Mastering Long Division

Overview

This 60-minute lesson is designed for Grade 5 students following the British Columbia (BC) Mathematics Curriculum. It focuses on developing students’ understanding and skills in long division with multi-digit dividends and single-digit divisors. The lesson incorporates hands-on, practical activities that encourage conceptual understanding and procedural fluency.

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Curriculum Alignment

BC Mathematics Curriculum – Grade 5

• Number: Operations and Computation

  • Learning Standards:
    • Apply and explain strategies for multiplying and dividing whole numbers (5N2)
    • Demonstrate understanding of division by solving problems involving multi-digit dividends (5N2.2)
    • Develop efficient mental and written strategies for division (5N2.3)

• Mathematical Processes and Practices (integrated throughout)

  • Reasoning and Analyzing
  • Connecting and Reflecting
  • Communicating and Representing
  • Strategic Thinking

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Learning Objectives

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

1. Demonstrate step-by-step long division to divide multi-digit numbers by single-digit numbers.
2. Explain the reasoning behind each step in the long division process.
3. Apply long division to solve real-world word problems.
4. Self-assess and peer-assess understanding of long division steps and accuracy.

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Materials Needed

• Whiteboard and markers
• Student whiteboards and markers or paper and pencil
• Printed division problem cards (10-15 problems)
• Base-10 blocks or place value charts (for visual modelling)
• Exit tickets (small sheets with 2 problems)
• Timer or stopwatch

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Lesson Breakdown (60 minutes)

1. Introduction & Activation (10 minutes)

Objective: Build on prior knowledge of division and introduce the long division algorithm.

• Begin with a quick whole-class warm-up: oral division problems with small dividends (e.g., 24 ÷ 3, 56 ÷ 7) to activate existing strategies.
• Ask: “How do you know how many times one number fits into another?”
• Introduce the vocabulary and symbols of long division (dividend, divisor, quotient, remainder). Write an example on the board: 154 ÷ 7.
• Use base-10 blocks or a place value chart to model how division can be represented concretely (e.g., dividing 154 into 7 groups).

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2. Explicit Teaching: Step-by-Step Long Division (15 minutes)

Objective: Demonstrate and model the long division algorithm clearly.

• Display an example problem on the board: 154 ÷ 7.
• Break down the process:
  1. Divide the first digit(s): ask, “How many times does 7 go into 15?”
  2. Multiply: 7 × 2 = 14
  3. Subtract: 15 - 14 = 1
  4. Bring down the next digit (4) to make 14
  5. Repeat division: How many times does 7 go into 14? (2)
  6. Multiply: 7 × 2 = 14
  7. Subtract: 14 - 14 = 0 (No remainder)
• Write each step on the board and use clear language, linking to the concrete model.
• Encourage students to verbalise the process aloud with you.
• Emphasise checking work by multiplying quotient and divisor; add remainder if applicable to see if it matches the dividend.

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3. Guided Practice with Peer Collaboration (15 minutes)

Objective: Students practise long division with teacher support, explaining thinking to a partner.

• Hand out printed division problem cards (e.g., 186 ÷ 3, 247 ÷ 5).
• Students work in pairs to solve two problems using long division on whiteboards or paper.
• Encourage partners to:
  • Take turns explaining each step
  • Use place value language (divide, multiply, subtract, bring down)
  • Check each other's calculations
• Teacher circulates, asking probing questions like: “Why did you bring down that number?” or “What does the remainder mean here?”
• Share one or two examples from pairs on the board, highlighting correct process and common errors.

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4. Real-World Application & Problem Solving (10 minutes)

Objective: Apply long division skills to solve practical problems.

• Present a word problem contextualised for Grade 5, e.g.:
  “A bakery has 368 cupcakes to package evenly into boxes that hold 8 cupcakes each. How many boxes are needed? Will there be any cupcakes left over?”
• Read and discuss the problem with the class.
• Guide students to identify dividend (368), divisor (8), and what the quotient and remainder represent in this context.
• Let students work independently or in pairs to solve the problem and write their answer in a complete sentence.
• Ask a few students to share their approaches and answers.

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5. Closing & Assessment (10 minutes)

Objective: Check individual understanding and reflect on learning.

• Distribute exit tickets with two long division problems (e.g., 225 ÷ 9, 143 ÷ 4).
• Students complete independently within 5 minutes.
• Collect for assessment.
• End with a quick reflective question: “What part of long division makes the most sense to you? What part is still tricky?”
• Invite 2-3 brief student responses to consolidate learning and inform next steps.

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Assessment Ideas

• Formative: Observation during partner work, teacher questioning, and class discussions.
• Exit Tickets: Evaluate accuracy and steps shown; note misunderstandings.
• Peer Assessment: Use a simple checklist to confirm steps were followed (Divide - Multiply - Subtract - Bring Down) and clear explanation.
• Self-Reflection: Encourage students to identify areas of strength and challenge for future learning focus.

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Differentiation & Extensions

• Support: Use base-10 blocks or place value charts for those needing concrete reinforcement; provide partially completed problems.
• Challenge: Introduce problems with remainders or divisors with two digits, or explore the interpretation of remainders in different contexts (rounding up, leftover, etc.).
• Cross-Curricular: Connect with science (e.g., dividing resources in an experiment) or social studies (dividing supplies).

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Teacher’s Tips

• Use precise mathematical vocabulary consistently.
• Model thinking aloud to demystify the process.
• Encourage students to estimate before dividing, reinforcing number sense.
• Celebrate effort and gradual mastery with positive reinforcement.

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By following this lesson plan, teachers will engage Grade 5 learners in building a solid, conceptual and procedural understanding of long division that aligns closely with the British Columbia curriculum standards.