Subtract unlike fractions and check differences against estimates.
Teaching companion · Version 2.0.0
Subtract common-unit counts and restore the removed amount to check.
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 both quantities before finding 5/6 − 1/4.
Look for: 10/12 − 3/12 = 7/12.
If you observe: Subtracts 5 − 1 and 6 − 4 to obtain 4/2.
Respond: Build ten twelfths and physically remove three; keep the size label on every remaining piece.
How would you check a proposed difference of 7/12 for 5/6 − 1/4?
Look for: Add back 1/4: 7/12 + 3/12 = 10/12 = 5/6.
If you observe: Adds the difference to the starting amount instead of the removed amount.
Respond: Label three roles on a bar: starting amount, removed portion, and remainder. Reassemble the removed portion with the remainder.
Check independently: Calculate 3/4 − 1/3 and check it by addition.
5/12; 5/12 + 4/12 = 9/12 = 3/4.
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 7/12 for 5/6 − 1/4. e2 also meets its criterion: e2 states difference + removed amount = starting amount, or applies 7/12 + 1/4 = 5/6.
Continue to the linked next lesson. Add an exchange of one whole when the fractional part is too small to remove the requested amount.
Next lesson: Mixed Number Repaire1 does not yet meet this criterion: e1 gives 7/12 for 5/6 − 1/4.
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 states difference + removed amount = starting amount, or applies 7/12 + 1/4 = 5/6.
Ask the learner to label the removed 1/4 and the remaining 7/12 on e1, then join them to construct the e2 check.
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: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
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.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
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.
Watch for: Accepts an exact answer that contradicts the size or direction of the operation.
Try: Before calculating, mark the starting amount and predict the direction of change. A positive sum must exceed either addend; a positive subtraction result is below the starting amount. Use 0, 1/2, 1, or 2 to bound the result, then compare the exact answer with that bound.
Look for in the response:
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Look for in the response:
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Look for in the response:
Watch for: Chooses an operation from the numbers without identifying whether the task combines, takes a part, shares, or counts groups.
Try: Ask the learner to finish “I know …; I need …” with units. Act out the quantity: combine disjoint colors, overlap two fractional selections, share one amount, or count fixed-size pieces. Write an equation only after the action is identified.
Look for in the response:
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Watch for: Subtracts unlike numerator or denominator counts without preserving equivalent values.
Try: Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
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 a trail of length 5/6 mile and mark the first 1/4 mile as completed.
Use twelfths to find the remaining trail.
Partners estimate a difference, compute it, then check it by adding back.
Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Calculate 5/6 - 1/4. Show a model or your reasoning. What addition equation checks a subtraction?
Subtracts unlike numerator or denominator counts without preserving equivalent values.
Show 5/6 as 10/12 and 1/4 as 3/12 on a shared unit. Remove three of the ten twelfths. Check 7/12 + 3/12 = 10/12 before returning to the original fractions.
Teacher answer key. Open responses include a rubric and one valid sample.
5/6 - 1/4 = 7/12. Use equal-sized parts before combining or removing them.
3/4 - 1/3 = 5/12. Use equal-sized parts before combining or removing them.
7/8 - 1/2 = 3/8. Use equal-sized parts before combining or removing them.
4/5 - 1/6 = 19/30. Use equal-sized parts before combining or removing them.
2/3 - 1/5 = 7/15. Use equal-sized parts before combining or removing them.
9/10 - 3/4 = 3/20. Use equal-sized parts before combining or removing them.
5/8 - 1/3 = 7/24. Use equal-sized parts before combining or removing them.
7/9 - 1/6 = 11/18. Use equal-sized parts before combining or removing them.
3/4 - 1/2 = 1/4. Use equal-sized parts before combining or removing them.
2/3 - 1/3 = 1/3. Use equal-sized parts before combining or removing them.
5/6 - 1/2 = 1/3. Use equal-sized parts before combining or removing them.
3/5 - 1/5 = 2/5. Use equal-sized parts before combining or removing them.
It is a little more than one half; exact result 7/12.
5/12 + 1/3 = 9/12 = 3/4.
They describe unit sizes, which must be matched, not removed.
A 3/4 mile trail with 1/4 mile completed leaves 1/2 mile.
5/6 - 1/4 = 7/12. Use equal-sized parts before combining or removing them.
Difference plus the removed amount must equal the starting amount.
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. Subtract unlike fractions and check differences against estimates.
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.