Explore · round-number multiplication
Calculate 90 × 60 by factoring 60.
Singapore Math 5A · Independent learning
Multiplying by Tens, Hundreds, and Thousands
Learning target: Decompose round-number factors and justify partial products and zeros.
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.
Use an array or distributive property to calculate 13 × 6.
Understand the idea
Decompose round-number factors and justify partial products and zeros.
A multiple of ten such as 70 is 7 × 10, not an unrelated symbol. First multiply by the nonzero factor, then scale by ten; for hundreds or thousands scale more times. Use an area grid or distributive property to explain why the factors produce the final magnitude.
Vocabulary focus: place-value positions, inverse scaling, round-number factors. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Appending the wrong number of zeros without reasoning about factors.
Model to study: Array/place-value product model.
Worked examples
Worked examples 1 · round-number multiplication
Calculate 18 × 900 by factoring 900.
Solution: 16,200
Why: 900 = 9 × 100; first 18 × 9 = 162, then 162 × 100 = 16,200.
Worked examples 2 · round-number multiplication
Calculate 16 × 4,000 by factoring 4,000.
Solution: 64,000
Why: 4,000 = 4 × 1,000; first 16 × 4 = 64, then 64 × 1,000 = 64,000.
Worked examples 3 · round-number multiplication
Calculate 21 × 70 by factoring 70.
Solution: 1,470
Why: 70 = 7 × 10; first 21 × 7 = 147, then 147 × 10 = 1,470.
Check understanding
Check understanding 1 · round-number multiplication
Calculate 30 × 700 by factoring 700.
Check understanding 2 · round-number multiplication
Calculate 40 × 2,000 by factoring 2,000.
Guided practice
Guided practice 1 · round-number multiplication
Calculate 18 × 40 by factoring 40.
Guided practice 2 · round-number multiplication
Calculate 42 × 200 by factoring 200.
Guided practice 3 · round-number multiplication
Calculate 86 × 6,000 by factoring 6,000.
Independent practice
Independent practice 1 · round-number multiplication
Calculate 16 × 30 by factoring 30.
Independent practice 2 · round-number multiplication
Calculate 74 × 700 by factoring 700.
Independent practice 3 · round-number multiplication
Calculate 86 × 2,000 by factoring 2,000.
Independent practice 4 · round-number multiplication
Calculate 77 × 80 by factoring 80.
Independent practice 5 · round-number multiplication
Calculate 37 × 700 by factoring 700.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “71 × 200 = 1420. The final factor 10 does not affect the result.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Calculate 71 × 200 by factoring 200.
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). Calculate 58 × 9,000 by factoring 9,000.
Exit check
Exit check 1 · round-number multiplication
Calculate 59 × 2,000 by factoring 2,000.
Exit check 2 · round-number multiplication
Calculate 71 × 30 by factoring 30.
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.