Same Numerator Picnic
Compare same-numerator fractions by reasoning about part size.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
c2. Compare 1/2 and 1/8. Choose <, =, or >. The wholes are the same size.
c3. Compare 2/3 and 2/6. Choose <, =, or >. The wholes are the same size.
c4. Compare 3/4 and 3/8. Choose <, =, or >. The wholes are the same size.
c5. Compare 1/6 and 1/8. Choose <, =, or >. The wholes are the same size.
c6. Compare 2/4 and 2/8. Choose <, =, or >. The wholes are the same size.
c7. Compare 1/3 and 1/6. Choose <, =, or >. The wholes are the same size.
c8. Compare 3/6 and 3/8. Choose <, =, or >. The wholes are the same size.
e1. Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
e2. How does dividing one whole into more pieces affect each piece?
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 identical picnic sandwiches partitioned into thirds and fourths.
- Shade one part in each. Explain which serving is larger.
- Partners repeat with two thirds and two fourths and compare the same number of pieces.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw identical picnic sandwiches partitioned into thirds and fourths.
Shade one part in each. Explain which serving is larger.
Partners repeat with two thirds and two fourths and compare the same number of pieces.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size. How does dividing one whole into more pieces affect each piece?
Watch for this misconception
Thinking a larger denominator means a larger fraction.
Hold the whole fixed and compare the size of one piece.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
1/3 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
c2. Compare 1/2 and 1/8. Choose <, =, or >. The wholes are the same size.
1/2 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 2/3 and 2/6. Choose <, =, or >. The wholes are the same size.
2/3 > 2/6. Rename them as equal-sized parts or place them on the same unit number line.
c4. Compare 3/4 and 3/8. Choose <, =, or >. The wholes are the same size.
3/4 > 3/8. Rename them as equal-sized parts or place them on the same unit number line.
c5. Compare 1/6 and 1/8. Choose <, =, or >. The wholes are the same size.
1/6 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 2/4 and 2/8. Choose <, =, or >. The wholes are the same size.
2/4 > 2/8. Rename them as equal-sized parts or place them on the same unit number line.
c7. Compare 1/3 and 1/6. Choose <, =, or >. The wholes are the same size.
1/3 > 1/6. Rename them as equal-sized parts or place them on the same unit number line.
c8. Compare 3/6 and 3/8. Choose <, =, or >. The wholes are the same size.
3/6 > 3/8. 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 1/3 and 1/6. Choose <, =, or >. The wholes are the same size.
1/3 > 1/6. Rename them as equal-sized parts or place them on the same unit number line.
s3. Compare 1/4 and 1/8. Choose <, =, or >. The wholes are the same size.
1/4 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
s4. Compare 2/3 and 2/6. Choose <, =, or >. The wholes are the same size.
2/3 > 2/6. Rename them as equal-sized parts or place them on the same unit number line.
h1. Why is 1/3 greater than 1/4 of the same sandwich?
Thirds divide it into fewer equal pieces, so each piece is larger.
- 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. Show 2/4 and 2/8 with identical strips.
Shade two quarters and two eighths; the two quarters cover more.
- 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. Correct the claim that eighths are larger because eight is larger.
Eight counts more pieces of a fixed whole, so each eighth is smaller.
- 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. Describe when the same-numerator rule can be used.
Use the same numerator and same-sized wholes, then compare part sizes.
- 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 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
1/3 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
e2. How does dividing one whole into more pieces affect each piece?
Each equal piece becomes smaller.
- 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 1/3 and 1/6. Choose <, =, or >. The wholes are the same size.
s3. Compare 1/4 and 1/8. Choose <, =, or >. The wholes are the same size.
s4. Compare 2/3 and 2/6. Choose <, =, or >. The wholes are the same size.
e1. Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
e2. How does dividing one whole into more pieces affect each piece?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Why is 1/3 greater than 1/4 of the same sandwich?
h2. Show 2/4 and 2/8 with identical strips.
h3. Correct the claim that eighths are larger because eight is larger.
h4. Describe when the same-numerator rule can be used.
e1. Compare 1/3 and 1/4. Choose <, =, or >. The wholes are the same size.
e2. How does dividing one whole into more pieces affect each piece?
Teaching notes & lesson sources
Designed for Grade 3. Compare same-numerator fractions by reasoning about part size.
3.NF.A.3d 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.