Use a benchmark, then justify

Answer or sample response: Below. 1/2 = 6/12 and 5/12 < 6/12.

Listen for this difficulty: Comparing numerator and denominator without a benchmark quantity.

Try this response: Split twelve equal parts into two groups of six.

Look for:

• Names 6/12 as one half.
• Places 5/12 below it.

Answer or sample response: 3/8 < 5/6 because 3/8 < 1/2 and 5/6 > 1/2.

Listen for this difficulty: Seeking a common denominator before considering useful landmarks.

Try this response: Show 4/8 and 3/6 as the half marks on equal wholes.

Look for:

• Locates both fractions relative to half.
• Uses the separating benchmark to compare.

Answer or sample response: No. Use distance from 1 or equivalent fractions; 2/3 < 3/4.

Listen for this difficulty: Treating a shared benchmark region as a complete comparison.

Try this response: Place both in the right half of a line and ask whether their order is yet known.

Look for:

• Recognizes the half benchmark is insufficient.
• Gives a justified comparison by another method.

Listen for this difficulty: Assuming an odd denominator prevents using one half.

Try this response: Double the selected count to check whether it fills the whole, without needing a whole-number half of 5.

Look for:

• Justifies the position of each fraction.
• Uses half as a separating benchmark.

Listen for this difficulty: Ordering the missing pieces in the same direction as the remaining amounts.

Try this response: Draw both fractions ending at 1 and compare the unfilled gaps.

Look for:

• Compares the gaps correctly.
• Reverses gap size to compare the remaining fractions.

Answer or sample response: 2/5 is below; 4/8 is equal; 5/6 is above.

Listen for this difficulty: Using numerator size alone across different denominators.

Try this response: Check whether doubling each numerator is less than, equal to, or greater than its denominator.

Look for:

• Places all three correctly.
• Explains at least one placement with equal parts or doubling.

Answer or sample response: 3/10 < 3/5, since 3/10 < 5/10 and two copies of 3/5 exceed 1.

Listen for this difficulty: Treating 10 as evidence that 3/10 is larger.

Try this response: Compare each fraction with its own half benchmark before comparing them.

Look for:

• Locates each on opposite sides of half.
• Writes the correct comparison.

Answer or sample response: 5/6 is closer because its missing 1/6 is smaller than 1/5.

Listen for this difficulty: Confusing the larger missing fraction with being closer.

Try this response: Complete both wholes with the missing piece and compare its size.

Look for:

• Chooses 5/6.
• Compares the gaps 1/5 and 1/6.

Answer or sample response: Being below half does not mean being equal. 1/3 = 2/6 < 2/5 because sixths are smaller than fifths of the same whole.

Listen for this difficulty: Treating benchmark categories as exact values.

Try this response: Draw two different points in the left half of a number line.

Look for:

• Rejects the equality.
• Uses an accurate drawing or equivalent fractions to show 1/3 < 2/5.

Answer or sample response: 1 separates them: 7/8 < 1 < 9/8.

Listen for this difficulty: Assuming comparison benchmarks stop at proper fractions.

Try this response: Mark 8/8 under 1 and locate each neighboring fraction.

Look for:

• Selects 1.
• Correctly orders both fractions around it.

Answer or sample response: For example, 2/5 is below and 3/5 is above because twice 2 is less than 5 and twice 3 is greater than 5.

Listen for this difficulty: Expecting one half to have an integer numerator over every denominator.

Try this response: Use two copies of each selected fraction to compare with one whole.

Look for:

• Provides valid fifths on opposite sides of half.
• Justifies both; other valid choices count.

Answer or sample response: The 3/5 bottle has more. 5/12 is below half and 3/5 is above half; the bottles must have equal capacities for this amount comparison.

Listen for this difficulty: Applying fraction order to amounts without checking the wholes.

Try this response: Mark the halfway fill on both identical bottle outlines.

Look for:

• Uses half correctly.
• States that equal capacities make the amount comparison valid.

Answer or sample response: 5/6 > 3/4. Both are above half, but 5/6 = 10/12 and 3/4 = 9/12.

Listen for this difficulty: Stopping after an inconclusive benchmark check.

Try this response: Ask for a finer scale within the upper half of the unit.

Look for:

• Explains the limitation of the half benchmark.
• Completes a correct common-denominator or distance comparison.