Fraction Classroom · 2.0.0 · Teacher answers & responses
Unit Fraction Sharing: teaching companion
Name an equal share of a unit fraction relative to the original whole. Student pages include two diagnostic probes, a reteaching check, and the original exit ticket. The teacher copy includes the complete lesson preparation, teaching sequence, diagnostic responses, all original question guides, and updated rubrics.
Complete lesson preparation
Grade 5 · 45 minutes. Divide a unit fraction by a whole number through equal sharing.
materials. Materials: Pencil: 1 per student; Plain paper sheets: 2 per student; Projector: 1 per class (optional).
activity-1. Draw half of a whole sheet and divide that half into three equal shares.
activity-2. Count six such shares across the original whole; name one share 1/6.
activity-3. Partners share a quarter among two and among three and compare the shares.
phase-1. 5 min · warmup: Look at the first model or task. What is the whole? What do you notice?
Answer: Students: Sketch an initial prediction and explain it to a partner.
phase-2. 8 min · model: Draw half of a whole sheet and divide that half into three equal shares.
Answer: Students: Follow the model; label the whole and the equal parts.
phase-3. 10 min · partner: Count six such shares across the original whole; name one share 1/6.
Answer: Students: Work in pairs. One models, the other checks; switch roles.
phase-4. 7 min · discussion: Partners share a quarter among two and among three and compare the shares.
Answer: Students: Compare two solutions and explain the relationship.
phase-5. 10 min · practice: Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Answer: Students: Solve independently, then compare the reasoning.
phase-6. 5 min · exit: Calculate 1/2 ÷ 3. Show a model or your reasoning. What whole is used to name the final share?
Answer: Students: Complete the two exit questions independently.
Diagnostic probes
Explain or draw your reasoning. Your teacher will use these responses to choose what to revisit.
d1. Half of one sheet is shared equally among three people. What fraction of the original sheet does each get?
Answer: 1/6 of the original sheet.
Teacher response: If the learner answers 1/3 by treating the shaded half as the whole. Extend the three equal share lengths across the unshaded half and count six matching shares in the original sheet.
d2. How can multiplication check whether 1/6 is one of three equal shares of 1/2?
Answer: 3 × 1/6 = 3/6 = 1/2.
Teacher response: If the learner multiplies by the original denominator two instead of the number of recipients three. Place three recipient cards beside the three sixth-pieces and join those shares to rebuild the shaded half.
Check after reteaching
Complete this check independently after discussing the model.
r1. One fourth of a liter is shared equally among three people. Name one share and check it.
Answer: 1/12 liter per person; 3 × 1/12 = 1/4 liter.
Exit ticket
Complete both original exit questions independently. Use a drawing or explanation when asked.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
Answer: 1/6
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
e2. What whole is used to name the final share?
Answer: The original whole, not the already shaded half.
Look for:
- Name the original whole as the reference for the answer.
- Distinguish one third of the shaded half from one third of the original whole.
- Explain that e1 gives 1/6 of the original whole.
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Focused reteach
Name an equal share of a unit fraction relative to the original whole.
teach-1. Outline the original whole, then shade only the fraction being shared.
teach-2. Partition the shaded fraction equally among the recipients and extend that piece size across the whole.
teach-3. Name one share from the original whole and rebuild the starting fraction with all recipient shares.
Use the exit evidence
A wrong answer invites a follow-up probe; it does not by itself establish a particular misconception. Check e1 and e2 separately.
next-1. e1 meets its criterion: e1 gives 1/6 for 1/2 ÷ 3. e2 also meets its criterion: e2 names the original whole, rather than the shaded half, as the reference for the final share.
Teacher response: Continue to the linked next lesson. Contrast finding the size of one share with counting fixed-size servings. Next original lesson: /lessons/how-many-servings/.
next-2. e1 does not yet meet this criterion: e1 gives 1/6 for 1/2 ÷ 3.
