How Many Servings
Divide a whole number by a unit fraction by counting servings.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 2 ÷ 1/4. Show a model or your reasoning.
c2. Calculate 3 ÷ 1/2. Show a model or your reasoning.
c3. Calculate 4 ÷ 1/3. Show a model or your reasoning.
c4. Calculate 2 ÷ 1/5. Show a model or your reasoning.
c5. Calculate 5 ÷ 1/6. Show a model or your reasoning.
c6. Calculate 3 ÷ 1/8. Show a model or your reasoning.
c7. Calculate 6 ÷ 1/4. Show a model or your reasoning.
c8. Calculate 1 ÷ 1/7. Show a model or your reasoning.
e1. Calculate 2 ÷ 1/4. Show a model or your reasoning.
e2. What unit belongs on the answer?
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 two whole liters and mark quarter-liter serving intervals.
- Count eight servings, then write 2 ÷ 1/4 = 8.
- Partners repeat with different unit fractions and check the total by multiplication.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw two whole liters and mark quarter-liter serving intervals.
Count eight servings, then write 2 ÷ 1/4 = 8.
Partners repeat with different unit fractions and check the total by multiplication.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 2 ÷ 1/4. Show a model or your reasoning. What unit belongs on the answer?
Watch for this misconception
Treating division as always reducing the number.
Count how many smaller serving units fit inside the total.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 2 ÷ 1/4. Show a model or your reasoning.
2 ÷ 1/4 = 8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c2. Calculate 3 ÷ 1/2. Show a model or your reasoning.
3 ÷ 1/2 = 6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c3. Calculate 4 ÷ 1/3. Show a model or your reasoning.
4 ÷ 1/3 = 12. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c4. Calculate 2 ÷ 1/5. Show a model or your reasoning.
2 ÷ 1/5 = 10. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c5. Calculate 5 ÷ 1/6. Show a model or your reasoning.
5 ÷ 1/6 = 30. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c6. Calculate 3 ÷ 1/8. Show a model or your reasoning.
3 ÷ 1/8 = 24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c7. Calculate 6 ÷ 1/4. Show a model or your reasoning.
6 ÷ 1/4 = 24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
c8. Calculate 1 ÷ 1/7. Show a model or your reasoning.
1 ÷ 1/7 = 7. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s1. Calculate 1 ÷ 1/2. Show a model or your reasoning.
1 ÷ 1/2 = 2. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s2. Calculate 1 ÷ 1/4. Show a model or your reasoning.
1 ÷ 1/4 = 4. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s3. Calculate 2 ÷ 1/2. Show a model or your reasoning.
2 ÷ 1/2 = 4. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
s4. Calculate 2 ÷ 1/3. Show a model or your reasoning.
2 ÷ 1/3 = 6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
h1. Model 2 ÷ 1/4 as servings.
Each whole contains four quarters; two wholes contain eight servings.
- 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. Why does dividing by a fraction below one give more servings?
Each serving is smaller than a whole, so multiple servings fit in each whole.
- 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. Compare 2 ÷ 1/4 with 1/4 ÷ 2.
The first counts eight servings; the second shares a quarter into eighths.
- 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. Check 3 ÷ 1/2 by multiplication.
Six servings times 1/2 each recover three wholes.
- 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 2 ÷ 1/4. Show a model or your reasoning.
2 ÷ 1/4 = 8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
e2. What unit belongs on the answer?
The answer counts servings, not liters per serving.
- 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 ÷ 1/2. Show a model or your reasoning.
s2. Calculate 1 ÷ 1/4. Show a model or your reasoning.
s3. Calculate 2 ÷ 1/2. Show a model or your reasoning.
s4. Calculate 2 ÷ 1/3. Show a model or your reasoning.
e1. Calculate 2 ÷ 1/4. Show a model or your reasoning.
e2. What unit belongs on the answer?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Model 2 ÷ 1/4 as servings.
h2. Why does dividing by a fraction below one give more servings?
h3. Compare 2 ÷ 1/4 with 1/4 ÷ 2.
h4. Check 3 ÷ 1/2 by multiplication.
e1. Calculate 2 ÷ 1/4. Show a model or your reasoning.
e2. What unit belongs on the answer?
Teaching notes & lesson sources
Designed for Grade 5. Divide a whole number by a unit fraction by counting servings.
5.NF.B.7b 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.