When we try to share anything between two or more people or things, we are performing division. Sometimes when we share there are going to be leftovers. I often use the example of ordering a pizza pie. Pizza pies, at least the round ones, are traditional cut into 8 slices. When you have four friends to share that pizza with, you will each get two slices. But, what happens when you have 3 friends? You will each get two slices, but there will also be two slices left. Who get the third slice? The left-over slices they are remainders. Remainders in the real world are a great source of conflict on the planet. Everyone is all for sharing, but who get the remainders? Remainders are foreign to students when they first hear of them. If you present the fact that division is just a form of repeated subtraction, students quickly grasp the notion that numbers will be left over. If your students are not familiar with the concept, start them off with the lessons. If there is a good level of familiarity there start them off with the repeated practice sheets.

These worksheets explain how to perform long division with and without remainders. We try to use a good assortment of picture tokens for each different exercise. I would have students first see if a remainder is present and then proceed from there with the worksheet. We will run your through lessons and worksheets that include remainders and, in some cases, do not. This is meant to keep you honest and critical in your evaluation.