Build a whole by repeating a unit fraction.
Teaching companion · Version 2.0.0
Name one equal part and connect repeated unit fractions to the whole.
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 strip is split into six equal parts. Name one part, then say how many copies fill the strip.
Look for: One part is 1/6; six copies make 6/6 = 1.
If you observe: Names one part 1/5 by counting only the other pieces.
Respond: Bracket all six pieces as one whole; touch the selected piece as well as the five others while counting the denominator.
Build one whole with five 1/6 pieces. Is the whole complete?
Look for: No. It needs one more sixth.
If you observe: Treats five pieces as a whole because they form a connected strip.
Respond: Keep the whole outline visible and compare the assembled pieces with the unfilled sixth.
Check independently: A whole has eight equal parts. Name one part and the number of copies needed for the whole.
One part is 1/8; eight copies make one whole.
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 1/4 for one of four equal parts. e2 also meets its criterion: e2 explains that six sixths cover all six equal parts exactly.
Continue to the linked next lesson. Use the unit fraction as the piece size when counting several shaded pieces.
Next lesson: Fraction Strip Detectivee1 does not yet meet this criterion: e1 gives 1/4 for one of four equal parts.
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 six sixths cover all six equal parts exactly.
Ask the learner to assemble six 1/6 pieces inside a fixed outline, then describe why both the piece size and the count are needed.
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 6 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 8 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 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.
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.
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 6 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 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 6 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.
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: 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: 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: 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.
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:
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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 one strip. Make six equal sections and label one section 1/6.
Cover the whole with six copies of that section. Repeat with thirds and fourths.
Partners name the unit and explain how many copies make one whole.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
What is one part when a whole has four equal parts? Why do six copies of 1/6 make one whole?
Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole.
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.
Teacher answer key. Open responses include a rubric and one valid sample.
One of six equal parts is 1/6.
One of eight equal parts is 1/8.
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.
Four fourths form a whole.
Three thirds form a whole.
Two copies of 1/6 cover 2/6.
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.
1 parts of size 1/6 represent 1/6.
Sixths split the whole into more equal parts, so each is smaller.
Repeat the quarter piece three times.
Add one more sixth; six sixths are one whole.
Two halves or four fourths each fill the same strip.
Each equal part is one fourth.
Six copies cover all six equal parts exactly.
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. Build a whole by repeating a unit fraction.
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.