Use a benchmark estimate to catch denominator-addition errors, then combine or subtract equivalent fractions.
An estimate constrains the result; exact addition and subtraction require equal-sized fractional units.
Materials: Paper; Pencil; Optional fraction strips.
The second worked example, three unused practice tasks, and remaining transfer task are available for a follow-up session. Allow more time if the group needs to build the models.
Teaching move: Write an expected range before any exact work. After renaming fractions, ask what the common denominator names and compare the final result with the range.
Open an interactive fraction strip model →1 · Quick diagnosis
Use the answer notes to interpret what you hear. Choose a response for each question to get a suggested teaching step. These choices describe this brief check and are not a mastery score.
Explain with a drawing, objects, or words.
Answer or sample response: Yes. Both addends exceed 1/2, so their sum exceeds 1.
Listen for this difficulty: Adding numerators and denominators without checking magnitude.
Try this response: Place each addend above the half mark and combine two half-sized lower bounds.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 2/5 is less than 1/2, but adding a positive 1/3 to 1/2 must make the result greater than 1/2.
Listen for this difficulty: Adding the denominators along with the numerators.
Try this response: Ask whether a positive addition can make the starting amount smaller.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: No. Rename them as 10/12 and 3/12 first; the difference is 7/12.
Listen for this difficulty: Subtracting counts that refer to different-sized pieces.
Try this response: Compare a sixth-sized piece with a fourth-sized piece, then partition both into twelfths.
Look for:
2 · Model together
Use one now. Ask the learner to explain each step before revealing the next part of your drawing.
Result: 17/12 = 1 5/12, between 1 and 1 1/2.
Listen for this difficulty: Reporting 5/7 after adding unlike fraction symbols.
Try this response: Keep the unit word “twelfths” in the addition sentence.
Look for:
Result: 13/24, a little more than 1/2.
Listen for this difficulty: Subtracting denominators or overlooking an unreasonable magnitude.
Try this response: Show the half benchmark at 12/24 on the same line as the difference.
Look for:
3 · Guided practice
Mix a calculation or drawing with an explanation or error repair. Keep the other tasks for another short session.
Explain with a drawing, objects, or words.
Answer or sample response: Above 1; 5/6 is 1/6 short of 1 and 1/4 exceeds 1/6. The sum is 13/12 = 1 1/12.
Listen for this difficulty: Using a whole-number denominator sum of 10.
Try this response: Compare the missing sixth with the quarter being added before using twelfths.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 4/6 − 1/6 = 3/6 = 1/2; both counts must refer to sixths.
Listen for this difficulty: Subtracting 1 from 2 while ignoring different units.
Try this response: Split every third into two sixths.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The sum must exceed 1/2, but 3/8 does not. 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3.
Listen for this difficulty: Treating a plausible-looking fraction as sufficient without a magnitude check.
Try this response: Compare the reported sum with the starting half.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 1/12, less than 1/4. In twelfths, 10/12 − 9/12 = 1/12.
Listen for this difficulty: Expecting a large difference because both fractions are large.
Try this response: Place the two amounts near each other on a unit line and inspect the gap.
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Explain with a drawing, objects, or words.
Answer or sample response: 4/12 + 3/12 = 7/12; or 8/24 + 6/24 = 14/24, which equals 7/12.
Listen for this difficulty: Believing only the least common denominator can produce a correct sum.
Try this response: Split every twelfth in half to connect the two valid representations.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The missing amount is above 1/2: 5/6 − 1/4 = 10/12 − 3/12 = 7/12.
Listen for this difficulty: Adding to find a missing addend without considering the inverse relation.
Try this response: Compare 1/2 + 1/4 = 3/4 with the required 5/6.
Look for:
4 · Independent transfer
Choose one task without coaching. Check the explanation against both criteria in its teaching notes; use the other task for a later check.
Explain with a drawing, objects, or words.
Answer or sample response: The report is too small because both walks exceed half a mile. The total is 15/24 + 16/24 = 31/24 = 1 7/24 miles.
Listen for this difficulty: Accepting an exact-looking output without checking its scale.
Try this response: Make the two half-mile lower bounds visible before computing.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 7/20 liter remains: 15/20 − 8/20 = 7/20. The remainder exceeds 1/4 because less than 1/2 liter was removed, so 1/9 is too small.
Listen for this difficulty: Subtracting numerator and denominator independently.
Try this response: First remove an imagined half liter to establish a quarter-liter lower bound.
Look for:
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
Standards: 5.NF.A.1, 5.NF.A.2. Grade 5 alignment describes the mathematical work in this pack.
The tasks, worked examples, and teacher responses are original Fraction Classroom materials, version 2.0.0. The teaching approach draws on noticing the unit, moving between representations, and responding to student reasoning in the linked Illustrative Mathematics lesson. Its text and exercises are not reproduced here.