Compare a positive multiplier with 1 to predict whether a length shrinks, stays the same, or grows.
For a positive starting amount, factors below 1 shrink it, 1 preserves it, and factors above 1 enlarge it.
Materials: 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: Draw an original strip and label its length. Before multiplying, ask whether the factor calls for less than one copy, one copy, or more than one copy of that strip.
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: The product is less than 8 because it takes three quarters of the original positive amount.
Listen for this difficulty: Assuming multiplication always makes a number greater.
Try this response: Shade three out of four equal parts of a strip labeled 8.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The product is greater than 8 because 5/4 is more than one copy.
Listen for this difficulty: Assuming every fraction is below 1.
Try this response: Show 5/4 as 1 + 1/4 of the starting strip.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 6/6 = 1, so the product equals 7.
Listen for this difficulty: Judging a factor by its numerator instead of its value.
Try this response: Group six sixths into exactly one whole copy.
Look for:
2 · Model together
Use one now. Ask the learner to explain each step before revealing the next part of your drawing.
Result: The new length is 8 cm, less than 12 cm.
Listen for this difficulty: Interpreting a multiplier as an amount to add.
Try this response: Show two thirds of the original length rather than attaching an extra two-thirds-centimeter piece.
Look for:
Result: 9 cm, greater than 6 cm.
Listen for this difficulty: Treating the denominator as a command to make every product smaller.
Try this response: Represent three halves as one whole copy and one half copy.
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: It is less than 24 because 7/8 < 1 and the starting amount is positive.
Listen for this difficulty: Focusing on the whole number 24 while ignoring the scale factor.
Try this response: Ask whether seven eighths is a full copy of the original.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: It is greater than 24 because 9/8 > 1.
Listen for this difficulty: Treating any written fraction as a reduction.
Try this response: Rewrite nine eighths as one whole and one eighth.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 4/4, because it equals 1.
Listen for this difficulty: Choosing a factor by denominator rather than total value.
Try this response: Build the factor from fourth-sized pieces to see which makes exactly one copy.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: The result is smaller: 6 cm.
Listen for this difficulty: Adding 2/5 to 15 instead of taking part of 15.
Try this response: Divide the original length into five equal 3 cm parts and select two.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 4/3 × 18 is greater. It uses twice as many third-sized copies; the results are 12 and 24.
Listen for this difficulty: Comparing the common denominator alone.
Try this response: Hold the starting length constant and compare two thirds with four thirds.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: No. The factor is 2/3; 3/2 would enlarge the length to 13 1/2 cm.
Listen for this difficulty: Reversing the factor between new and original lengths.
Try this response: Compare the new length with the original: 6/9 = 2/3.
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 whole factor is 5/4, greater than 1, so it enlarges. An 8 cm length becomes 10 cm.
Listen for this difficulty: Ignoring the whole-number part of a mixed multiplier.
Try this response: Show one entire copy plus a quarter copy of the original.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Examples: 2/3, 1, and 4/3. For a starting amount of 0 the result stays 0, so the strict shrinking statement needs a positive starting amount.
Listen for this difficulty: Applying a strict size-change rule to zero.
Try this response: Draw zero length and ask how taking a part could make it shorter.
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.B.5.a, 5.NF.B.5.b. 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.