Explore · scaling
Calculate 290 ÷ 10. Use the inverse multiplication to check.
Great Inheritance Mathematics Term A · Independent learning
Dividing by 10, 100, and 1,000
Learning target: Use place-value grouping to divide whole numbers by powers of ten; interpret noninteger quotients where appropriate.
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 number multiplied by 10 gives 650?
Understand the idea
Use place-value grouping to divide whole numbers by powers of ten; interpret noninteger quotients where appropriate.
Division by ten makes each place-value group one-tenth as large. If the dividend is not a multiple of the divisor, either express the result as a quotient with remainder or, when suitable, with a fraction or decimal; do not discard the leftover. Check by multiplying the quotient back and adding the remainder.
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: Discarding the remainder when division does not give a whole number.
Model to study: Place-value exchange and inverse scaling arrows.
Worked examples
Worked examples 1 · scaling
Calculate 3,300 ÷ 100. Use the inverse multiplication to check.
Solution: 33
Why: 33 × 100 = 3,300, so 3,300 ÷ 100 = 33.
Worked examples 2 · scaling
Calculate 51,000 ÷ 1,000. Use the inverse multiplication to check.
Solution: 51
Why: 51 × 1,000 = 51,000, so 51,000 ÷ 1,000 = 51.
Worked examples 3 · scaling
Calculate 780 ÷ 10. Use the inverse multiplication to check.
Solution: 78
Why: 78 × 10 = 780, so 780 ÷ 10 = 78.
Check understanding
Check understanding 1 · division with remainder
Calculate 4,258 ÷ 100. Give a whole-number quotient and remainder.
Check understanding 2 · scaling
Calculate 89,000 ÷ 1,000. Use the inverse multiplication to check.
Guided practice
Guided practice 1 · scaling
Calculate 280 ÷ 10. Use the inverse multiplication to check.
Guided practice 2 · scaling
Calculate 8,500 ÷ 100. Use the inverse multiplication to check.
Guided practice 3 · division with remainder
Calculate 86,691 ÷ 1,000. Give a whole-number quotient and remainder.
Independent practice
Independent practice 1 · scaling
Calculate 600 ÷ 10. Use the inverse multiplication to check.
Independent practice 2 · scaling
Calculate 6,800 ÷ 100. Use the inverse multiplication to check.
Independent practice 3 · scaling
Calculate 75,000 ÷ 1,000. Use the inverse multiplication to check.
Independent practice 4 · division with remainder
Calculate 587 ÷ 10. Give a whole-number quotient and remainder.
Independent practice 5 · scaling
Calculate 670 ÷ 10. Use the inverse multiplication to check.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “8322 ÷ 100 = 832. I divided by 10 because the zero can disappear from just the divisor.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Calculate 8,322 ÷ 100. Give a whole-number quotient and 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). Calculate 65,000 ÷ 1,000. Use the inverse multiplication to check.
Targeted mastery: model, calculate, explain
These additional original examples address specific 5A mastery requirements. Compare the visual and the reasoning before trying the independent questions.
Targeted 1 · targeted mastery: fraction
Calculate 735 ÷ 10 as a mixed number AND a decimal; show the remainder interpretation.
Solution: 73 1/2 = 73.5
Why: 735 = 73×10 + 5. So 735/10 = 73 + 5/10 = 73 1/2 = 73.5. A remainder of 5 is half of the divisor 10.
Targeted 2 · targeted mastery: fraction
Express 425 ÷ 100 as a mixed number and decimal.
Solution: 4 1/4 = 4.25
Why: 425/100 = 4 + 25/100 = 4 1/4 = 4.25, not just 4 R 25 if a precise quotient is requested.
Targeted 3 · targeted mastery: fraction
A 95 cm strip is cut into 10 equal pieces. What is each length in cm?
Targeted 4 · targeted mastery: fraction
Write 237 ÷ 10 as both whole-number quotient with remainder and exact decimal.
Exit check
Exit check 1 · scaling
Calculate 74,000 ÷ 1,000. Use the inverse multiplication to check.
Exit check 2 · scaling
Calculate 590 ÷ 10. Use the inverse multiplication to check.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.