Common Denominator Kitchen
Add unlike fractions by renaming both ingredients in common units.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Calculate 1/3 + 1/4. Show a model or your reasoning.
c2. Calculate 2/5 + 1/2. Show a model or your reasoning.
c3. Calculate 3/4 + 1/6. Show a model or your reasoning.
c4. Calculate 1/2 + 2/3. Show a model or your reasoning.
c5. Calculate 5/8 + 1/4. Show a model or your reasoning.
c6. Calculate 2/3 + 3/5. Show a model or your reasoning.
c7. Calculate 1/6 + 3/8. Show a model or your reasoning.
c8. Calculate 3/10 + 2/5. Show a model or your reasoning.
e1. Calculate 1/3 + 1/4. Show a model or your reasoning.
e2. Why must the pieces have the same size before adding?
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
- Model one third cup plus one fourth cup using equal-sized cup diagrams.
- Repartition both into twelfths and count seven twelfths in all.
- Partners prepare a second recipe and estimate before adding.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Model one third cup plus one fourth cup using equal-sized cup diagrams.
Repartition both into twelfths and count seven twelfths in all.
Partners prepare a second recipe and estimate before adding.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 1/3 + 1/4. Show a model or your reasoning. Why must the pieces have the same size before adding?
Watch for this misconception
Adding numerators and denominators separately.
Rename each ingredient using an equal-sized common part.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Calculate 1/3 + 1/4. Show a model or your reasoning.
1/3 + 1/4 = 7/12. Use equal-sized parts before combining or removing them.
c2. Calculate 2/5 + 1/2. Show a model or your reasoning.
2/5 + 1/2 = 9/10. Use equal-sized parts before combining or removing them.
c3. Calculate 3/4 + 1/6. Show a model or your reasoning.
3/4 + 1/6 = 11/12. Use equal-sized parts before combining or removing them.
c4. Calculate 1/2 + 2/3. Show a model or your reasoning.
1/2 + 2/3 = 7/6. Use equal-sized parts before combining or removing them.
c5. Calculate 5/8 + 1/4. Show a model or your reasoning.
5/8 + 1/4 = 7/8. Use equal-sized parts before combining or removing them.
c6. Calculate 2/3 + 3/5. Show a model or your reasoning.
2/3 + 3/5 = 19/15. Use equal-sized parts before combining or removing them.
c7. Calculate 1/6 + 3/8. Show a model or your reasoning.
1/6 + 3/8 = 13/24. Use equal-sized parts before combining or removing them.
c8. Calculate 3/10 + 2/5. Show a model or your reasoning.
3/10 + 2/5 = 7/10. Use equal-sized parts before combining or removing them.
s1. Calculate 1/2 + 1/4. Show a model or your reasoning.
1/2 + 1/4 = 3/4. Use equal-sized parts before combining or removing them.
s2. Calculate 1/3 + 1/6. Show a model or your reasoning.
1/3 + 1/6 = 1/2. Use equal-sized parts before combining or removing them.
s3. Calculate 1/4 + 1/8. Show a model or your reasoning.
1/4 + 1/8 = 3/8. Use equal-sized parts before combining or removing them.
s4. Calculate 1/5 + 2/5. Show a model or your reasoning.
1/5 + 2/5 = 3/5. Use equal-sized parts before combining or removing them.
h1. Explain 1/3 + 1/4 with a model.
Four twelfths plus three twelfths gives seven twelfths.
- 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 is 1/3 + 1/4 not 2/7?
The pieces have different sizes; the denominators cannot simply be added.
- 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. Find two common denominators for thirds and fourths.
12 and 24 both work and produce equivalent sums.
- 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. Invent a recipe using unlike fractions totaling one cup.
Use 1/2 cup of oats, 1/4 cup of seeds and 1/4 cup of dried fruit: the total is one cup.
- 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 1/3 + 1/4. Show a model or your reasoning.
1/3 + 1/4 = 7/12. Use equal-sized parts before combining or removing them.
e2. Why must the pieces have the same size before adding?
A numerator counts units; both counts must refer to the same fractional unit.
- 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 + 1/4. Show a model or your reasoning.
s2. Calculate 1/3 + 1/6. Show a model or your reasoning.
s3. Calculate 1/4 + 1/8. Show a model or your reasoning.
s4. Calculate 1/5 + 2/5. Show a model or your reasoning.
e1. Calculate 1/3 + 1/4. Show a model or your reasoning.
e2. Why must the pieces have the same size before adding?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain 1/3 + 1/4 with a model.
h2. Why is 1/3 + 1/4 not 2/7?
h3. Find two common denominators for thirds and fourths.
h4. Invent a recipe using unlike fractions totaling one cup.
e1. Calculate 1/3 + 1/4. Show a model or your reasoning.
e2. Why must the pieces have the same size before adding?
Teaching notes & lesson sources
Designed for Grade 5. Add unlike fractions by renaming both ingredients in common units.
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.