Same Denominator Race
Compare fractions with the same denominator and the same whole.
Preview the complete lesson
Eight core questions and a two-question exit ticket. Print one set per student.
c1. Compare 3/8 and 5/8. Choose <, =, or >. The wholes are the same size.
c2. Compare 2/3 and 1/3. Choose <, =, or >. The wholes are the same size.
c3. Compare 3/4 and 2/4. Choose <, =, or >. The wholes are the same size.
c4. Compare 5/6 and 4/6. Choose <, =, or >. The wholes are the same size.
c5. Compare 1/2 and 2/2. Choose <, =, or >. The wholes are the same size.
c6. Compare 7/8 and 6/8. Choose <, =, or >. The wholes are the same size.
c7. Compare 2/6 and 2/6. Choose <, =, or >. The wholes are the same size.
c8. Compare 1/4 and 3/4. Choose <, =, or >. The wholes are the same size.
e1. Compare 5/8 and 3/8. Choose <, =, or >. The wholes are the same size.
e2. What must be true about the wholes?
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 strips partitioned into eighths. Mark racers at 3/8 and 5/8.
- Explain which racer is farther from zero without using whole-number guessing.
- Partners make four new same-denominator races and defend each result.
45-minute teaching sequence
Look at the first model or task. What is the whole? What do you notice?
Draw identical strips partitioned into eighths. Mark racers at 3/8 and 5/8.
Explain which racer is farther from zero without using whole-number guessing.
Partners make four new same-denominator races and defend each result.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 5/8 and 3/8. Choose <, =, or >. The wholes are the same size. What must be true about the wholes?
Watch for this misconception
Comparing part counts without checking equal wholes.
Align the whole strips before comparing the shaded parts.
Teacher answer key. Open responses include a rubric and one valid sample.
c1. Compare 3/8 and 5/8. Choose <, =, or >. The wholes are the same size.
3/8 < 5/8. Rename them as equal-sized parts or place them on the same unit number line.
c2. Compare 2/3 and 1/3. Choose <, =, or >. The wholes are the same size.
2/3 > 1/3. Rename them as equal-sized parts or place them on the same unit number line.
c3. Compare 3/4 and 2/4. Choose <, =, or >. The wholes are the same size.
3/4 > 2/4. Rename them as equal-sized parts or place them on the same unit number line.
c4. Compare 5/6 and 4/6. Choose <, =, or >. The wholes are the same size.
5/6 > 4/6. Rename them as equal-sized parts or place them on the same unit number line.
c5. Compare 1/2 and 2/2. Choose <, =, or >. The wholes are the same size.
1/2 < 2/2. Rename them as equal-sized parts or place them on the same unit number line.
c6. Compare 7/8 and 6/8. Choose <, =, or >. The wholes are the same size.
7/8 > 6/8. Rename them as equal-sized parts or place them on the same unit number line.
c7. Compare 2/6 and 2/6. Choose <, =, or >. The wholes are the same size.
2/6 = 2/6. Rename them as equal-sized parts or place them on the same unit number line.
c8. Compare 1/4 and 3/4. Choose <, =, or >. The wholes are the same size.
1/4 < 3/4. Rename them as equal-sized parts or place them on the same unit number line.
s1. Compare 1/2 and 2/2. Choose <, =, or >. The wholes are the same size.
1/2 < 2/2. Rename them as equal-sized parts or place them on the same unit number line.
s2. 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.
s3. Compare 1/4 and 2/4. Choose <, =, or >. The wholes are the same size.
1/4 < 2/4. Rename them as equal-sized parts or place them on the same unit number line.
s4. Compare 2/6 and 3/6. Choose <, =, or >. The wholes are the same size.
2/6 < 3/6. Rename them as equal-sized parts or place them on the same unit number line.
h1. Explain why 5/8 is greater than 3/8.
Both have eighth-size parts; five parts exceed three parts.
- 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. Invent two different fractions between 2/8 and 6/8.
3/8 and 5/8 lie between them.
- 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. Does this rule work for strips of different sizes?
The amounts cannot be compared from the labels alone without equal wholes.
- 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. Make an eighths race that ends in a tie.
4/8 compared with 4/8 ends at the same point.
- 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 5/8 and 3/8. Choose <, =, or >. The wholes are the same size.
5/8 > 3/8. Rename them as equal-sized parts or place them on the same unit number line.
e2. What must be true about the wholes?
The wholes must be the same size.
- 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 2/2. Choose <, =, or >. The wholes are the same size.
s2. Compare 1/3 and 2/3. Choose <, =, or >. The wholes are the same size.
s3. Compare 1/4 and 2/4. Choose <, =, or >. The wholes are the same size.
s4. Compare 2/6 and 3/6. Choose <, =, or >. The wholes are the same size.
e1. Compare 5/8 and 3/8. Choose <, =, or >. The wholes are the same size.
e2. What must be true about the wholes?
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
h1. Explain why 5/8 is greater than 3/8.
h2. Invent two different fractions between 2/8 and 6/8.
h3. Does this rule work for strips of different sizes?
h4. Make an eighths race that ends in a tie.
e1. Compare 5/8 and 3/8. Choose <, =, or >. The wholes are the same size.
e2. What must be true about the wholes?
Teaching notes & lesson sources
Designed for Grade 3. Compare fractions with the same denominator and the same whole.
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.