Unfair Sharing: Division with Remainder

Contributor: Erika Wargo. Lesson ID: 12100

Are you hungry to learn more about division? Do you like leftovers? Sometimes it's hard to divide things up fairly and equally. Learn what do to when your division problem doesn't play fair and equal!



learning style
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!


Can the pizza be shared equally? Who gets the leftover pieces?

Division is splitting into equal parts or groups, similar to sharing.

Sometimes when dividing, we can't share fairly. When we divide and have something left over, it is called a remainder.

Gather 16 pennies and draw 5 squares on a piece of paper. Now, let's consider this question:

If 16 pennies are divided among 5 children, how many pennies will each child receive?

Try to divide 16 into 5 equal groups with your pennies. Did you get something that looks like this?

There is no whole number that allows us to evenly distribute the 16 pennies among 5 groups. We can put three pennies in each of the five groups, but we don’t have enough pennies to put another penny in each.

Let’s think about this question: “How many fives is close to, but not more than, 16?” We can see above that by putting three pennies in each group, we get five groups of three, which is fifteen pennies. That leaves one penny out of a group, or remaining. So, let’s put this in a division problem:

  5 1 6  


  5 1 6  
    1 5  


  5 1 6  
  - 1 5  


      3 R1
  5 1 6  
  - 1 5  


Let's take a few minutes to review our division terms:

  • Dividend a number that is divided by another number. 16 is the dividend.
  • Divisor a number that divides another number. 5 is the divisor.
  • Quotient the result of division. 3 is the quotient.
  • Remainder the number “left over” when two numbers are divided. 1 is the remainder.

Remember, multiplication and division are inverse, or opposite, operations. We can also think of division problems as backwards multiplication. In the problem above, we could think, “What number times five will get us close to 16?” I know that 5 x 3 = 15, which is only 1 away from 16. So, the answer is 3 remainder 1.

Discuss with your parent or teacher:

  • What strategies can you use to determine if a problem has a remainder before dividing?
  • What does the remainder mean if we were sharing something, like candy?
  • Can you think of a time when the remainder couldn’t be shared equally?

Now that you have talked about remainders, let’s go practice finding remainders and understanding what they mean in a problem! Move on to the Got It? section.

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