Compare fractions with the same denominator and the same whole.
Teaching companion · Version 2.0.0
Compare selected counts only after confirming equal unit sizes.
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.
On identical wholes, compare 3/8 and 5/8. What stays the same and what changes?
Look for: 3/8 < 5/8; eighth-piece size stays the same and the selected count changes.
If you observe: Says they are equal because both denominators are eight.
Respond: Match three shaded eighths on each strip, then point to the two extra eighths in the second.
One strip is twice as long as another. Can comparing their shaded counts of eighths alone compare actual lengths?
Look for: No. Their eighth-sized pieces have different physical lengths.
If you observe: Uses numerator count alone without checking the wholes.
Respond: Measure an eighth of each strip, then replace them with same-length strips before applying the count comparison.
Check independently: Using the same-sized whole, compare 6/8 and 4/8 and state why.
6/8 > 4/8 because six equal eighths exceed four equal eighths.
Use the whole size short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives > for 5/8 compared with 3/8. e2 also meets its criterion: e2 states that the wholes must be the same size for comparing these amounts.
Continue to the linked next lesson. Contrast equal-sized pieces with equal counts of differently sized pieces.
Next lesson: Same Numerator Picnice1 does not yet meet this criterion: e1 gives > for 5/8 compared with 3/8.
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 states that the wholes must be the same size for comparing these amounts.
Keep e1 visible while replacing one strip with a longer strip. Ask the learner to state the condition needed to restore the original proof.
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: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Look for in the response:
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
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.
Look for in the response:
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Look for in the response:
Watch for: Ignores how many equal-sized parts are selected when denominators match.
Try: Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
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.
Look for in the response:
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
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 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?
Ignores how many equal-sized parts are selected when denominators match.
Align two equal-length strips with the same partition. Pair their selected pieces one by one. The strip with extra pieces has the greater amount; equal counts end together.
Teacher answer key. Open responses include a rubric and one valid sample.
3/8 < 5/8. Rename them as equal-sized parts or place them on the same unit number line.
2/3 > 1/3. Rename them as equal-sized parts or place them on the same unit number line.
3/4 > 2/4. Rename them as equal-sized parts or place them on the same unit number line.
5/6 > 4/6. Rename them as equal-sized parts or place them on the same unit number line.
1/2 < 2/2. Rename them as equal-sized parts or place them on the same unit number line.
7/8 > 6/8. Rename them as equal-sized parts or place them on the same unit number line.
2/6 = 2/6. Rename them as equal-sized parts or place them on the same unit number line.
1/4 < 3/4. Rename them as equal-sized parts or place them on the same unit number line.
1/2 < 2/2. Rename them as equal-sized parts or place them on the same unit number line.
1/3 < 2/3. Rename them as equal-sized parts or place them on the same unit number line.
1/4 < 2/4. Rename them as equal-sized parts or place them on the same unit number line.
2/6 < 3/6. Rename them as equal-sized parts or place them on the same unit number line.
Both have eighth-size parts; five parts exceed three parts.
3/8 and 5/8 lie between them.
The amounts cannot be compared from the labels alone without equal wholes.
4/8 compared with 4/8 ends at the same point.
5/8 > 3/8. Rename them as equal-sized parts or place them on the same unit number line.
The wholes must be the same size.
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 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.