Singapore Math 5A · Independent learning

Dividing a Whole Number by a Unit Fraction

Learning target: Count how many unit fractions fit inside a whole-number quantity.

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

Opening task

Explore · measurement division

How many 1/8-meter pieces can you cut from 3 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 24 pieces

How it works: Each meter contains 8 pieces of length 1/8 m. 3 meters contain 3×8=24 pieces. Check 24×1/8=3 m.

Lesson-specific prerequisite checkpoint

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

How many 1/4 units fit into one whole?

Show answer and worked explanation

Answer: 4

How it works: Four quarter-sized pieces together make a whole.

Understand the idea

Count how many unit fractions fit inside a whole-number quantity.

Whole-number division by a unit fraction asks how many small equal-length pieces fit in the whole length. Because each whole contains denominator-many unit fractions, count whole×denominator pieces. The answer is a number of groups, not a smaller length.

Vocabulary focus: sharing interpretation, measurement interpretation, inverse multiplication. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Assuming division always makes a number smaller.

Model to study: Tiled whole-number strips.

Worked examples

Worked examples 1 · measurement division

How many 1/5-meter pieces can you cut from 5 meters of ribbon with no waste?

Solution: 25 pieces

Why: Each meter contains 5 pieces of length 1/5 m. 5 meters contain 5×5=25 pieces. Check 25×1/5=5 m.

Worked examples 2 · measurement division

How many 1/8-meter pieces can you cut from 4 meters of ribbon with no waste?

Solution: 32 pieces

Why: Each meter contains 8 pieces of length 1/8 m. 4 meters contain 4×8=32 pieces. Check 32×1/8=4 m.

Worked examples 3 · measurement division

How many 1/3-meter pieces can you cut from 5 meters of ribbon with no waste?

Solution: 15 pieces

Why: Each meter contains 3 pieces of length 1/3 m. 5 meters contain 5×3=15 pieces. Check 15×1/3=5 m.

Check understanding

Check understanding 1 · measurement division

How many 1/2-meter pieces can you cut from 5 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 10 pieces

How it works: Each meter contains 2 pieces of length 1/2 m. 5 meters contain 5×2=10 pieces. Check 10×1/2=5 m.

Check understanding 2 · measurement division

How many 1/3-meter pieces can you cut from 4 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 12 pieces

How it works: Each meter contains 3 pieces of length 1/3 m. 4 meters contain 4×3=12 pieces. Check 12×1/3=4 m.

Guided practice

Guided practice 1 · measurement division

How many 1/5-meter pieces can you cut from 4 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 20 pieces

How it works: Each meter contains 5 pieces of length 1/5 m. 4 meters contain 4×5=20 pieces. Check 20×1/5=4 m.

Guided practice 2 · measurement division

How many 1/3-meter pieces can you cut from 2 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 6 pieces

How it works: Each meter contains 3 pieces of length 1/3 m. 2 meters contain 2×3=6 pieces. Check 6×1/3=2 m.

Guided practice 3 · measurement division

How many 1/3-meter pieces can you cut from 3 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 9 pieces

How it works: Each meter contains 3 pieces of length 1/3 m. 3 meters contain 3×3=9 pieces. Check 9×1/3=3 m.

Independent practice

Independent practice 1 · measurement division

How many 1/8-meter pieces can you cut from 5 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 40 pieces

How it works: Each meter contains 8 pieces of length 1/8 m. 5 meters contain 5×8=40 pieces. Check 40×1/8=5 m.

Independent practice 2 · measurement division

How many 1/4-meter pieces can you cut from 2 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 8 pieces

How it works: Each meter contains 4 pieces of length 1/4 m. 2 meters contain 2×4=8 pieces. Check 8×1/4=2 m.

Independent practice 3 · measurement division

How many 1/5-meter pieces can you cut from 3 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 15 pieces

How it works: Each meter contains 5 pieces of length 1/5 m. 3 meters contain 3×5=15 pieces. Check 15×1/5=3 m.

Independent practice 4 · measurement division

How many 1/4-meter pieces can you cut from 4 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 16 pieces

How it works: Each meter contains 4 pieces of length 1/4 m. 4 meters contain 4×4=16 pieces. Check 16×1/4=4 m.

Independent practice 5 · measurement division

How many 1/8-meter pieces can you cut from 2 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 16 pieces

How it works: Each meter contains 8 pieces of length 1/8 m. 2 meters contain 2×8=16 pieces. Check 16×1/8=2 m.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “6 ÷ 1/4 = 3/2; I multiplied instead of counting how many 1/4-size groups fit.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: How many 1/4-meter pieces can you cut from 6 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 24 pieces

How it works: Wrong step/assumption: Learner notebook (LESSON): “6 ÷ 1/4 = 3/2; I multiplied instead of counting how many 1/4-size groups fit.” Diagnosis: Differentiate equal sharing from measuring group count, and check the inverse multiplication with the correct quotient unit. Correct computation: Each meter contains 4 pieces of length 1/4 m. 6 meters contain 6×4=24 pieces. Check 24×1/4=6 m.

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). How many 1/8-meter pieces can you cut from 6 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 48 pieces

How it works: Each meter contains 8 pieces of length 1/8 m. 6 meters contain 6×8=48 pieces. Check 48×1/8=6 m. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · measurement division

How many 1/5-meter pieces can you cut from 6 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 30 pieces

How it works: Each meter contains 5 pieces of length 1/5 m. 6 meters contain 6×5=30 pieces. Check 30×1/5=6 m.

Exit check 2 · measurement division

How many 1/2-meter pieces can you cut from 3 meters of ribbon with no waste?

Show answer and worked explanation

Answer: 6 pieces

How it works: Each meter contains 2 pieces of length 1/2 m. 3 meters contain 3×2=6 pieces. Check 6×1/2=3 m.

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.