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Great Inheritance Mathematics Term A · Independent learning

Divide a 2-digit Number by a 2-digit Number

Learning target: Find sensible quotients by estimation and multiplication checks.

Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.

Opening task

Explore · two-digit division

Find 75 ÷ 17. State any remainder and check.

Show answer and worked explanation

Answer: 4 R 7

How it works: 17×4=68; 75-68=7, with 0 ≤ 7 < 17.

Lesson-specific prerequisite checkpoint

Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.

What is 6 × 14 and how can it check a quotient?

Show answer and worked explanation

Answer: 84

How it works: 6×14 = 84. Inverse operation: 84÷14 = 6 (or 84÷6 = 14), so multiplication checks the quotient.

Understand the idea

Find sensible quotients by estimation and multiplication checks.

For two-digit division, locate two nearby multiples of the divisor. Select the greatest whole multiple that does not exceed the dividend. State any remainder and show that it is smaller than the divisor.

Vocabulary focus: partial products, quotient, remainder. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Guessing a quotient without checking its product.

Model to study: Equal-groups model and quotient bounds.

Worked examples

Worked examples 1 · two-digit division

Find 80 ÷ 39. State any remainder and check.

Solution: 2 R 2

Why: 39×2=78; 80-78=2, with 0 ≤ 2 < 39.

Worked examples 2 · two-digit division

Find 48 ÷ 14. State any remainder and check.

Solution: 3 R 6

Why: 14×3=42; 48-42=6, with 0 ≤ 6 < 14.

Worked examples 3 · two-digit division

Find 41 ÷ 16. State any remainder and check.

Solution: 2 R 9

Why: 16×2=32; 41-32=9, with 0 ≤ 9 < 16.

Check understanding

Check understanding 1 · two-digit division

Find 94 ÷ 31. State any remainder and check.

Show answer and worked explanation

Answer: 3 R 1

How it works: 31×3=93; 94-93=1, with 0 ≤ 1 < 31.

Check understanding 2 · two-digit division

Find 49 ÷ 14. State any remainder and check.

Show answer and worked explanation

Answer: 3 R 7

How it works: 14×3=42; 49-42=7, with 0 ≤ 7 < 14.

Guided practice

Guided practice 1 · two-digit division

Find 86 ÷ 14. State any remainder and check.

Show answer and worked explanation

Answer: 6 R 2

How it works: 14×6=84; 86-84=2, with 0 ≤ 2 < 14.

Guided practice 2 · two-digit division

Find 79 ÷ 38. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 3

How it works: 38×2=76; 79-76=3, with 0 ≤ 3 < 38.

Guided practice 3 · two-digit division

Find 60 ÷ 27. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 6

How it works: 27×2=54; 60-54=6, with 0 ≤ 6 < 27.

Independent practice

Independent practice 1 · two-digit division

Find 39 ÷ 16. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 7

How it works: 16×2=32; 39-32=7, with 0 ≤ 7 < 16.

Independent practice 2 · two-digit division

Find 68 ÷ 30. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 8

How it works: 30×2=60; 68-60=8, with 0 ≤ 8 < 30.

Independent practice 3 · two-digit division

Find 46 ÷ 23. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 0

How it works: 23×2=46; 46-46=0, with 0 ≤ 0 < 23.

Independent practice 4 · two-digit division

Find 81 ÷ 16. State any remainder and check.

Show answer and worked explanation

Answer: 5 R 1

How it works: 16×5=80; 81-80=1, with 0 ≤ 1 < 16.

Independent practice 5 · two-digit division

Find 48 ÷ 24. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 0

How it works: 24×2=48; 48-48=0, with 0 ≤ 0 < 24.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “75 ÷ 36 = 15/7. 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: Find 75 ÷ 36. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 3

How it works: Wrong step/assumption: Learner notebook (LESSON): “75 ÷ 36 = 15/7. I reduced only the divisor by one and did not verify with inverse multiplication.” Diagnosis: Use every tens/ones partial product or preserve every quotient position, then verify divisor×quotient+remainder. Correct computation: 36×2=72; 75-72=3, with 0 ≤ 3 < 36.

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 50 ÷ 12. State any remainder and check.

Show answer and worked explanation

Answer: 4 R 2

How it works: 12×4=48; 50-48=2, with 0 ≤ 2 < 12. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · two-digit division

Find 74 ÷ 33. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 8

How it works: 33×2=66; 74-66=8, with 0 ≤ 8 < 33.

Exit check 2 · two-digit division

Find 65 ÷ 30. State any remainder and check.

Show answer and worked explanation

Answer: 2 R 5

How it works: 30×2=60; 65-60=5, with 0 ≤ 5 < 30.

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.