Compare same-numerator fractions by reasoning about part size.
Teaching companion · Version 2.0.0
For equal numerators and a fixed whole, compare the size of the pieces.
The original lesson PDFs remain version 1.0.0. This supplement adds diagnostic probes, teaching responses, and question-specific rubrics. Use the supplement below for the updated guidance.
Ask for an explanation or drawing before choosing a response. A wrong answer alone does not identify its cause.
Compare one third and one sixth of identical sandwiches. Which is larger?
Look for: 1/3 is larger; one third covers two sixths.
If you observe: Chooses 1/6 because six exceeds three.
Respond: Overlay a third on a sixth-partitioned copy and count two sixths under it.
Compare 2/4 and 2/8 of identical strips. Are two pieces always the same amount?
Look for: No. Two fourths cover more than two eighths.
If you observe: Says equal numerators guarantee equal amounts.
Respond: Select two pieces from each strip and align endpoints, then ask which piece size was repeated.
Check independently: Of the same whole, which is larger: 3/4 or 3/8? Explain without decimal division.
3/4 is larger because three fourth-size pieces exceed three eighth-size pieces.
Use the denominator size short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives > for 1/3 compared with 1/4. e2 also meets its criterion: e2 explains that more equal pieces in one fixed whole make each piece smaller.
Continue to the linked next lesson. Test why the equal-whole condition is necessary for physical comparisons.
Next lesson: Whole Size Matterse1 does not yet meet this criterion: e1 gives > for 1/3 compared with 1/4.
Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on.
Open the linked short interventione1 meets its criterion, but e2 does not yet show this evidence: e2 explains that more equal pieces in one fixed whole make each piece smaller.
Ask the learner to fold an identical strip once more and describe what happened to each part before restating the e2 explanation.
Open the linked short interventionUse these as follow-up prompts, then examine the learner’s model or explanation. Open responses may differ from the sample while satisfying the criteria.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Look for in the response:
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Look for in the response:
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Look for in the response:
Watch for: Assumes equal fraction labels guarantee equal physical amounts even when the wholes differ.
Try: Compare half of a 12 cm strip with half of a 6 cm strip. Measure 6 cm and 3 cm. Keep the fraction label visible and ask what changed; then repeat the comparison using two equal-length strips.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Look for in the response:
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Watch for: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Try: Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Look for in the response:
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Eight core questions and a two-question exit ticket. Print one set per student.
Recognize a whole and count equal parts.
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?
Assumes a larger denominator makes a larger piece when the whole and numerator are fixed.
Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
Teacher answer key. Open responses include a rubric and one valid sample.
1/3 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
1/2 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
2/3 > 2/6. Rename them as equal-sized parts or place them on the same unit number line.
3/4 > 3/8. Rename them as equal-sized parts or place them on the same unit number line.
1/6 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
2/4 > 2/8. Rename them as equal-sized parts or place them on the same unit number line.
1/3 > 1/6. Rename them as equal-sized parts or place them on the same unit number line.
3/6 > 3/8. Rename them as equal-sized parts or place them on the same unit number line.
1/2 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
1/3 > 1/6. Rename them as equal-sized parts or place them on the same unit number line.
1/4 > 1/8. Rename them as equal-sized parts or place them on the same unit number line.
2/3 > 2/6. Rename them as equal-sized parts or place them on the same unit number line.
Thirds divide it into fewer equal pieces, so each piece is larger.
Shade two quarters and two eighths; the two quarters cover more.
Eight counts more pieces of a fixed whole, so each eighth is smaller.
Use the same numerator and same-sized wholes, then compare part sizes.
1/3 > 1/4. Rename them as equal-sized parts or place them on the same unit number line.
Each equal piece becomes smaller.
Use the whole and equal-part prompts before moving to independent practice. Some items revisit the core concept with simpler models.
Explain, transfer, and critique. More than one valid response may satisfy the rubric.
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.