I’m always looking for ways to make math easier for our students and fun at the same time. That’s why I love partial quotients! Long division can be quite the challenge – particularly for 4th graders just starting to get the hang of it. But teaching the partial quotients method can transform the long division process into something simpler and more approachable for kids. In this post, we will take a look at the partial quotient division strategy and I’ll walk you step-by-step through how I teach it in my own classroom.
What is partial quotient division?
First, let’s learn what partial quotients mean. Quotients are the results of a division problem. Rather than having to divide a number as a whole, using partial quotients breaks the original number into smaller parts that are easier to work with, making the problem into a series of smaller and faster calculations compared to the divide-multiply-subtract-bring down strategy.
When I taught 3rd grade math, I thought teaching students about compatible numbers along with rounding seemed nonsensical. Until I moved to 4th grade and started teaching division. Partial quotient division is simply using compatible numbers to make a division problem easier to solve! Let’s break this down with an example.
For partial quotient division, we want to use numbers that are easy to work with, so we try to use friendly numbers like 10, 50 and 100. First, we write 100 on the right side to show that we are taking out 100 groups.
100 groups of 4 makes 400, so we subtract 400 from 673. This leaves us with 273.
We know that we can make at least 50 more groups, so we write 50 on the right side. 50 groups of 4 make 200, so we take 200 away from 273 and we are left with 73.
We continue to find partial quotients until the remaining dividend is too small to be divided and it becomes the remainder.
Finally, add the partial quotients to find the full quotient.
How I teach the partial quotient strategy:
Step 1: Introduce partial quotient division with a whole group mini-lesson and anchor chart
When I teach this strategy we do many, many examples together. I model a few, then we do several problems together, and on our final problem together we create an anchor chart that walks through the steps above and labels parts of the problem with division vocabulary such as divisor and dividend. The anchor chart gives students something visual to refer to when they start working independently. To end the lesson I have students work one example by themselves, while I wander around the room and assist where needed.
Step 2: Practice partial quotient division with a cooperative activity
The next step is give students some opportunity to practice with classmates in a no-pressure and interactive environment. I put kids in groups of 3-5 students and give each group a set of partial quotient division cards to place face-down in the middle of the group. Taking turns as the leader, each student will draw and read a card. All members of the group will solve the problem on their own. Once the leader sees that all members of the group have an answer, he/she will give a signal and all members of the group will compare answers.
Step 3: Practice partial quotient division with math stations
After we’ve had time to practice together and the students have gained confidence, we break into small groups and rotate through math station work time.
Station 1:Interactive Notebooks
Have students create a matching flaps notebook entry like below. Students cut out the quotient flaps and cut on the vertical lines to make flaps between each one. Then they glue this piece into their notebooks by using glue only along the top edge. Finally, they will cut apart the solution cards and match them to the correct quotient by gluing each one underneath the matching flap.
Station 2: Partner Games
The game we play to practice partial quotient division is a twist on Scrabble. I pair students up and give each player a set of letter cards and a game instruction sheet. You can grab a free copy of the division game letter cards here and the directions are below!
Materials:
- Partner
- Letter cards
Directions:
- Cut apart the cards and place them face down.
- On each player’s turn they will draw a card and solve the equation. If they are correct, they keep the card. If they are wrong the card goes back to the bottom of the pile.
- Once all the cards have been won, players will use the letters on their cards to spell a word.
How to Win:
- The player who correctly spells the longest word is the winner.
Station 3: Paper and Pencil Practice
Use your textbook assignment or the worksheet in this lesson to give students a chance to show you what they’ve learned about partial quotient divison and provide you with a quick assessment of their understanding. I’m sharing my math rubric to make grading quick for you and effective for students!
You can grab all these activities in this lesson on partial quotient division in my TPT store or grab the whole division unit on TPT or in my webstore. Happy teaching!
