Create and critique exhibits showing equal fraction values.
Teaching companion · Version 2.0.0
Audit fraction exhibits for equal parts, accurate labels, and equivalent values.
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.
One exhibit shades one of two equal parts; another shades three of six equal parts on an identical whole. Do they show the same amount?
Look for: Yes. Both show one half of the same-sized whole.
If you observe: Says three selected pieces must exceed one selected piece.
Respond: Align the shaded endpoints and split each half into three sixths to connect the counts.
An exhibit labeled 2/3 shows two of four equal parts shaded. What repair would make it accurate?
Look for: Change the label to 2/4 (or 1/2), or repartition into thirds and shade two.
If you observe: Keeps the label because two pieces are shaded.
Respond: Ask the learner to name one piece from the whole’s partition before counting selected pieces.
Check independently: Would an uneven six-part picture be ready to display as 3/6 just because three pieces are shaded?
No. First verify or repair equal part areas; count alone does not establish sixths.
Use the equivalent factors short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives = for 1/2 compared with 3/6. e2 also meets its criterion: e2 describes a concrete model check and what evidence would pass it, using its rubric.
Continue to the linked next lesson. Explain equivalent exhibits by repartitioning the same fixed whole.
Next lesson: Equivalent Strip Labe1 does not yet meet this criterion: e1 gives = for 1/2 compared with 3/6.
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 describes a concrete model check and what evidence would pass it, using its rubric.
Present the mislabeled exhibit again. Ask the learner to apply the proposed e2 check and say exactly what would need repair.
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.
Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 4 equal parts; 2 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 6 equal parts; 3 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Strip model: 1 same-sized whole, each divided into 8 equal parts; 4 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Watch for: Does not recognize that b copies of 1/b make one whole.
Try: Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Watch for: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole.
Try: Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
Strip model: 1 same-sized whole, each divided into 3 equal parts; 1 parts are shaded altogether.
Watch for: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole.
Try: Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
Strip model: 1 same-sized whole, each divided into 4 equal parts; 1 parts are shaded altogether.
Watch for: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole.
Try: Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
Strip model: 1 same-sized whole, each divided into 4 equal parts; 2 parts are shaded altogether.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Look for in the response:
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Look for in the response:
Watch for: Does not recognize that b copies of 1/b make one whole.
Try: Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Look for in the response:
Watch for: Counts pieces without checking equal area.
Try: Keep one rectangle fixed. Draw four unequal pieces beside four equal-area pieces. Ask which set lets every piece be called one fourth, then have the learner repair the unequal partition.
Look for in the response:
Watch for: Changes one part of a fraction without scaling numerator and denominator by the same factor.
Try: Shade 2/3 of a fixed strip and split each third into two equal parts. Count four shaded sixths out of six. Write ×2 on both arrows and check that the shaded endpoint did not move.
Watch for: Counts pieces without checking equal area.
Try: Keep one rectangle fixed. Draw four unequal pieces beside four equal-area pieces. Ask which set lets every piece be called one fourth, then have the learner repair the unequal partition.
Watch for: Reverses the shaded count and the total equal-part count.
Try: Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
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?
Create a small exhibit with a labeled strip and a matching number line.
Exchange exhibits. Check equal partitions, labels and the whole.
Write a curator note explaining one repair and one equivalent name.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 1/2 and 3/6. Choose <, =, or >. The wholes are the same size. Give one check you would use before displaying a model.
Reverses the shaded count and the total equal-part count.
Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
Teacher answer key. Open responses include a rubric and one valid sample.
1 parts of size 1/2 represent 1/2.
2 parts of size 1/4 represent 2/4.
3 parts of size 1/6 represent 3/6.
4 parts of size 1/8 represent 4/8.
1/2 = 2/4. Rename them as equal-sized parts or place them on the same unit number line.
2/3 = 4/6. Rename them as equal-sized parts or place them on the same unit number line.
3/4 = 6/8. Rename them as equal-sized parts or place them on the same unit number line.
2/2 = 3/3. Rename them as equal-sized parts or place them on the same unit number line.
1 parts of size 1/2 represent 1/2.
1 parts of size 1/3 represent 1/3.
1 parts of size 1/4 represent 1/4.
2 parts of size 1/4 represent 2/4.
Shade one of two parts or two of four equal parts in equal-sized strips.
Change the label to 2/4, or redraw thirds and shade two.
All three thirds are included, so the value is one whole.
The shading is clear; equalize the partition sizes so the fraction label is accurate.
1/2 = 3/6. Rename them as equal-sized parts or place them on the same unit number line.
Verify equal-sized parts and a label matching the shaded count.
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. Create and critique exhibits showing equal fraction values.
3.NF.A.3b 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.