Explore · long division
Divide 451 by 41; show quotient place values and the remainder.
Singapore Math 5A · Independent learning
Divide a 3-digit Number by a 2-digit Number — Part 1
Learning target: Divide three-digit numbers by two-digit divisors using place-value groups and estimates.
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 is the largest multiple of 21 not above 100?
Understand the idea
Divide three-digit numbers by two-digit divisors using place-value groups and estimates.
Divide three-digit numbers by two-digit numbers with an estimate or partial quotients. Subtract a convenient multiple of the divisor, then collect the partial quotients. Check both the product and the remainder.
Vocabulary focus: partial products, quotient, remainder. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Choosing a quotient digit that is too large.
Model to study: Partial-quotient subtraction bars.
Worked examples
Worked examples 1 · long division
Divide 418 by 38; show quotient place values and the remainder.
Solution: 11 R 0
Why: 38×11=418; 418−418=0. The remainder 0 is less than 38. Check 38×11+0=418.
Worked examples 2 · long division
Divide 533 by 41; show quotient place values and the remainder.
Solution: 13 R 0
Why: 41×13=533; 533−533=0. The remainder 0 is less than 41. Check 41×13+0=533.
Worked examples 3 · long division
Divide 874 by 46; show quotient place values and the remainder.
Solution: 19 R 0
Why: 46×19=874; 874−874=0. The remainder 0 is less than 46. Check 46×19+0=874.
Check understanding
Check understanding 1 · long division
Divide 306 by 18; show quotient place values and the remainder.
Check understanding 2 · long division
Divide 168 by 14; show quotient place values and the remainder.
Guided practice
Guided practice 1 · long division
Divide 496 by 31; show quotient place values and the remainder.
Guided practice 2 · long division
Divide 396 by 36; show quotient place values and the remainder.
Guided practice 3 · long division
Divide 551 by 29; show quotient place values and the remainder.
Independent practice
Independent practice 1 · long division
Divide 210 by 15; show quotient place values and the remainder.
Independent practice 2 · long division
Divide 448 by 32; show quotient place values and the remainder.
Independent practice 3 · long division
Divide 418 by 22; show quotient place values and the remainder.
Independent practice 4 · long division
Divide 663 by 39; show quotient place values and the remainder.
Independent practice 5 · long division
Divide 646 by 38; 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): “448 ÷ 28 = 448/27. 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 448 by 28; 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 480 by 30; show quotient place values and the remainder.
Exit check
Exit check 1 · long division
Divide 504 by 28; show quotient place values and the remainder.
Exit check 2 · long division
Divide 195 by 13; 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.