Lesson Plan
Divide Using Partial Quotients Lesson Plan
Students will learn to use the partial quotients method to divide multi-digit numbers by breaking the divisor into manageable chunks, practice the strategy through guided problems, and apply it independently to build computational fluency.
This lesson deepens division concept understanding, promotes number sense, and offers a flexible strategy that boosts confidence and prepares students for more advanced division tasks and real-world problem solving.
Audience
5th Grade Students
Time
30 minutes
Approach
Modeling, scaffolded practice, and independent application of partial quotients.
Materials
- Whiteboard and Markers, - Projector or Interactive Whiteboard, - Partial Quotients Anchor Chart, - Partial Quotients Guided Practice Worksheet, and - Partial Quotients Independent Practice Worksheet
Prep
Teacher Preparation
10 minutes
- Review the Partial Quotients Anchor Chart and familiarize yourself with each step.
- Print and copy the Partial Quotients Guided Practice Worksheet and Partial Quotients Independent Practice Worksheet.
- Set up the anchor chart visibly in the classroom or project it.
- Gather whiteboard markers and ensure the projector/smartboard is working properly.
Step 1
Warm-Up
5 minutes
- Write two division problems on the board (e.g., 78 ÷ 3; 145 ÷ 5).
- Ask students to solve mentally or with their preferred method.
- Discuss strategies and recall of basic division facts.
Step 2
Direct Instruction
7 minutes
- Display the Partial Quotients Anchor Chart.
- Model dividing 145 ÷ 5 using partial quotients:
- Choose a large chunk (e.g., 100÷5=20), subtract, then handle the remainder (45÷5=9).
- Record each partial quotient and subtract stepwise.
- Sum the partial quotients for the final answer.
- Emphasize vocabulary: divisor, dividend, quotient, partial quotient.
Step 3
Guided Practice
8 minutes
- Distribute the Partial Quotients Guided Practice Worksheet.
- Work through the first problem together, modeling thinking aloud.
- Students pair up to solve the next two problems, using the partial quotients method.
- Circulate, prompt students to explain each subtraction and quotient step.
Step 4
Independent Practice
7 minutes
- Hand out the Partial Quotients Independent Practice Worksheet.
- Students complete problems individually, showing all partial quotient steps.
- Offer targeted support to students who need clarification.
Step 5
Cool-Down / Exit Ticket
3 minutes
- Display a final division problem (e.g., 328 ÷ 4) on the board.
- Students solve it on a sticky note or mini whiteboard using partial quotients.
- Collect responses to gauge understanding and plan next steps.
Slide Deck
Divide Using Partial Quotients
A flexible strategy for dividing multi-digit numbers by taking off “chunks” of the dividend.
Welcome students! Introduce today’s focus on the partial quotients method for division. Explain that this strategy breaks a division problem into manageable chunks to build understanding and confidence.
Warm-Up
Solve mentally or with your favorite method:
• 78 ÷ 3
• 145 ÷ 5
Discuss the strategies you used.
Begin with a quick warm-up to activate prior knowledge. Write the two problems on the board as students enter.
Learning Objectives
By the end of this lesson, you will be able to:
• Use the partial quotients method to divide multi-digit numbers.
• Explain how each “chunk” is chosen and subtracted.
• Combine partial quotients to find the final quotient.
Share today’s learning targets so students know the goals.
Key Vocabulary
• Dividend: the number being divided.
• Divisor: the number you divide by.
• Quotient: the result of division.
• Partial Quotient: each chunk of the quotient found step by step.
Introduce key terms; reinforce correct usage during the lesson.
Partial Quotients Anchor Chart
Follow these steps when dividing:
- Decide on a large, easy chunk to divide the dividend by the divisor.
- Record the partial quotient and subtract the product from the dividend.
- Repeat with the new remainder until it’s smaller than the divisor.
- Add all partial quotients for the final answer.
Display or hand out the anchor chart. Point to each step as you explain.
Model Example
Problem: 145 ÷ 5
- Choose 100 ÷ 5 = 20. 145 – 100 = 45.
- Choose 45 ÷ 5 = 9. 45 – 45 = 0.
- Partial quotients: 20 + 9 = 29.
Quotient = 29
Model 145 ÷ 5 step by step. Think aloud: why you pick each chunk, how you subtract, and how you record partial quotients.
Guided Practice
• Distribute Guided Practice Worksheet.
• Work through Problem 1 together.
• In pairs, solve Problems 2 and 3 using partial quotients.
Guide students through the first problem. Then have them work in pairs for the next two. Circulate and ask them to explain each subtraction.
Independent Practice
• Hand out Independent Practice Worksheet.
• Complete all problems on your own, showing each partial quotient and subtraction.
• Raise your hand if you need help.
Students work individually. Offer support where needed, asking them to show all partial quotient steps.
Exit Ticket
Solve 328 ÷ 4 using the partial quotients method. Show all steps on a sticky note or mini whiteboard.
Collect responses as students finish.
Use this exit ticket to check for understanding and plan next steps.
Worksheet
Partial Quotients Guided Practice
Use the partial quotients method to divide each problem. Refer to the Partial Quotients Anchor Chart for each step.
