Build equivalent fractions by repartitioning the same whole.
Complete teacher pack: Free 17-page PDF with a teacher guide, core, support and challenge practice, exit ticket, and answers.
Before starting: Recognize a whole and count equal parts. 4.NF.A.1 curriculum reference.
Teaching companion · Version 2.0.0
Preserve the whole and endpoint while multiplying both fraction counts by the same factor.
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.
Rename 2/3 in sixths. Explain what happens to each third.
Look for: 2/3 = 4/6; every third is split into two sixths.
If you observe: Writes 2/6 by changing only the denominator.
Respond: Split each third of the same shaded strip in two and recount all six pieces and the four shaded pieces.
A learner claims 2/3 = 3/4 because both numbers increase by one. Does the claim preserve the endpoint?
Look for: No. 2/3 = 8/12 while 3/4 = 9/12.
If you observe: Uses an additive rule for equivalent fractions.
Respond: Use a twelfths strip to expose the different endpoints, then contrast with multiplying both counts by two.
Check independently: Rename 3/4 in twelfths and explain why its amount stays the same.
3/4 = 9/12: each fourth becomes three twelfths, while the shaded endpoint stays fixed.
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 3/6 compared with 1/2. e2 also meets its criterion: e2 explains 1/2 = 2/4 by splitting each half into two fourths of the same whole without moving the endpoint.
Continue to the linked next lesson. Use the repartitioning factor to solve missing numerators and denominators.
Next lesson: Missing Number Bridgese1 does not yet meet this criterion: e1 gives = for 3/6 compared with 1/2.
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 1/2 = 2/4 by splitting each half into two fourths of the same whole without moving the endpoint.
Ask the learner to demonstrate the specific half-to-fourths repartition in e2, naming what changes and what stays fixed.
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 4 equal parts; 2 parts are shaded altogether.
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.
Strip model: 1 same-sized whole, each divided into 8 equal parts; 6 parts are shaded altogether.
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.
Strip model: 1 same-sized whole, each divided into 12 equal parts; 8 parts are shaded altogether.
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.
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.
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.
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.
Look for in the response:
Watch for: Adds the same number to numerator and denominator and claims the fraction stays equal.
Try: Put 2/3 and 3/4 on the same twelfths strip: 8/12 and 9/12 have different endpoints. Contrast this with 2/3 = 4/6, where both counts are multiplied by two.
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.
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: 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.
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 three strips of exactly the same length. Shade one half of the first.
Divide the second into fourths and the third into sixths. Shade to the same endpoint.
Pair up to explain what changed and what stayed equal. Repeat with two thirds and sixths.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Compare 3/6 and 1/2. Choose <, =, or >. The wholes are the same size. Explain why 1/2 and 2/4 are equivalent.
Changes one part of a fraction without scaling numerator and denominator by the same factor.
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.
Teacher answer key. Open responses include a rubric and one valid sample.
Two of four equal parts cover half of the same whole.
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.
Split each fourth into two eighths: three fourths becomes six eighths.
3/6 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
2/5 = 4/10. Rename them as equal-sized parts or place them on the same unit number line.
Eight twelfths and two thirds share the same endpoint.
3/4 = 9/12. Rename them as equal-sized parts or place them on the same unit number line.
Two of four equal parts are shaded.
1/2 = 2/4. Rename them as equal-sized parts or place them on the same unit number line.
Three of six equal parts are shaded.
1/3 = 2/6. Rename them as equal-sized parts or place them on the same unit number line.
2/3, 4/6 and 8/12 cover the same share of equal-length strips.
Two thirds is 8/12 and three fourths is 9/12, so their endpoints differ.
Split each fourth into three twelfths. Three groups of three make 9/12.
Equal fraction labels describe relative shares, but unequal wholes do not establish equal lengths.
3/6 = 1/2. Rename them as equal-sized parts or place them on the same unit number line.
Repartition the same whole: each half becomes two fourths, and the shaded endpoint stays fixed.
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 4. Build equivalent fractions by repartitioning the same whole.
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.