Estimating quotients & Dividing by 2-digit divisors (long division)

Grade 4 · Mathematics

Semester 2 | Period 4 | Week 22

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Subject: Mathematics

Semester: 2

Period: 4

Week: 22

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 4
Date: Week 22
Lesson Duration: 45 minutes
Week & Period: Week 22, Period 4
Topic: Estimating quotients & Dividing by 2-digit divisors (long division)
Sub-topic: Long division with remainders

Learning Objectives
By the end of the lesson, students should be able to:

  1. Estimate quotients to verify long division solutions.
  2. Divide 3- and 4-digit numbers by 2-digit divisors, including remainders.
  3. Solve real-life word problems involving division.

Previous Knowledge
Students already know mental division and multiplication of 2-digit numbers.

Instructional Materials
Mathematics textbook, graph paper, number lines, counters.

Lesson Development – ABC Model

A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher presents: “Divide 3,492 ÷ 23. How can estimation help?” Students discuss.

B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes

Teacher demonstrates division of large numbers by two-digit divisors using estimation followed by long division and verification steps.

Step-by-step example: 6,540 ÷ 45

  1. Estimate quotient: Round divisor 45 to 50 to simplify; estimate 6,540 ÷ 50 ≈ 130
  2. Perform long division:
  • Divide 65 by 45 → 1 (write 1 in quotient) remainder 20
  • Bring down 4 (making 204)
  • Divide 204 by 45 → 4 (write 4 in quotient) remainder 204 – (45 × 4) = 204 – 180 = 24
  • Bring down 0 (making 240)
  • Divide 240 by 45 → 5 (write 5 in quotient) remainder 240 – (45 × 5) = 240 – 225 = 15
    Quotient = 145, remainder = 15
  1. Verify with multiplication:
    45 × 145 = 6,525
    6,525 + 15 = 6,540 (original dividend) → verification correct

Additional Examples:

  • 3,200 ÷ 26
    Estimate: 3,200 ÷ 25 = 128
    Long division to find exact quotient and remainder
  • 3,492 ÷ 23
    Estimate: 3,492 ÷ 20 = 174.6
    Long division for exact result

Learners’ Activities (Expanded):

  • Students work in pairs to practice division of 3,200 ÷ 26 and 3,492 ÷ 23 using guided step-by-step scaffolded instructions provided by the teacher.
  • Pairs swap papers for peer review, checking for correct estimation, division steps, and final answers.
  • Encourage students to use calculators to verify results after manual calculations for reinforcement.
  • Use graph paper to align digits correctly during long division.

Assessment Checks:

  • Estimate first, then calculate: What is the quotient and remainder when dividing 4,308 ÷ 42? (Expected: Estimate ~ 100, quotient 102 remainder 24)
  • Calculate 5,670 ÷ 36 and verify with multiplication.
  • Explain why estimation helps before performing long division.
  • What is the remainder when 7,523 ÷ 51?
  • How does checking multiplication help confirm division results?

Notes (Expanded & Detailed):
• Estimation provides a useful starting point that helps students anticipate the size of the quotient and avoid mistakes.
• Long division breaks down complex division into manageable steps, reinforcing place value understanding and algorithmic skills.
• Verification through multiplication and addition of remainder solidifies understanding of division relationship with multiplication.
• Peer review and scaffolded guidance promote collaborative learning and accuracy.
• Graph paper aids in neatness and alignment to prevent errors in multi-digit division.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Long division with 2-digit divisors involves estimation, correct placement of digits, and remainder handling.

Evaluation Method (Expanded):
Exit slip: 6,384 ÷ 48.
Teacher provides feedback and clarifies common errors.

Assignment (Expanded):
Divide 3,960 ÷ 33, 5,460 ÷ 42, 2,880 ÷ 36.
Create a story problem involving dividing items among groups.

Follow-up Activity:
Peer practice using classroom objects for hands-on long division.

Differentiation / Inclusive Strategies
Provide step charts for struggling learners; advanced learners solve word problems with multiple steps or remainders.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low