Explore · long division
Divide 4,145 by 40; show quotient place values and the remainder.
Singapore Math 5A · Independent learning
Divide a 4-digit Number by a 2-digit Number
Learning target: Divide four-digit dividends by two-digit divisors and justify every quotient place.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
What digit belongs in the tens place of 105?
Understand the idea
Divide four-digit dividends by two-digit divisors and justify every quotient place.
Each quotient digit has a place value. A missing tens or ones contribution must still be represented by zero where appropriate. Verify the entire four-digit dividend with divisor × quotient + remainder.
Vocabulary focus: partial products, quotient, remainder. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Misplacing an internal zero in the quotient.
Model to study: Four-digit place-value quotient ledger.
Worked examples
Worked examples 1 · long division
Divide 5,539 by 41; show quotient place values and the remainder.
Solution: 135 R 4
Why: 41×135=5,535; 5,539−5,535=4. The remainder 4 is less than 41. Check 41×135+4=5,539.
Worked examples 2 · long division
Divide 2,650 by 22; show quotient place values and the remainder.
Solution: 120 R 10
Why: 22×120=2,640; 2,650−2,640=10. The remainder 10 is less than 22. Check 22×120+10=2,650.
Worked examples 3 · long division
Divide 3,855 by 38; show quotient place values and the remainder.
Solution: 101 R 17
Why: 38×101=3,838; 3,855−3,838=17. The remainder 17 is less than 38. Check 38×101+17=3,855.
Check understanding
Check understanding 1 · long division
Divide 6,505 by 48; show quotient place values and the remainder.
Check understanding 2 · long division
Divide 5,095 by 49; show quotient place values and the remainder.
Guided practice
Guided practice 1 · long division
Divide 5,548 by 46; show quotient place values and the remainder.
Guided practice 2 · long division
Divide 7,275 by 35; show quotient place values and the remainder.
Guided practice 3 · long division
Divide 6,626 by 49; show quotient place values and the remainder.
Independent practice
Independent practice 1 · long division
Divide 4,176 by 41; show quotient place values and the remainder.
Independent practice 2 · long division
Divide 4,819 by 40; show quotient place values and the remainder.
Independent practice 3 · long division
Divide 4,991 by 24; show quotient place values and the remainder.
Independent practice 4 · long division
Divide 5,076 by 49; show quotient place values and the remainder.
Independent practice 5 · long division
Divide 6,106 by 45; show quotient place values and the remainder.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “3362 ÷ 33 = 1681/16. I reduced only the divisor by one and did not verify with inverse multiplication.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Divide 3,362 by 33; show quotient place values and the remainder.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Divide 1,319 by 13; show quotient place values and the remainder.
Exit check
Exit check 1 · long division
Divide 5,076 by 42; show quotient place values and the remainder.
Exit check 2 · long division
Divide 6,012 by 29; show quotient place values and the remainder.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.