Mastering Long Division

Overview

This 25-minute lesson engages Year 5 students in mastering long division through a collaborative, hands-on approach aligned with the IE Curriculum (International Education Curriculum). By working in pairs to solve increasingly challenging division problems and verbalising their thinking processes, students develop fluency, confidence, and conceptual understanding in long division.

---

Curriculum Alignment

IE Curriculum Standards & Competencies Addressed:

• Mathematics: Number and Operations

  • Learning Outcome: Apply efficient strategies for division with up to 4-digit dividends and 1-digit divisors.
  • Competency: Demonstrate procedural fluency and reasoning by explaining steps and justifying solutions.
  • Skill Focus: Collaborative problem solving and mathematical communication.

• Critical Thinking and Communication

  • Collaborate effectively in pairs, articulate reasoning strategies clearly, and adapt approaches based on peer feedback.

---

Learning Objectives

By the end of this lesson, students will be able to:

• Confidently perform long division with 3- and 4-digit dividends by 1-digit divisors using the step-by-step algorithm.
• Verbalise and explain each step of their division process clearly to a peer.
• Collaborate to solve problems progressively increasing in difficulty, refining understanding through peer discussion.
• Identify and correct errors collaboratively in their solution methods.

---

Resources

• Whiteboard and markers
• Long division worksheets with 5 problems (ranging from easy to challenging)
• Visual aids showing the long division steps in a clear graphic organiser
• Scratch-paper or notebooks for calculations
• Timer or clock visible to class

---

Lesson Structure

1. Introduction & Recap (5 minutes)

• Briefly review the concept and steps of long division using a large (3-digit dividend ÷ 1-digit divisor) example on the whiteboard.
• Use the graphic organiser visible to all to reinforce the sequential steps: Divide, Multiply, Subtract, Bring down.
• Emphasise the importance of explaining every step aloud—this promotes deeper understanding and error checking.

Teacher Script:
“Today, you'll become division detectives. You’ll solve problems together and explain each part of your calculations so your partner can understand how you worked through the problem.”

---

2. Paired Collaborative Problem-Solving Activity (15 minutes)

Organisation:

• Students form pairs (10 pairs).
• Each pair receives a worksheet with five division problems ordered by increasing difficulty (e.g., 144 ÷ 3, 528 ÷ 4, 1728 ÷ 6, 3996 ÷ 7, 4092 ÷ 8).

Instructions:

• For each problem, take turns solving and explaining your process step-by-step aloud. The listener asks questions if any step is unclear.
• Use the graphic organiser to guide explanations and structure thinking.
• If stuck, pairs discuss and try alternative approaches—encourage sharing mental strategies.

Teacher Role:

• Circulate to listen to explanations, prompt richer discussion with questions such as:
  “Can you explain why you subtracted that number here?”
  “How did you decide what to bring down next?”
• Offer scaffolding for pairs needing extra support, suggest checking work step-by-step.

---

3. Reflection and Wrap-up (5 minutes)

• Invite two pairs to demonstrate their explanation of one division problem to the class, modelling clear, step-by-step reasoning.
• Facilitate a short discussion on common challenges and how talking through their steps helped solve these problems.
• Summarise key messages:
  “Explaining your thinking helps catch mistakes and deepens your understanding. Working with a partner makes challenging problems more manageable.”

---

Assessment

• Formative:
  Teacher observes pair interactions and monitor explanations for accuracy and reasoning depth.
• Peer Assessment:
  Students provide feedback on clarity and correctness of explanations within their pairs.
• Exit Reflection:
  Quick round-robin asking each pupil to say one step of long division and one thing they learned from their partner.

---

Differentiation

• For struggling students:
  Provide simpler questions initially (2-digit dividends) and pairing with a stronger peer. Provide sentence stems to scaffold explanations, e.g., "First I divide because...".
• For advanced students:
  Challenge with 4-digit dividends by 2-digit divisors or ask them to create and explain their own division problems to partners.

---

Teacher Tips to Wow the Class

• Introduce a “Division Detective” theme: students earn detective badges/stickers for clear explanations and teamwork.
• Use a “Math Talk” stopwatch where each student gets a timed turn to explain their reasoning, turning collaborative learning into a dynamic game.
• Record one pair’s explanation (audio or video) and play back to class for self-assessment and celebration.

---

Summary

This highly interactive, IE-curriculum-aligned lesson develops Year 5 students’ mastery of long division by embedding collaboration, reasoning, and progressive challenge. It cultivates mathematical fluency alongside powerful communication skills—setting a firm foundation for success in more complex operations.