Compare and Defend
Compare unlike denominators using common units and defend the result.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
c2. Compare 3/5 and 5/8. Choose <, =, or >. The wholes are the same size.
c3. Compare 4/6 and 2/3. Choose <, =, or >. The wholes are the same size.
c4. Compare 7/10 and 2/3. Choose <, =, or >. The wholes are the same size.
c5. Compare 5/6 and 7/8. Choose <, =, or >. The wholes are the same size.
c6. Compare 2/5 and 3/7. Choose <, =, or >. The wholes are the same size.
c7. Compare 3/4 and 5/6. Choose <, =, or >. The wholes are the same size.
c8. Compare 7/12 and 4/9. Choose <, =, or >. The wholes are the same size.
e1. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
e2. What makes a comparison proof convincing?
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
- Choose 2/3 and 3/4 on identical wholes. Predict the larger amount.
- Partition both wholes into twelfths and locate their endpoints.
- Partners alternate between a common-denominator proof and a number-line proof.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Choose 2/3 and 3/4 on identical wholes. Predict the larger amount.
Partition both wholes into twelfths and locate their endpoints.
Partners alternate between a common-denominator proof and a number-line proof.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size. What makes a comparison proof convincing?
Watch for this misconception
Comparing numerators or denominators separately.
Rename both fractions in common units on the same whole.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
2/3 < 3/4. Rename them as equal-sized parts or place them on the same unit number line.
c2. Compare 3/5 and 5/8. Choose <, =, or >. The wholes are the same size.
3/5 < 5/8. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 4/6 and 2/3. Choose <, =, or >. The wholes are the same size.
4/6 = 2/3. Rename them as equal-sized parts or place them on the same unit number line.
c4. Compare 7/10 and 2/3. Choose <, =, or >. The wholes are the same size.
7/10 > 2/3. Rename them as equal-sized parts or place them on the same unit number line.
c5. Compare 5/6 and 7/8. Choose <, =, or >. The wholes are the same size.
5/6 < 7/8. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 2/5 and 3/7. Choose <, =, or >. The wholes are the same size.
2/5 < 3/7. Rename them as equal-sized parts or place them on the same unit number line.
c7. Compare 3/4 and 5/6. Choose <, =, or >. The wholes are the same size.
3/4 < 5/6. Rename them as equal-sized parts or place them on the same unit number line.
c8. Compare 7/12 and 4/9. Choose <, =, or >. The wholes are the same size.
7/12 > 4/9. Rename them as equal-sized parts or place them on the same unit number line.
s1. Compare 1/2 and 1/4. Choose <, =, or >. The wholes are the same size.
1/2 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
s2. Compare 2/4 and 3/4. Choose <, =, or >. The wholes are the same size.
2/4 < 3/4. Rename them as equal-sized parts or place them on the same unit number line.
s3. Compare 1/3 and 2/3. Choose <, =, or >. The wholes are the same size.
1/3 < 2/3. Rename them as equal-sized parts or place them on the same unit number line.
s4. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.
1/2 = 2/4. Rename them as equal-sized parts or place them on the same unit number line.
h1. Defend 2/3 < 3/4 with common units.
Eight twelfths is less than nine 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. Explain why bigger numerator alone is not enough.
2/3 is greater than 3/8 even though two is less than three.
- 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. Show 3/5 and 5/8 on a common partition.
24/40 is less than 25/40.
- 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 comparison that is easier with a benchmark than a common denominator.
3/8 < 5/6 because one is below half and the other is above half.
- 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. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
2/3 < 3/4. Rename them as equal-sized parts or place them on the same unit number line.
e2. What makes a comparison proof convincing?
It states the same whole and compares equal-sized units or distances.
- 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. Compare 1/2 and 1/4. Choose <, =, or >. The wholes are the same size.
s2. Compare 2/4 and 3/4. Choose <, =, or >. The wholes are the same size.
s3. Compare 1/3 and 2/3. Choose <, =, or >. The wholes are the same size.
s4. Compare 1/2 and 2/4. Choose <, =, or >. The wholes are the same size.
e1. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
e2. What makes a comparison proof convincing?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Defend 2/3 < 3/4 with common units.
h2. Explain why bigger numerator alone is not enough.
h3. Show 3/5 and 5/8 on a common partition.
h4. Invent a comparison that is easier with a benchmark than a common denominator.
e1. Compare 2/3 and 3/4. Choose <, =, or >. The wholes are the same size.
e2. What makes a comparison proof convincing?
Teaching notes & lesson sources
Designed for Grade 4. Compare unlike denominators using common units and defend the result.
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.