Mixed Number Repair
Regroup mixed numbers to subtract unlike fractional parts.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
c2. Calculate 3 1/3 - 1 3/4. Show a model or your reasoning.
c3. Calculate 2 1/5 - 1 1/2. Show a model or your reasoning.
c4. Calculate 4 1/6 - 2 2/3. Show a model or your reasoning.
c5. Calculate 3 1/8 - 1 5/6. Show a model or your reasoning.
c6. Calculate 2 1/2 - 1 3/5. Show a model or your reasoning.
c7. Calculate 5 1/4 - 2 2/3. Show a model or your reasoning.
c8. Calculate 3 2/5 - 1 7/10. Show a model or your reasoning.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. What value does regrouping preserve?
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
- Build 2 1/4 with whole and quarter strips. Remove 3/4 by trading a whole for quarters.
- Rebuild with sixths and fourths; decide a common unit before regrouping.
- Partners identify and repair a worked subtraction that reverses the fractional subtraction.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Build 2 1/4 with whole and quarter strips. Remove 3/4 by trading a whole for quarters.
Rebuild with sixths and fourths; decide a common unit before regrouping.
Partners identify and repair a worked subtraction that reverses the fractional subtraction.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 2 1/4 - 3/4. Show a model or your reasoning. What value does regrouping preserve?
Watch for this misconception
Keeping the whole count unchanged while reversing fractional subtraction.
Exchange one whole for fractional parts, then remove in the original order.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
2 1/4 - 3/4 = 3/2. Use equal-sized parts before combining or removing them.
c2. Calculate 3 1/3 - 1 3/4. Show a model or your reasoning.
3 1/3 - 1 3/4 = 19/12. Use equal-sized parts before combining or removing them.
c3. Calculate 2 1/5 - 1 1/2. Show a model or your reasoning.
2 1/5 - 1 1/2 = 7/10. Use equal-sized parts before combining or removing them.
c4. Calculate 4 1/6 - 2 2/3. Show a model or your reasoning.
4 1/6 - 2 2/3 = 3/2. Use equal-sized parts before combining or removing them.
c5. Calculate 3 1/8 - 1 5/6. Show a model or your reasoning.
3 1/8 - 1 5/6 = 31/24. Use equal-sized parts before combining or removing them.
c6. Calculate 2 1/2 - 1 3/5. Show a model or your reasoning.
2 1/2 - 1 3/5 = 9/10. Use equal-sized parts before combining or removing them.
c7. Calculate 5 1/4 - 2 2/3. Show a model or your reasoning.
5 1/4 - 2 2/3 = 31/12. Use equal-sized parts before combining or removing them.
c8. Calculate 3 2/5 - 1 7/10. Show a model or your reasoning.
3 2/5 - 1 7/10 = 17/10. Use equal-sized parts before combining or removing them.
s1. Calculate 1 1/4 - 1/2. Show a model or your reasoning.
1 1/4 - 1/2 = 3/4. Use equal-sized parts before combining or removing them.
s2. Calculate 2 1/3 - 2/3. Show a model or your reasoning.
2 1/3 - 2/3 = 5/3. Use equal-sized parts before combining or removing them.
s3. Calculate 1 1/5 - 2/5. Show a model or your reasoning.
1 1/5 - 2/5 = 4/5. Use equal-sized parts before combining or removing them.
s4. Calculate 2 1/2 - 3/4. Show a model or your reasoning.
2 1/2 - 3/4 = 7/4. Use equal-sized parts before combining or removing them.
h1. Explain 2 1/4 - 3/4 using regrouping.
2 1/4 = 1 5/4; removing 3/4 leaves 1 2/4 = 1 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.
h2. Repair 2 1/4 - 3/4 = 2 2/4.
The subtraction was reversed; regroup before removing to get 1 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. Check a regrouped result by addition.
1 1/2 + 3/4 = 2 1/4.
- Identify the whole and use equal-sized parts where needed.
- Show a correct model or numerical relationship.
- Explain why the model supports your conclusion.
h4. Why should common units be found before regrouping unlike fractions?
Then the whole can be exchanged into exactly the parts being 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.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
2 1/4 - 3/4 = 3/2. Use equal-sized parts before combining or removing them.
e2. What value does regrouping preserve?
The total starting amount stays unchanged.
- 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 1/4 - 1/2. Show a model or your reasoning.
s2. Calculate 2 1/3 - 2/3. Show a model or your reasoning.
s3. Calculate 1 1/5 - 2/5. Show a model or your reasoning.
s4. Calculate 2 1/2 - 3/4. Show a model or your reasoning.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. What value does regrouping preserve?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain 2 1/4 - 3/4 using regrouping.
h2. Repair 2 1/4 - 3/4 = 2 2/4.
h3. Check a regrouped result by addition.
h4. Why should common units be found before regrouping unlike fractions?
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. What value does regrouping preserve?
Teaching notes & lesson sources
Designed for Grade 5. Regroup mixed numbers to subtract unlike fractional parts.
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.