Lesson objective: Analyze real-world division problems to determine how to interpret a remainder.
This lesson helps to build procedural skill with interpreting remainders in division word problems. Tape diagrams are used here because it supports students' understanding of the dividend, divisor, quotient, and remainder. This work develops students' understanding that we can use addition, subtraction, multiplication, and division to solve multi-step measurement problems.
Students engage in Mathematical Practice 1 (Make sense and persevere) as they analyze the given information and explain the meaning of the problem. Students should ask themselves, "Does this make sense?" when interpreting what to do with remainders. Additionally, this work engages in Mathematical Practice 2 (Reason abstractly and quantitatively) as they reason about how to use remainders in division problems and create a logical explanation for what to do with the remainders.
Special materials needed:
- Possible mentor text, Remainder of One, by Elinot J. Pinzes
- Smartboard, document camera, or overhead projector
How to interpret the remainder
This lesson will show 4 ways to interpret the remainder. Depending on the division problem you are solving, the 4 ways to interpret the remainder are the following.
- Write the remainder as a fraction
- Use only the remainder (or drop the quotient)
- Drop the remainder (or use only the quotient)
Write the remainder as a fraction
Sarah has a piece of twizzlers candy that is 16 inches long. She wants to share the whole candy with four friends so that each person has the same amount.
How long will each piece be?
Divide 16 by 5. The answer is 3 r1
The remainder, 1 inch, can be divided into 5 equal pieces.
Add 1 to the quotient
Thirty people are going to a wedding. They want to put 4 people in each car so that people can sit comfortably. How many cars will be needed?
Divide 30 by 4. The answer is 7 r2
The answer shows that 7 cars will be needed, but 2 people still need to go to a car.
Therefore, they will need 8 cars.
Use only the remainder
David has 20 dollars in his pocket. He wants to give the same amount of money to 3 friends. The rest of the money, if any, will go to his sister to buy candies. How much money will go to his sister if David wants to give away everything he has?
Divide 20 by 3. The answer is 6 r2
The remainder is 2, so 2 dollars will go to his sister.
Drop the remainder
Darlene has 50 dollars in her pocket. She wants to buy meals for 6 best friends. If each meal costs 9 dollars, will Darlene be able to keep all her friends happy?
Divide 50 by 9. The answer is 5 r5
Darlene can only buys 5 meals. Therefore, somebody will not be happy.
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