Explore · equivalent quotient
Find 2,640 ÷ 30. Explain which shared factor can be removed.
Great Inheritance Mathematics Term A · Independent learning
Dividing by Tens, Hundreds, and Thousands
Learning target: Factor and cancel matching powers of ten while preserving the quotient.
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 the missing factor: 8 × ___ = 96.
Understand the idea
Factor and cancel matching powers of ten while preserving the quotient.
A quotient stays unchanged when both the dividend and divisor are divided by the same nonzero factor. For example, 840 ÷ 30 equals 84 ÷ 3. Do not cross out a zero on just one side. Multiplication verifies every equivalent quotient.
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: Canceling zeros from only one side of a division.
Model to study: Inverse equal-factor table and scaled quotient model.
Worked examples
Worked examples 1 · equivalent quotient
Find 30,800 ÷ 400. Explain which shared factor can be removed.
Solution: 77
Why: 30,800 ÷ 400 = (308 ÷ 4) = 77 because both dividend and divisor are divided by 100. Check 77 × 400 = 30,800.
Worked examples 2 · equivalent quotient
Find 123,000 ÷ 3,000. Explain which shared factor can be removed.
Solution: 41
Why: 123,000 ÷ 3,000 = (123 ÷ 3) = 41 because both dividend and divisor are divided by 1,000. Check 41 × 3,000 = 123,000.
Worked examples 3 · equivalent quotient
Find 3,510 ÷ 90. Explain which shared factor can be removed.
Solution: 39
Why: 3,510 ÷ 90 = (351 ÷ 9) = 39 because both dividend and divisor are divided by 10. Check 39 × 90 = 3,510.
Check understanding
Check understanding 1 · equivalent quotient
Find 33,600 ÷ 600. Explain which shared factor can be removed.
Check understanding 2 · equivalent quotient
Find 294,000 ÷ 6,000. Explain which shared factor can be removed.
Guided practice
Guided practice 1 · equivalent quotient
Find 3,520 ÷ 40. Explain which shared factor can be removed.
Guided practice 2 · equivalent quotient
Find 32,000 ÷ 400. Explain which shared factor can be removed.
Guided practice 3 · equivalent quotient
Find 225,000 ÷ 3,000. Explain which shared factor can be removed.
Independent practice
Independent practice 1 · equivalent quotient
Find 3,720 ÷ 60. Explain which shared factor can be removed.
Independent practice 2 · equivalent quotient
Find 60,000 ÷ 800. Explain which shared factor can be removed.
Independent practice 3 · equivalent quotient
Find 162,000 ÷ 9,000. Explain which shared factor can be removed.
Independent practice 4 · equivalent quotient
Find 1,750 ÷ 70. Explain which shared factor can be removed.
Independent practice 5 · equivalent quotient
Find 19,800 ÷ 900. Explain which shared factor can be removed.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “27000 ÷ 900 = 300. I reduced the divisor by 10 but not the dividend.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 27,000 ÷ 900. Explain which shared factor can be removed.
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). Find 405,000 ÷ 5,000. Explain which shared factor can be removed.
Exit check
Exit check 1 · equivalent quotient
Find 837,000 ÷ 9,000. Explain which shared factor can be removed.
Exit check 2 · equivalent quotient
Find 2,480 ÷ 80. Explain which shared factor can be removed.
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.