Authentic Lessons for 21st Century Learning

My Teacher's Record-Breaking Cup

Partial Quotients Division Method

K20 Center, Christine Cox | Published: September 22nd, 2020 by Oklahoma Young Scholars/Javits

  • Grade Level Grade Level 5th
  • Subject Subject Mathematics
  • Course Course Elementary Mathematics
  • Time Frame Time Frame 1-2 class period(s)
  • Duration More 120 minutes


Students will use a fun problem to discover and practice the partial quotients process for multiple-digit division.

Essential Question(s)

How can a large number be divided? 



Students engage in a division problem dealing with their teacher's favorite cup.


Students use manipulatives to construct different ways to divide a multi-digit number.


Students first explain how and why they divided the multi-digit number, and then the teacher formalizes new knowledge by connecting to the method of partial quotients for division.


Students use the Commit and Toss strategy to practice writing and solving division problems using the partial quotients method.


Students individually solve another division problem using the partial quotient method.


  • The teacher's favorite water bottle, coffee cup, or other beverage container

  • 1000, 100, 10, and 1 blocks

  • Paper/pencils

  • Whiteboard/markers for practice


Go to slide 3. Display a reusable cup or mug and share your LOVE for your favorite beverage (coffee, water, soda, etc). Explain that you refill this cup five (5) times a every day.

Go to slide 4. Students will use a Think, Pair, Share activity and collaborate to find the solutions for each of the following questions:

  • How many refills would I have in one school week (Monday through Friday only)?

  • How many refills would I have in one month?

  • About how many refills would I have in a year?


Go to slide 5. Explain to students that you have tracked the number of times you have refilled your cup, but not the number of days. Tell them, "I have refilled my cup 5,235 times, and I refill it 5 times each day."

Go to slide 6. Pass out copies of the Strategy Harvest handout from the attachments. Ask students to use the Strategy Harvest strategy and figure out how many days the cup has been used.

Allow students to think about how to represent the number 5,235 and also attempt to solve the problem. Tell them that it might be helpful to think about how we represent large numbers first. Students might first rewrite the number using expanded notation (5000+200+30+5) or base 10 blocks or rewrite it into friendly numbers like 5000+200+35.

Go to slide 7. As students begin to finish the problem, instruct them to find others who are done and compare notes about what strategies each used to solve the problem. Students should record details about others' strategies on their Strategy Harvest handout.


Go to slide 8. As a class, have students share strategies that they have used to solve the problem. Build upon student responses and be ready to connect their strategies to the partial quotients strategy.

Go to slide 9. Walk through the partial quotients method by talking about how students divided the quotient to start. You can point out how different groups approached the problems for examples.

  • When you divide the quotient, do you start with the smallest pieces or the biggest pieces first? The thousands or the ones?

  • Model how to “show the work.”

Go to slide 10. Work through this problem as a class:

759 ? 3

Go to slide 11. Have students work in pairs to solve the problems below. After each problem, have the students pair up with another pair and review the other pair's strategies and answers.

1,926 ? 6

3,380 ? 4


Go to slide 12. Follow the prompts on slides 12-17 to engage in a version of the Commit and Toss strategy that will help students practice estimating and evaluating their work.

  1. (Slide 12) Write a division problem on the paper. Toss and pick up a new paper.

  2. (Slide 13) Use estimation to find a reasonable answer for the written problem. Discuss, toss, and pick up a new paper.

  3. (Slide 14) Solve the division problem on the paper. Discuss, toss, and pick up a new paper.

  4. (Slide 15) Evaluate/provide feedback for the solution.

  5. (Slide 16) Write a “real-world” situation to match the problem. Remember that key words such as “per,” “each,” and “evenly between” often cue us that a problem is a division problem.

  6. (Slide 17) Share problems with the class as time permits.


Go to slide 18. Pass out copies of the Exit Ticket handout and have students answer the questions below.

Mrs. Kennedy is preparing a STEM activity where students will build a bridge out of plastic drinking straws. She has 642 straws that need to be shared between the 6 groups of students. Estimate how many straws each group gets.

Next, calculate the exact number of straws each group gets. Remember to show your work.

Why is your estimate higher or lower than your calculated value?