Division Situations and Remainders 

New Math Concepts:
Division Situations and Remainders
Over the past week, we have been focusing on successful and mathematically sound division strategies. All of these strategies center on a very solid knowledge of multiplication clusters that are easy to compute and make sense in our baseten world. In addition, we started to write our own division “situations” (word problems), and explain what we do with any leftovers (remainders). Traditionally, students have only been asked to solve division problems and include the remainder in a prescribed fashion. As an example, in the problem 18 ¸ 4 = n, students have most often been asked to record the answer either as 4 R2, 4 2/4, or as 4.5. We are trying to get students to understand that remainders are handled in very different manners depending on the division situation.
As examples I offer the following situations:
4 screaming toddlers want to share 18 animal stickers evenly. How many stickers will each child get? Here the answer better be four! As you can imagine, if you gave two of the kids 5 stickers, the rest of your day would be horrific! Here, we ignore the remainder. We throw away the last two stickers using great care not to be seen! The answer is: Each toddler will receive 4 stickers.
4 teenagers want to share $18 evenly. How much money will each teenager receive? Well, I have never met a teenager yet that wants to ignore or throw away money! So the remainder of 2 (which is two dollars) will be divided evenly between the 4 teenagers, and believe me kids know how to split up money! Here, the answer would be: Each teenager will receive $4.50 .
Similarly, large food items like pizzas are usually not ignored. Pizzas would provide and opportunity for a fractional remainder. Each person would receive 4 2/4 or 4 ½ pizzas.
4 classmates want to share 18 markers evenly. How many markers will each classmate receive? Each will receive 4 markers, and the two left over will go to Mrs. Phillips, everybody’s favorite math teacher. Here it would not make sense to ignore or throw away the last two markers, and we also cannot split them up.
18 students need to ride to the zoo in cars that can only hold 4 students. How many cars will be needed? Here, in the answer of 4 R 2 it is very important to realize what the leftovers are! They are kids, and they will cry if you leave them behind. If you try to split kids up into fractions, it is quite messy and unreasonable. So the only rationale thing to do is to get another car. So, the answer becomes 5. Five cars will be needed to transport the students to the zoo.
Please note that all of these situations state that the items are to be divided evenly. Otherwise, one could share very unevenly (I’ll take all $18 !) and that does not represent division.