children? Here's where fractions as division come in.
You can see that we essentially divide each item by the number of children. Then each child gets one piece of each item.
My students' textbook shows it like this, which I think is confusing. Sure, adults who have fully conceptualized this topic will understand. But will kids?
I'm going to present it like this today instead. My students will understand that EACH candy bar needs to be shared equally by the students. After seeing this, we can move to the model above to prove that the amount equals 3/4.
We will also begin using the word "per" today. For this problem, we can say 3/4 candy bar per child. This will provide a springboard to my class's current science concept, speed. In order to calculate speed, we divide distance by time, and that is written as miles per hour (mi/hr) or kilometers per hour (km/hr). Yes, that little slash you see when you say per is the same slash you use in a fraction. So dividing distance (miles or kilometers) by time (hours) is written as a fraction.
Not only do I want my students to know that a fraction represents a division problem, I want them to think of a fraction as a division problem. This takes them one step closer to becoming great mathematicians.