Fraction Difference Trail
Subtract unlike fractions and check differences against estimates.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 5/6 - 1/4. Show a model or your reasoning.
c2. Calculate 3/4 - 1/3. Show a model or your reasoning.
c3. Calculate 7/8 - 1/2. Show a model or your reasoning.
c4. Calculate 4/5 - 1/6. Show a model or your reasoning.
c5. Calculate 2/3 - 1/5. Show a model or your reasoning.
c6. Calculate 9/10 - 3/4. Show a model or your reasoning.
c7. Calculate 5/8 - 1/3. Show a model or your reasoning.
c8. Calculate 7/9 - 1/6. Show a model or your reasoning.
e1. Calculate 5/6 - 1/4. Show a model or your reasoning.
e2. What addition equation checks a subtraction?
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 a trail of length 5/6 mile and mark the first 1/4 mile as completed.
- Use twelfths to find the remaining trail.
- Partners estimate a difference, compute it, then check it by adding back.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw a trail of length 5/6 mile and mark the first 1/4 mile as completed.
Use twelfths to find the remaining trail.
Partners estimate a difference, compute it, then check it by adding back.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 5/6 - 1/4. Show a model or your reasoning. What addition equation checks a subtraction?
Watch for this misconception
Subtracting denominator values.
Match part sizes, remove the count of those common parts.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 5/6 - 1/4. Show a model or your reasoning.
5/6 - 1/4 = 7/12. Use equal-sized parts before combining or removing them.
c2. Calculate 3/4 - 1/3. Show a model or your reasoning.
3/4 - 1/3 = 5/12. Use equal-sized parts before combining or removing them.
c3. Calculate 7/8 - 1/2. Show a model or your reasoning.
7/8 - 1/2 = 3/8. Use equal-sized parts before combining or removing them.
c4. Calculate 4/5 - 1/6. Show a model or your reasoning.
4/5 - 1/6 = 19/30. Use equal-sized parts before combining or removing them.
c5. Calculate 2/3 - 1/5. Show a model or your reasoning.
2/3 - 1/5 = 7/15. Use equal-sized parts before combining or removing them.
c6. Calculate 9/10 - 3/4. Show a model or your reasoning.
9/10 - 3/4 = 3/20. Use equal-sized parts before combining or removing them.
c7. Calculate 5/8 - 1/3. Show a model or your reasoning.
5/8 - 1/3 = 7/24. Use equal-sized parts before combining or removing them.
c8. Calculate 7/9 - 1/6. Show a model or your reasoning.
7/9 - 1/6 = 11/18. Use equal-sized parts before combining or removing them.
s1. Calculate 3/4 - 1/2. Show a model or your reasoning.
3/4 - 1/2 = 1/4. Use equal-sized parts before combining or removing them.
s2. Calculate 2/3 - 1/3. Show a model or your reasoning.
2/3 - 1/3 = 1/3. Use equal-sized parts before combining or removing them.
s3. Calculate 5/6 - 1/2. Show a model or your reasoning.
5/6 - 1/2 = 1/3. Use equal-sized parts before combining or removing them.
s4. Calculate 3/5 - 1/5. Show a model or your reasoning.
3/5 - 1/5 = 2/5. Use equal-sized parts before combining or removing them.
h1. Estimate 5/6 - 1/4 before calculating.
It is a little more than one half; exact result 7/12.
- 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 3/4 - 1/3 by adding back.
5/12 + 1/3 = 9/12 = 3/4.
- 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 cannot denominators be subtracted?
They describe unit sizes, which must be matched, not removed.
- 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 trail story with a remainder of 1/2 mile.
A 3/4 mile trail with 1/4 mile completed leaves 1/2 mile.
- 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 5/6 - 1/4. Show a model or your reasoning.
5/6 - 1/4 = 7/12. Use equal-sized parts before combining or removing them.
e2. What addition equation checks a subtraction?
Difference plus the removed amount must equal the starting amount.
- 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 3/4 - 1/2. Show a model or your reasoning.
s2. Calculate 2/3 - 1/3. Show a model or your reasoning.
s3. Calculate 5/6 - 1/2. Show a model or your reasoning.
s4. Calculate 3/5 - 1/5. Show a model or your reasoning.
e1. Calculate 5/6 - 1/4. Show a model or your reasoning.
e2. What addition equation checks a subtraction?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Estimate 5/6 - 1/4 before calculating.
h2. Check 3/4 - 1/3 by adding back.
h3. Why cannot denominators be subtracted?
h4. Write a trail story with a remainder of 1/2 mile.
e1. Calculate 5/6 - 1/4. Show a model or your reasoning.
e2. What addition equation checks a subtraction?
Teaching notes & lesson sources
Designed for Grade 5. Subtract unlike fractions and check differences against estimates.
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.