Compose and decompose one whole using same-denominator fractions.
Teaching companion · Version 2.0.0
Find a complement to one by counting missing pieces of the same unit.
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.
A whole is 8/8 and 3/8 is shaded. What amount is missing?
Look for: 5/8; three eighths plus five eighths fill eight eighths.
If you observe: Answers 5 without the fractional unit.
Respond: Point to each of the five missing pieces and ask for the size of one piece before naming the total.
A learner writes 3/8 + 5/8 = 8/16. Did the pieces become sixteenths?
Look for: No. They remain eighths, so the sum is 8/8 = 1.
If you observe: Adds denominators when combining same-sized pieces.
Respond: Combine the physical eighth pieces without cutting them and ask what action would actually create sixteenths.
Check independently: Complete 7/10 + ? = 1 and explain the denominator.
3/10; seven tenths and three tenths make ten tenths. The pieces stay tenths.
Use the unlike estimation short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives 5/8 as the amount completing 3/8 to one. e2 also meets its criterion: e2 explains that the denominator stays fixed because the size of each piece stays the same.
Continue to the linked next lesson. Use a full collection of fractional pieces as the basis for exchanging one whole.
Next lesson: Mixed Number Markete1 does not yet meet this criterion: e1 gives 5/8 as the amount completing 3/8 to one.
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 the denominator stays fixed because the size of each piece stays the same.
Have the learner act out 3/8 + 5/8 with eighth pieces and name each piece while explaining why combining counts does not change sizes.
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: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Look for in the response:
Watch for: Adds, subtracts, or multiplies a denominator when combining counts of the same fractional unit.
Try: Place three eighth-size pieces beside five eighth-size pieces. Count eight pieces without recutting any of them. Write 8/8 and explain why 8/16 would describe smaller pieces than the ones on the table.
Look for in the response:
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Look for in the response:
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Look for in the response:
Watch for: Finds the missing count to one without retaining the fractional unit.
Try: Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Watch for: Adds, subtracts, or multiplies a denominator when combining counts of the same fractional unit.
Try: Place three eighth-size pieces beside five eighth-size pieces. Count eight pieces without recutting any of them. Write 8/8 and explain why 8/16 would describe smaller pieces than the ones on the table.
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?
Shade 3/8 of a strip. Identify the amount needed to finish the whole.
Pair cards that sum to one and verify each with a strip.
Write two different decompositions of one using eighths.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
How much completes 3/8 to one? Why does the denominator stay fixed?
Finds the missing count to one without retaining the fractional unit.
Build one as eight eighths, shade three eighths, and count the five unshaded eighths. Write 3/8 + 5/8 = 8/8 = 1 and ask the learner to name the size of every missing piece.
Teacher answer key. Open responses include a rubric and one valid sample.
1 - 3/8 = 5/8. Use equal-sized parts before combining or removing them.
1 - 1/4 = 3/4. Use equal-sized parts before combining or removing them.
1 - 2/5 = 3/5. Use equal-sized parts before combining or removing them.
1 - 5/6 = 1/6. Use equal-sized parts before combining or removing them.
1 - 7/10 = 3/10. Use equal-sized parts before combining or removing them.
1 - 2/3 = 1/3. Use equal-sized parts before combining or removing them.
1 - 1/8 = 7/8. Use equal-sized parts before combining or removing them.
1 - 3/4 = 1/4. Use equal-sized parts before combining or removing them.
1 - 1/2 = 1/2. Use equal-sized parts before combining or removing them.
1 - 1/3 = 2/3. Use equal-sized parts before combining or removing them.
1 - 1/4 = 3/4. Use equal-sized parts before combining or removing them.
1 - 2/4 = 1/2. Use equal-sized parts before combining or removing them.
1/8 + 2/8 + 5/8 = 8/8 = 1.
We count eight eighth-size pieces; their size did not change.
1/4 + 1/4 + 2/4 = 1.
Three more tenths fill the ten equal parts.
1 - 3/8 = 5/8. Use equal-sized parts before combining or removing them.
The size of each part stays the same while the counts combine.
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. Compose and decompose one whole using same-denominator fractions.
4.NF.B.3a 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.