Unit Fraction Sharing
Divide a unit fraction by a whole number through equal sharing.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
c2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
c3. Calculate 1/4 ÷ 3. Show a model or your reasoning.
c4. Calculate 1/5 ÷ 2. Show a model or your reasoning.
c5. Calculate 1/6 ÷ 4. Show a model or your reasoning.
c6. Calculate 1/8 ÷ 3. Show a model or your reasoning.
c7. Calculate 1/3 ÷ 5. Show a model or your reasoning.
c8. Calculate 1/4 ÷ 4. Show a model or your reasoning.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
e2. What whole is used to name the final share?
Before the lesson
Recognize a whole and count equal parts.
Materials
- Pencil: 1 per student
- Plain paper sheets: 2 per student
- Projector: 1 per class (optional)
Activity
- Draw half of a whole sheet and divide that half into three equal shares.
- Count six such shares across the original whole; name one share 1/6.
- Partners share a quarter among two and among three and compare the shares.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw half of a whole sheet and divide that half into three equal shares.
Count six such shares across the original whole; name one share 1/6.
Partners share a quarter among two and among three and compare the shares.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 1/2 ÷ 3. Show a model or your reasoning. What whole is used to name the final share?
Watch for this misconception
Naming the share relative only to the shaded part.
Extend the new equal partitions across the original whole.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
1/2 ÷ 3 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
1/3 ÷ 2 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c3. Calculate 1/4 ÷ 3. Show a model or your reasoning.
1/4 ÷ 3 = 1/12. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c4. Calculate 1/5 ÷ 2. Show a model or your reasoning.
1/5 ÷ 2 = 1/10. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c5. Calculate 1/6 ÷ 4. Show a model or your reasoning.
1/6 ÷ 4 = 1/24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c6. Calculate 1/8 ÷ 3. Show a model or your reasoning.
1/8 ÷ 3 = 1/24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c7. Calculate 1/3 ÷ 5. Show a model or your reasoning.
1/3 ÷ 5 = 1/15. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c8. Calculate 1/4 ÷ 4. Show a model or your reasoning.
1/4 ÷ 4 = 1/16. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s1. Calculate 1/2 ÷ 2. Show a model or your reasoning.
1/2 ÷ 2 = 1/4. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
1/3 ÷ 2 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s3. Calculate 1/4 ÷ 2. Show a model or your reasoning.
1/4 ÷ 2 = 1/8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s4. Calculate 1/2 ÷ 4. Show a model or your reasoning.
1/2 ÷ 4 = 1/8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
h1. Explain 1/2 ÷ 3 with a model.
Split a half into three equal shares; six shares would fill the original whole, so each is 1/6.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h2. Check one sixth as the share by multiplication.
Three times 1/6 equals 1/2.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h3. Why is the share less than the starting unit fraction?
A positive amount split among more than one person gives smaller shares.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h4. Write a story for 1/4 ÷ 3.
A quarter liter is shared equally by three people; each gets 1/12 liter.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
1/2 ÷ 3 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
e2. What whole is used to name the final share?
The original whole, not the already shaded half.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
s1. Calculate 1/2 ÷ 2. Show a model or your reasoning.
s2. Calculate 1/3 ÷ 2. Show a model or your reasoning.
s3. Calculate 1/4 ÷ 2. Show a model or your reasoning.
s4. Calculate 1/2 ÷ 4. Show a model or your reasoning.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
e2. What whole is used to name the final share?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain 1/2 ÷ 3 with a model.
h2. Check one sixth as the share by multiplication.
h3. Why is the share less than the starting unit fraction?
h4. Write a story for 1/4 ÷ 3.
e1. Calculate 1/2 ÷ 3. Show a model or your reasoning.
e2. What whole is used to name the final share?
Teaching notes & lesson sources
Designed for Grade 5. Divide a unit fraction by a whole number through equal sharing.
5.NF.B.7a curriculum reference
Version 1.0.0. Original, AI-assisted lesson content. Free local classroom use; public reuse terms have not yet been assigned.
These lessons have not yet been field-tested in classrooms. Use the exit ticket and student explanations to decide what to revisit.