My favorite way to begin teaching division to third graders (or fair shares with younger students) is to read Stuart J. Murphy’s Divide and Ride book. This is a short story about kids who go to an amusement park to ride roller a roller coaster and various other rides. In each scenario of the story different amounts of seats are available with different amounts of children to fill each seat. These scenarios provide a way to discuss division to students. Remainders are even discussed when students must be left off of the ride because there are no more seats. After reading this book, students can use a circle mat or egg carton to represent the rides with counters or beans to represent children on each ride. If you want to be extra cutesy, you can decorate an egg carton like a roller coaster and place puffballs with googly eyes inside to represent students 
. For a free CircleMat which is useful for multiplication or division, click the link.
