Explore · long division
Divide 849 by 48; show quotient place values and the remainder.
Singapore Math 5A · Independent learning
Divide a 3-digit Number by a 2-digit Number — Part 2
Learning target: Handle harder regrouping and remainders with a multiplication verification.
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.
Find quotient and remainder of 79 ÷ 8.
Understand the idea
Handle harder regrouping and remainders with a multiplication verification.
Harder three-digit division may require repeated estimates. After subtracting the selected divisor multiple, the final remainder must be nonnegative and smaller than the divisor. An excessive quotient digit makes the subtraction negative.
Vocabulary focus: partial products, quotient, remainder. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Recording a remainder equal to or above the divisor.
Model to study: Long-division place-value trace.
Worked examples
Worked examples 1 · long division
Divide 619 by 38; show quotient place values and the remainder.
Solution: 16 R 11
Why: 38×16=608; 619−608=11. The remainder 11 is less than 38. Check 38×16+11=619.
Worked examples 2 · long division
Divide 239 by 17; show quotient place values and the remainder.
Solution: 14 R 1
Why: 17×14=238; 239−238=1. The remainder 1 is less than 17. Check 17×14+1=239.
Worked examples 3 · long division
Divide 715 by 41; show quotient place values and the remainder.
Solution: 17 R 18
Why: 41×17=697; 715−697=18. The remainder 18 is less than 41. Check 41×17+18=715.
Check understanding
Check understanding 1 · long division
Divide 296 by 19; show quotient place values and the remainder.
Check understanding 2 · long division
Divide 255 by 16; show quotient place values and the remainder.
Guided practice
Guided practice 1 · long division
Divide 497 by 32; show quotient place values and the remainder.
Guided practice 2 · long division
Divide 508 by 29; show quotient place values and the remainder.
Guided practice 3 · long division
Divide 304 by 22; show quotient place values and the remainder.
Independent practice
Independent practice 1 · long division
Divide 616 by 43; show quotient place values and the remainder.
Independent practice 2 · long division
Divide 679 by 35; show quotient place values and the remainder.
Independent practice 3 · long division
Divide 502 by 28; show quotient place values and the remainder.
Independent practice 4 · long division
Divide 764 by 47; show quotient place values and the remainder.
Independent practice 5 · long division
Divide 838 by 47; 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): “309 ÷ 26 = 309/25. 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 309 by 26; 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 453 by 24; show quotient place values and the remainder.
Exit check
Exit check 1 · long division
Divide 780 by 43; show quotient place values and the remainder.
Exit check 2 · long division
Divide 529 by 31; 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.