Mixed Number Market
Add and subtract mixed numbers with like denominators using regrouping.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 1 3/4 + 2 2/4. Show a model or your reasoning.
c2. Calculate 2 1/3 + 1 2/3. Show a model or your reasoning.
c3. Calculate 1 5/6 + 2 2/6. Show a model or your reasoning.
c4. Calculate 3 1/8 + 1 7/8. Show a model or your reasoning.
c5. Calculate 2 1/4 - 2/4. Show a model or your reasoning.
c6. Calculate 3 2/5 - 1 4/5. Show a model or your reasoning.
c7. Calculate 4 1/6 - 2 5/6. Show a model or your reasoning.
c8. Calculate 2 3/8 - 1 5/8. Show a model or your reasoning.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. Why is regrouping a whole allowed?
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
- Represent a market purchase of 1 3/4 yards plus 2 2/4 yards with strips.
- Combine whole strips and quarter pieces; trade four quarters for a whole.
- Partners model a return of 2/4 yard from 2 1/4 yards by regrouping one whole.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Represent a market purchase of 1 3/4 yards plus 2 2/4 yards with strips.
Combine whole strips and quarter pieces; trade four quarters for a whole.
Partners model a return of 2/4 yard from 2 1/4 yards by regrouping one whole.
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. Why is regrouping a whole allowed?
Watch for this misconception
Subtracting fractional parts in the wrong order to avoid regrouping.
Rename one whole as denominator-sized parts before subtracting.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 1 3/4 + 2 2/4. Show a model or your reasoning.
1 3/4 + 2 2/4 = 17/4. Use equal-sized parts before combining or removing them.
c2. Calculate 2 1/3 + 1 2/3. Show a model or your reasoning.
2 1/3 + 1 2/3 = 4. Use equal-sized parts before combining or removing them.
c3. Calculate 1 5/6 + 2 2/6. Show a model or your reasoning.
1 5/6 + 2 2/6 = 25/6. Use equal-sized parts before combining or removing them.
c4. Calculate 3 1/8 + 1 7/8. Show a model or your reasoning.
3 1/8 + 1 7/8 = 5. Use equal-sized parts before combining or removing them.
c5. Calculate 2 1/4 - 2/4. Show a model or your reasoning.
2 1/4 - 2/4 = 7/4. Use equal-sized parts before combining or removing them.
c6. Calculate 3 2/5 - 1 4/5. Show a model or your reasoning.
3 2/5 - 1 4/5 = 8/5. Use equal-sized parts before combining or removing them.
c7. Calculate 4 1/6 - 2 5/6. Show a model or your reasoning.
4 1/6 - 2 5/6 = 4/3. Use equal-sized parts before combining or removing them.
c8. Calculate 2 3/8 - 1 5/8. Show a model or your reasoning.
2 3/8 - 1 5/8 = 3/4. Use equal-sized parts before combining or removing them.
s1. Calculate 1 1/4 - 1/4. Show a model or your reasoning.
1 1/4 - 1/4 = 1. Use equal-sized parts before combining or removing them.
s2. Calculate 1 1/3 - 1/3. Show a model or your reasoning.
1 1/3 - 1/3 = 1. Use equal-sized parts before combining or removing them.
s3. Calculate 2 1/4 - 1 1/4. Show a model or your reasoning.
2 1/4 - 1 1/4 = 1. Use equal-sized parts before combining or removing them.
s4. Calculate 2 3/4 - 1/4. Show a model or your reasoning.
2 3/4 - 1/4 = 5/2. Use equal-sized parts before combining or removing them.
h1. Model 2 1/4 - 2/4 without changing the amount you start with.
Regroup as 1 5/4, then remove 2/4 to leave 1 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.
h2. Explain when four fourths must be traded for one whole.
After addition, each full group of four quarter pieces becomes one 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. Write a market story for 1 3/4 + 2 2/4.
Combine lengths of ribbon; the total is 4 1/4 yards.
- 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 2/5 - 1 4/5 by addition.
1 3/5 + 1 4/5 = 3 2/5.
- 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. Why is regrouping a whole allowed?
One whole and four fourths have the same value, so regrouping preserves the total.
- 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 - 1/4. Show a model or your reasoning.
s2. Calculate 1 1/3 - 1/3. Show a model or your reasoning.
s3. Calculate 2 1/4 - 1 1/4. Show a model or your reasoning.
s4. Calculate 2 3/4 - 1/4. Show a model or your reasoning.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. Why is regrouping a whole allowed?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Model 2 1/4 - 2/4 without changing the amount you start with.
h2. Explain when four fourths must be traded for one whole.
h3. Write a market story for 1 3/4 + 2 2/4.
h4. Check 3 2/5 - 1 4/5 by addition.
e1. Calculate 2 1/4 - 3/4. Show a model or your reasoning.
e2. Why is regrouping a whole allowed?
Teaching notes & lesson sources
Designed for Grade 4. Add and subtract mixed numbers with like denominators using regrouping.
4.NF.B.3c 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.