Exchange one whole for fractional parts, keep the total value, and explain mixed-number subtraction with same denominators.
Regrouping changes the form of a mixed number without changing its value.
Materials: Three equal paper strips; Pencil.
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: Keep a visible trade: cross out one whole strip only after replacing it with all of its fractional parts. Read the old and new amounts aloud as equal quantities.
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: 1 5/4. One whole became 4/4, which joins the existing 1/4.
Listen for this difficulty: Adding a whole to the fractional part without decreasing the whole-number count.
Try this response: Exchange one complete strip for four fourth-sized pieces.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Subtraction order cannot be reversed to avoid regrouping. 2 1/5 = 1 6/5, so the difference is 1 3/5.
Listen for this difficulty: Taking the positive difference of fractional numerators regardless of order.
Try this response: Start at 2 1/5 on a line and move left three fifths; the result must be below 2 1/5.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 2 4/4, because 4/4 is exactly one whole.
Listen for this difficulty: Trading a whole for one fewer part than the denominator.
Try this response: Reassemble four fourths into one full strip.
Look for:
2 · Model together
Use one now. Ask the learner to explain each step before revealing the next part of your drawing.
Result: 1 1/2, or 1 2/4.
Listen for this difficulty: Keeping three wholes after adding four fourths.
Try this response: Record the trade as an equality before doing any subtraction.
Look for:
Result: 1 1/6.
Listen for this difficulty: Treating the absent fraction in 2 as 0/6 and subtracting in reverse.
Try this response: Physically replace a whole with six equal parts before removing any.
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: 3 7/5.
Listen for this difficulty: Changing the whole count without preserving total value.
Try this response: Trade one of the four wholes for five fifths.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 1 2/3; 2 1/3 = 1 4/3.
Listen for this difficulty: Subtracting 1 from 2 in the fractional part to get a positive result.
Try this response: Show why taking away two thirds crosses below 2.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 2 1/8; 2 1/8 + 7/8 = 3.
Listen for this difficulty: Trading one whole for seven eighths instead of eight eighths.
Try this response: Use eight equal eighths for the traded whole, then remove seven.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: No. Five sixths can supply one sixth directly; the difference is 2 4/6 = 2 2/3.
Listen for this difficulty: Regrouping automatically without inspecting the fractional parts.
Try this response: Compare the available and required sixths before touching the wholes.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The original 1/4 was lost. The correct trade is 5 1/4 = 4 5/4.
Listen for this difficulty: Replacing rather than adding to the existing fractional part.
Try this response: Place the old fourth beside the four fourths received in the trade.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 1 1/2, or 1 4/8. Regroup 3 1/8 as 2 9/8 and subtract 1 5/8.
Listen for this difficulty: Ignoring the whole consumed when fractional parts cross one.
Try this response: Use the missing addend as a distance from 1 5/8 to 3 1/8.
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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: 1 1/3 meters remain. 4 1/6 = 3 7/6, so subtracting 2 5/6 leaves 1 2/6. The cut is between 2 1/6 and 3 1/6 meters, so the remainder is between 1 and 2.
Listen for this difficulty: Reversing the fractional subtraction and keeping too many wholes.
Try this response: Compare the cut with the lengths that would leave exactly 1 or exactly 2 meters.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Example: 2 1/4 − 3/4 = 1 1/2. Trade to 1 5/4 before removing 3/4.
Listen for this difficulty: Choosing a subtrahend that does not actually require a trade.
Try this response: Ask whether the fractional amount being removed exceeds the available one fourth.
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: 4.NF.B.3.c. Grade 4 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.