1. Scaffolded Example: 256 ÷ 4
a. Choose an initial chunk:
• ______ ÷ 4 = ______
• Record this partial quotient: ______
• Subtract: 256 – ______ = ______
b. Divide the remainder:
• ______ ÷ 4 = ______
• Record this partial quotient: ______
• Subtract: ______ – ______ = ______
c. Combine partial quotients:
• Add: ______ + ______ = ______
• Final Quotient: ______
2. Guided Practice: 389 ÷ 6
Show all partial quotient steps, subtractions, and your final quotient here:
3. Guided Practice: 714 ÷ 7
Show all partial quotient steps, subtractions, and your final quotient here:
Be sure to label each partial quotient and keep your work organized!
Worksheet
Partial Quotients Independent Practice
Use the partial quotients method to divide each problem. Show all partial quotient steps, subtractions, and your final quotient. Refer to the Partial Quotients Anchor Chart as needed.
1. 432 ÷ 3
Show all steps here:
2. 795 ÷ 5
Show all steps here:
3. 1,248 ÷ 4
Show all steps here:
4. 3,765 ÷ 6
Show all steps here:
5. Real-World Problem
A warehouse packs 4,512 items into boxes of 7 items each. How many full boxes can they fill? Use the partial quotients method to solve:
Be sure to label each partial quotient and keep your work organized!
Reading
Partial Quotients Anchor Chart
Follow these steps to divide using partial quotients:
- Choose a Friendly Chunk
- Pick a large, easy-to-divide portion of the dividend (e.g., hundreds or tens).
- Divide the Chunk
- Divide your chosen chunk by the divisor.
- Record & Subtract
- Write down the partial quotient.
- Subtract (partial quotient × divisor) from the current dividend or remainder.
- Repeat
- Use the new remainder and repeat until it’s smaller than the divisor.
- Add Partial Quotients
- Sum all partial quotients for the final quotient.
Example: 145 ÷ 5
• Chunk 1: 100 ÷ 5 = 20 → 145 – 100 = 45
• Chunk 2: 45 ÷ 5 = 9 → 45 – 45 = 0
Partial quotients: 20 + 9 = 29
Final Quotient: 29
Display this chart prominently during lessons to guide students through each step of the partial quotients method.
Answer Key
Partial Quotients Answer Key
Guided Practice
1. Scaffolded Example: 256 ÷ 4
a. Choose an initial chunk
- 200 ÷ 4 = 50 → Partial quotient = 50
- Subtract: 256 – 200 = 56
b. Divide the remainder
- 56 ÷ 4 = 14 → Partial quotient = 14
- Subtract: 56 – 56 = 0
c. Combine partial quotients
• 50 + 14 = 64
Final Quotient: 64
2. 389 ÷ 6
- Choose a large chunk: 360 ÷ 6 = 60 → 389 – 360 = 29 (PQ = 60)
- Next chunk: 24 ÷ 6 = 4 → 29 – 24 = 5 (PQ = 4)
- Remainder 5 is smaller than divisor 6, so stop.
Partial quotients: 60 + 4 = 64
Quotient: 64 R5
3. 714 ÷ 7
- Chunk: 700 ÷ 7 = 100 → 714 – 700 = 14 (PQ = 100)
- Chunk: 14 ÷ 7 = 2 → 14 – 14 = 0 (PQ = 2)
Partial quotients: 100 + 2 = 102
Final Quotient: 102
Independent Practice
1. 432 ÷ 3
- 300 ÷ 3 = 100 → 432 – 300 = 132 (PQ = 100)
- 120 ÷ 3 = 40 → 132 – 120 = 12 (PQ = 40)
- 12 ÷ 3 = 4 → 12 – 12 = 0 (PQ = 4)
Partial quotients: 100 + 40 + 4 = 144
Final Quotient: 144
2. 795 ÷ 5
- 700 ÷ 5 = 140 → 795 – 700 = 95 (PQ = 140)
- 95 ÷ 5 = 19 → 95 – 95 = 0 (PQ = 19)
Partial quotients: 140 + 19 = 159
Final Quotient: 159
3. 1,248 ÷ 4
- 1,200 ÷ 4 = 300 → 1,248 – 1,200 = 48 (PQ = 300)
- 48 ÷ 4 = 12 → 48 – 48 = 0 (PQ = 12)
Partial quotients: 300 + 12 = 312
Final Quotient: 312
4. 3,765 ÷ 6
- 3,600 ÷ 6 = 600 → 3,765 – 3,600 = 165 (PQ = 600)
- 165 ÷ 6 = 27 → 165 – 162 = 3 (PQ = 27)
Partial quotients: 600 + 27 = 627
Quotient: 627 R3
5. Real-World Problem: 4,512 ÷ 7
- 4,200 ÷ 7 = 600 → 4,512 – 4,200 = 312 (PQ = 600)
- 280 ÷ 7 = 40 → 312 – 280 = 32 (PQ = 40)
- 28 ÷ 7 = 4 → 32 – 28 = 4 (PQ = 4)
Partial quotients: 600 + 40 + 4 = 644
Full boxes: 644 (Remainder 4 items)