Singapore Math 5A · Independent learning

Dividing a Unit Fraction by a Whole Number

Learning target: Partition one unit-fraction quantity into equal shares and compute the resulting fraction.

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

Opening task

Explore · unit fraction sharing

Share 1/4 meter of ribbon equally among 4 people. How much does each receive?

Show answer and worked explanation

Answer: 1/16 m

How it works: One 4-th meter is partitioned into 4 equal shares: 1/(4×4) = 1/16 m. Check 4×1/16=1/4.

Prerequisite check (before instruction)

Attempt without help. A weak prerequisite signals review of 4A or 4B material, not a failed 5A lesson.

Draw three-quarters of a unit bar.

Show answer and worked explanation

Answer: Three of four equal parts shaded.

How it works: Draw a bar divided into four equal sections and shade exactly three sections. A correct labeled sketch is required.

Explain how to share 12 counters equally among 4 people.

Show answer and worked explanation

Answer: 3 counters each

How it works: Make four equal groups of 3 counters. Check 4 × 3 = 12.

Lesson-specific prerequisite checkpoint

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

Draw 1/4 of a bar and identify the whole.

Show answer and worked explanation

Answer: 1 of 4 equal parts

How it works: Draw [■|□|□|□]: four equally sized sections form one whole bar; exactly one is shaded as 1/4. Label the entire bar as the whole.

Understand the idea

Partition one unit-fraction quantity into equal shares and compute the resulting fraction.

Dividing one unit fraction into n equal shares creates pieces sized 1/(denominator×n). An equal-parts strip shows how the original piece is partitioned. Multiplying one share back by n verifies the original amount.

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: Multiplying by the whole number rather than dividing it.

Model to study: Fraction-strip subdivision.

Worked examples

Worked examples 1 · unit fraction sharing

Share 1/5 meter of ribbon equally among 2 people. How much does each receive?

Solution: 1/10 m

Why: One 5-th meter is partitioned into 2 equal shares: 1/(5×2) = 1/10 m. Check 2×1/10=1/5.

Worked examples 2 · unit fraction sharing

Share 1/5 meter of ribbon equally among 3 people. How much does each receive?

Solution: 1/15 m

Why: One 5-th meter is partitioned into 3 equal shares: 1/(5×3) = 1/15 m. Check 3×1/15=1/5.

Worked examples 3 · unit fraction sharing

Share 1/2 meter of ribbon equally among 2 people. How much does each receive?

Solution: 1/4 m

Why: One 2-th meter is partitioned into 2 equal shares: 1/(2×2) = 1/4 m. Check 2×1/4=1/2.

Check understanding

Check understanding 1 · unit fraction sharing

Share 1/4 meter of ribbon equally among 3 people. How much does each receive?

Show answer and worked explanation

Answer: 1/12 m

How it works: One 4-th meter is partitioned into 3 equal shares: 1/(4×3) = 1/12 m. Check 3×1/12=1/4.

Check understanding 2 · unit fraction sharing

Share 1/8 meter of ribbon equally among 3 people. How much does each receive?

Show answer and worked explanation

Answer: 1/24 m

How it works: One 8-th meter is partitioned into 3 equal shares: 1/(8×3) = 1/24 m. Check 3×1/24=1/8.

Guided practice

Guided practice 1 · unit fraction sharing

Share 1/3 meter of ribbon equally among 2 people. How much does each receive?

Show answer and worked explanation

Answer: 1/6 m

How it works: One 3-th meter is partitioned into 2 equal shares: 1/(3×2) = 1/6 m. Check 2×1/6=1/3.

Guided practice 2 · unit fraction sharing

Share 1/3 meter of ribbon equally among 5 people. How much does each receive?

Show answer and worked explanation

Answer: 1/15 m

How it works: One 3-th meter is partitioned into 5 equal shares: 1/(3×5) = 1/15 m. Check 5×1/15=1/3.

Guided practice 3 · unit fraction sharing

Share 1/6 meter of ribbon equally among 5 people. How much does each receive?

Show answer and worked explanation

Answer: 1/30 m

How it works: One 6-th meter is partitioned into 5 equal shares: 1/(6×5) = 1/30 m. Check 5×1/30=1/6.

Independent practice

Independent practice 1 · unit fraction sharing

Share 1/4 meter of ribbon equally among 5 people. How much does each receive?

Show answer and worked explanation

Answer: 1/20 m

How it works: One 4-th meter is partitioned into 5 equal shares: 1/(4×5) = 1/20 m. Check 5×1/20=1/4.

Independent practice 2 · unit fraction sharing

Share 1/3 meter of ribbon equally among 4 people. How much does each receive?

Show answer and worked explanation

Answer: 1/12 m

How it works: One 3-th meter is partitioned into 4 equal shares: 1/(3×4) = 1/12 m. Check 4×1/12=1/3.

Independent practice 3 · unit fraction sharing

Share 1/2 meter of ribbon equally among 3 people. How much does each receive?

Show answer and worked explanation

Answer: 1/6 m

How it works: One 2-th meter is partitioned into 3 equal shares: 1/(2×3) = 1/6 m. Check 3×1/6=1/2.

Independent practice 4 · unit fraction sharing

Share 1/5 meter of ribbon equally among 5 people. How much does each receive?

Show answer and worked explanation

Answer: 1/25 m

How it works: One 5-th meter is partitioned into 5 equal shares: 1/(5×5) = 1/25 m. Check 5×1/25=1/5.

Independent practice 5 · unit fraction sharing

Share 1/6 meter of ribbon equally among 4 people. How much does each receive?

Show answer and worked explanation

Answer: 1/24 m

How it works: One 6-th meter is partitioned into 4 equal shares: 1/(6×4) = 1/24 m. Check 4×1/24=1/6.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “Dividing 1/6 by 3 means multiplying, so I wrote 1/2 instead of finding the right group size.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Share 1/6 meter of ribbon equally among 3 people. How much does each receive?

Show answer and worked explanation

Answer: 1/18 m

How it works: Wrong step/assumption: Learner notebook (LESSON): “Dividing 1/6 by 3 means multiplying, so I wrote 1/2 instead of finding the right group size.” Diagnosis: Differentiate equal sharing from measuring group count, and check the inverse multiplication with the correct quotient unit. Correct computation: One 6-th meter is partitioned into 3 equal shares: 1/(6×3) = 1/18 m. Check 3×1/18=1/6.

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). Share 1/8 meter of ribbon equally among 5 people. How much does each receive?

Show answer and worked explanation

Answer: 1/40 m

How it works: One 8-th meter is partitioned into 5 equal shares: 1/(8×5) = 1/40 m. Check 5×1/40=1/8. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · unit fraction sharing

Share 1/8 meter of ribbon equally among 4 people. How much does each receive?

Show answer and worked explanation

Answer: 1/32 m

How it works: One 8-th meter is partitioned into 4 equal shares: 1/(8×4) = 1/32 m. Check 4×1/32=1/8.

Exit check 2 · unit fraction sharing

Share 1/8 meter of ribbon equally among 2 people. How much does each receive?

Show answer and worked explanation

Answer: 1/16 m

How it works: One 8-th meter is partitioned into 2 equal shares: 1/(8×2) = 1/16 m. Check 2×1/16=1/8.

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.