Repartition shaded strips to explain why equivalent fractions multiply both counts by the same factor.
Equivalent fractions count the same amount using different-sized equal parts.
Materials: Paper strips; Pencil and ruler.
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: Shade first, then draw new partition lines without changing the shaded boundary. Count what happened to both the shaded pieces and all pieces in the whole.
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: 4/6. The amount stays fixed while both counts double.
Listen for this difficulty: Doubling the denominator but leaving the numerator unchanged.
Try this response: Split both shaded thirds as well as the unshaded third, then recount.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 4/10. Both numerator and denominator are multiplied by 2.
Listen for this difficulty: Adding the same number to both terms preserves value.
Try this response: Compare the shaded boundaries of two same-sized strips.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 9/12. Each fourth was split into three equal pieces.
Listen for this difficulty: Adding 8 to both terms because 4 + 8 = 12.
Try this response: Draw three small pieces inside each fourth and count the shaded ones.
Look for:
2 · Model together
Use one now. Ask the learner to explain each step before revealing the next part of your drawing.
Result: Each third becomes four twelfths; two shaded thirds become eight shaded twelfths.
Listen for this difficulty: Changing fraction labels without connecting them to unchanged area.
Try this response: Keep the original shaded boundary visible while adding the new lines.
Look for:
Result: 6/8 = 3/4. Group all eight eighths in pairs, not only the shaded six.
Listen for this difficulty: Regrouping the shaded pieces while retaining the old total count.
Try this response: Circle pairs throughout the entire strip, including the unshaded region.
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: 6/8.
Listen for this difficulty: Leaving the shaded count as 3.
Try this response: Count the two smaller pieces in each of the three shaded fourths.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 4/12, using a factor of 4.
Listen for this difficulty: Using different factors for numerator and denominator.
Try this response: Ask how many smaller pieces replace each original third.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 1/3 = 2/6. Splitting each third in half creates sixths.
Listen for this difficulty: Adding one to numerator and denominator.
Try this response: Draw thirds and halves on equal strips to expose the changed amount.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: 2/3.
Listen for this difficulty: Dividing only the numerator when regrouping.
Try this response: Mark three groups of four across the whole and count the two shaded groups.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Yes. Both equal 1/2.
Listen for this difficulty: Believing equivalence requires one numerator to be an integer multiple of the other.
Try this response: Group each strip into two equal regions and compare the shaded halves.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Examples: 4/6 by multiplying both counts by 2, and 8/12 by multiplying both by 4.
Listen for this difficulty: Changing only the denominator to generate new names.
Try this response: Ask for the same split factor in every original third.
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: 9/12 cup, because each fourth contains three twelfths.
Listen for this difficulty: Treating a finer scale as a different amount.
Try this response: Partition each fourth of a drawn cup scale into three intervals.
Look for:
Explain with a drawing, objects, or words.
Answer or sample response: Adding 2 does not preserve the fraction. 2/3 = 4/6.
Listen for this difficulty: Assuming an equal additive change preserves a ratio.
Try this response: Split every third into two sixths and count both the shaded and total pieces.
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.A.1. 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.