Dividing with Remainders Background Information for Teachers, Parents and Caregivers
This page provides information to support educators and families in teaching K-3 students about dividing with remainders. It is designed to complement the Dividing with Remainders topic page on BrainPOP Jr.
This movie will introduce children to division with remainders. We highly recommend reviewing the Making Equal Groups movie before exploring this topic. Encourage children to use counters or draw pictures as they practice division with remainders. Help them employ different strategies so they can find the one that works best for them as they develop their math skills.
Quickly review how to make equal groups. Present 8 counters and tell children to split them into 2 equal groups. How many counters will be in each group? Divide the counters to show that 4 counters will be in each group. Guide children to write a number sentence to describe what they did: 8 ÷ 2 = 4. Then present the same number of counters and tell children to split them into 3 equal groups. What happens? Each group can have 2 counters, but there are 2 left over. Help children understand that they cannot divide 8 by 3 equally. Explain that a remainder is the number left over after dividing two numbers. Create a division sentence that represents what happened: 8 ÷ 3 = 2 R2. Explain that when you divide 8 items into 3 groups, you have 2 items in each group, and 2 items left over. Be sure to point out that the R stands for “remainder.”
Solve other number stories that involve division with remainders. For example, you might want to pose the following problem: “Moby and Annie share 11 stickers. How many does each person get? How many are left over?” You can use counters to model the number story together. Have children divide 11 counters into 2 groups, making sure each group has the same number of counters. There will be 5 counters in each group. Then point out how there is 1 counter left over—that is the remainder. Write the division sentence together: 11 ÷ 2 = 5 R1. Repeat the activity with other scenarios, helping children use their manipulatives and write division sentences. Be sure that children have practice in writing the division problems using both algorithms—in the equation format and in the “long division” format.
Break down a division sentence for children: In 22 ÷ 5 = 4 R2, the total number of items is 22, the number of groups is 5, and the number of items in each group is 4. The number of items left over is 2. Encourage children to check their work after they finish solving division number sentences. They can multiply the number of groups by the number of items in each group. Then they can add the product to the remainder. The answer should be the total number of items. So in 22 ÷ 5 = 4 R2, they can multiply 5 x 4 = 20 and then add the remainder: 20 + 2 = 22. Have children solve division sentences and then check their work by multiplying and adding. They should get into the habit of going back over their work, which will not only empower them to self-check but also develop their multiplication and addition skills!
Help children understand that in the real world, division problems often have remainders. Have them think of scenarios they have encountered where they could not divide something equally. What did they do? Discuss with children and share stories.