Teacher response: Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on. Short intervention: /interventions/unit-fraction-sharing/.
next-3. e1 meets its criterion, but e2 does not yet show this evidence: e2 names the original whole, rather than the shaded half, as the reference for the final share.
Teacher response: Ask the learner to label both “one original whole” and “amount being shared” on e1, then explain why one third of the half is one sixth of the whole. Short intervention: /interventions/unit-fraction-sharing/.
Original question guide and updated rubrics
Use these question-specific teaching responses alongside the original lesson. Accept other mathematically valid open responses that meet the criteria. The original question wording and mathematical answers are retained; model descriptions below make their references readable offline.
c1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
Answer: 1/6
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
Answer: 1/6
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c3. Calculate 1/4 ÷ 3. Show a model or your reasoning.
Answer: 1/12
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c4. Calculate 1/5 ÷ 2. Show a model or your reasoning.
Answer: 1/10
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c5. Calculate 1/6 ÷ 4. Show a model or your reasoning.
Answer: 1/24
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c6. Calculate 1/8 ÷ 3. Show a model or your reasoning.
Answer: 1/24
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c7. Calculate 1/3 ÷ 5. Show a model or your reasoning.
Answer: 1/15
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
c8. Calculate 1/4 ÷ 4. Show a model or your reasoning.
Answer: 1/16
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
s1. Calculate 1/2 ÷ 2. Show a model or your reasoning.
Answer: 1/4
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
s2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
Answer: 1/6
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
s3. Calculate 1/4 ÷ 2. Show a model or your reasoning.
Answer: 1/8
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
s4. Calculate 1/2 ÷ 4. Show a model or your reasoning.
Answer: 1/8
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
h1. Explain 1/2 ÷ 3 with a model.
Answer: Split a half into three equal shares; six shares would fill the original whole, so each is 1/6.
Look for:
- Draw one whole and identify its half.
- Split that half into three equal shares.
- Relate one share to the original whole as 1/6, explaining that six such shares fill it.
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
h2. Check one sixth as the share by multiplication.
Answer: Three times 1/6 equals 1/2.
Look for:
- Identify three shares of size 1/6.
- Write or model 3 × 1/6.
- Recover 3/6 = 1/2, the quantity originally shared.
Teacher response: Confuses the number of equal groups with the size of each group. Draw three separate bags, each holding 2/5 cup. Label “3 groups” and “2/5 cup per group.” Count six fifth-cup pieces in total and connect the drawing to 2/5 + 2/5 + 2/5.
h3. Why is the share less than the starting unit fraction?
Answer: A positive amount split among more than one person gives smaller shares.
Look for:
- Specify that the starting amount is positive and shared among more than one recipient.
- Explain that the equal shares together make the original amount.
- Conclude each share is smaller than that amount, using 1/2 ÷ 3 if helpful.
Teacher response: Assumes multiplication always enlarges a positive amount. Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
h4. Write a story for 1/4 ÷ 3.
Answer: A quarter liter is shared equally by three people; each gets 1/12 liter.
Look for:
- Use a starting amount of 1/4 of a named unit.
- Share it equally among three recipients or groups.
- State that each receives 1/12 of the original unit.
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
Answer: 1/6
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
e2. What whole is used to name the final share?
Answer: The original whole, not the already shaded half.
Look for:
- Name the original whole as the reference for the answer.
- Distinguish one third of the shaded half from one third of the original whole.
- Explain that e1 gives 1/6 of the original whole.
Teacher response: Names a share relative to the shaded fraction instead of the original whole. Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Teaching notes
- Teaching supplement version 2.0.0. Original lesson questions and PDF materials remain version 1.0.0. Original PDFs contain their original teaching notes and rubrics; use this supplement for the updated diagnostic guidance.
- Short intervention: /interventions/unit-fraction-sharing/. Use its model for the identified difficulty, then return to this lesson’s check and exit ticket.
- Next original lesson: /lessons/how-many-servings/. Contrast finding the size of one share with counting fixed-size servings.
- Open responses are reviewed by a teacher using the specific criteria. These materials have not been field-tested in classrooms.