Divide a unit fraction by a whole number through equal sharing.
Teaching companion · Version 2.0.0
Name an equal share of a unit fraction relative to the original 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.
Half of one sheet is shared equally among three people. What fraction of the original sheet does each get?
Look for: 1/6 of the original sheet.
If you observe: Answers 1/3 by treating the shaded half as the whole.
Respond: Extend the three equal share lengths across the unshaded half and count six matching shares in the original sheet.
How can multiplication check whether 1/6 is one of three equal shares of 1/2?
Look for: 3 × 1/6 = 3/6 = 1/2.
If you observe: Multiplies by the original denominator two instead of the number of recipients three.
Respond: Place three recipient cards beside the three sixth-pieces and join those shares to rebuild the shaded half.
Check independently: One fourth of a liter is shared equally among three people. Name one share and check it.
1/12 liter per person; 3 × 1/12 = 1/4 liter.
Use the unit fraction sharing short intervention if the difficulty persists. Return to this check before repeating the exit ticket.
e1 meets its criterion: e1 gives 1/6 for 1/2 ÷ 3. e2 also meets its criterion: e2 names the original whole, rather than the shaded half, as the reference for the final share.
Continue to the linked next lesson. Contrast finding the size of one share with counting fixed-size servings.
Next lesson: How Many Servingse1 does not yet meet this criterion: e1 gives 1/6 for 1/2 ÷ 3.
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 names the original whole, rather than the shaded half, as the reference for the final share.
Ask the learner to label both “one original whole” and “amount being shared” on e1, then explain why one third of the half is one sixth of the whole.
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: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Look for in the response:
Watch for: Confuses the number of equal groups with the size of each group.
Try: Draw three separate bags, each holding 2/5 cup. Label “3 groups” and “2/5 cup per group.” Count six fifth-cup pieces in total and connect the drawing to 2/5 + 2/5 + 2/5.
Look for in the response:
Watch for: Assumes multiplication always enlarges a positive amount.
Try: Keep a 3/4-meter ribbon as the starting amount. Compare half a copy, one copy, and two copies. Record 3/8, 3/4, and 3/2 meters, then relate each change to a factor below, equal to, or above one.
Look for in the response:
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Look for in the response:
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Watch for: Names a share relative to the shaded fraction instead of the original whole.
Try: Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
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 half of a whole sheet and divide that half into three equal shares.
Count six such shares across the original whole; name one share 1/6.
Partners share a quarter among two and among three and compare the shares.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 1/2 ÷ 3. Show a model or your reasoning. What whole is used to name the final share?
Names a share relative to the shaded fraction instead of the original whole.
Shade half of a whole strip and divide that half into three equal shares. Extend the same cuts across the unshaded half: six shares fill the original whole, so each is 1/6. Check 3 × 1/6 = 1/2.
Teacher answer key. Open responses include a rubric and one valid sample.
1/2 ÷ 3 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/3 ÷ 2 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/4 ÷ 3 = 1/12. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/5 ÷ 2 = 1/10. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/6 ÷ 4 = 1/24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/8 ÷ 3 = 1/24. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/3 ÷ 5 = 1/15. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/4 ÷ 4 = 1/16. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/2 ÷ 2 = 1/4. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/3 ÷ 2 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/4 ÷ 2 = 1/8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
1/2 ÷ 4 = 1/8. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
Split a half into three equal shares; six shares would fill the original whole, so each is 1/6.
Three times 1/6 equals 1/2.
A positive amount split among more than one person gives smaller shares.
A quarter liter is shared equally by three people; each gets 1/12 liter.
1/2 ÷ 3 = 1/6. Divide by multiplying by the reciprocal of the divisor. Check by multiplying back.
The original whole, not the already shaded half.
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 5. Divide a unit fraction by a whole number through equal sharing.
5.NF.B.7a 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.