Focus on the Remainder

When students need to use the remainder as their answer, we first discuss situations where we should focus on the “leftover” number after we make our complete groups. One way you can help students visualize this is by doing the “Goodie Bag” activity mentioned above, but modify it in the following way:

Make a “Goodie Bag”

• • Tell students that you need their help making goodie bags, and once they’re done, they will get to keep any leftover candy that didn’t go into the equal groups. (This usually gets them excited!)
  • Give each individual student a set number of candies and several small baggies (make sure you give a number of candy and bags that won’t divide evenly).
  • Instruct students to count the candy, then divide the candy evenly among their baggies. 
  • Have students write a division sentence that includes the total amount of candy they started with, the number of groups they split it into, and the amount of candy in each bag. They will write the number of leftover candy as the remainder at the end of their division sentence.
  • Discuss:

• If you only want to know the amount of candy you get to keep, what number should you focus on?

• Have students return the complete goodie bags to you, and they get to keep the “remainder.”

Round Up or “Add One More”

This way of interpreting remainders is usually the trickiest for my students to grasp without some kind of real-world application. I introduce this by asking students to tell me an example of a time when you absolutely can not drop the remainder. Oftentimes, I’m met with some blank stares. So here’s what we do:

• • Tell students to imagine they’re taking a field trip, and they have to split up into groups for the van ride. Each van can hold 6 passengers (change this number if your class divides evenly into 6. You want to make sure they will be a remainder), so divide the class into groups of 6.
  • Count the number of complete groups and write a division sentence on the board that shows the total number of students, the number of students in each group, then the number of groups as the quotient. Write the number of students who weren’t included in the complete groups as the remainder.
  • Point to the quotient and discuss:

• Our answer is (number), so we know we need (number) of vans to take the complete groups. But what do we do with the students who were left over? Do we just leave them behind?

Students will answer with a loud “No!” (Especially the ones in the “leftover” group!) Without me prompting them, they almost always suggest that I simply get another van. I explain to students that when we are dividing something and we must keep the remainder with us, we can round our quotient up to the next whole number or “add one more” so that we can keep the remainder with the quotient. Some other scenarios you can present your students with are:

• You are packing all of your books into boxes. When you have a remainder, you’ll need to add another box to the quotient so that you don’t have to leave any books behind.
• You are packing your boxes into a moving truck and can only fit a certain number of boxes per trip. If you have a remainder, you’ll need to add one more trip in order to move all of your boxes.

Ask students to come up with their own scenarios when you might have to “round up” or “add one more” to the remainder, and they might surprise you with some unique new examples!

Here are some of my favorite resources to use while teaching students to interpret remainders: