The Rounding Item Everyone Argues About
At the February grade-5 math meeting, the team reviews a district benchmark item: "Round 6.45 to the nearest tenth." The answer key marks 6.5. Across the four classes (n = 104), 46 students chose 6.5, 49 chose 6.4, and 9 chose something else. Ms. Alvarez's own two classes split almost identically. A colleague who looped up from sixth grade explains that her students were taught "round half to even" last winter, so an exact half goes to the even digit. The benchmark is used to place students into Tier 2 intervention for the spring, and rosters are due Friday. The grade-5 standard asks students to round decimals to any place using place value understanding. The team has 40 minutes to decide.
1. Is there a single defensible answer to this item as written? Explain what the item actually measures and why the class split is nearly even.
Read the worked answer
No. The item is convention-dependent, not reasoning-dependent.
- 6.4 and 6.5 are each exactly 0.05 away from 6.45, so the word "nearest" cannot choose between them. A tie-breaking rule has to.
- Two standard rules exist. "Five or more, round up" is the elementary convention. "Round half to even" is equally standard in science and statistics because it avoids upward bias when many values are rounded.
- The near-even split (46 vs. 49) across four different teachers is a signature of a convention artifact. A genuine misconception tends to concentrate on a small number of wrong answers, not to divide a population almost perfectly in half.
- What the standard actually targets is place-value reasoning: locating 6.45 between 6.4 and 6.5, recognizing the midpoint, and knowing a rule is needed at the midpoint. This item cannot detect any of that, because a student who reasons perfectly still has to guess which rule the key-writer used.
Conclusion: the item measures which convention a student was taught in a previous grade.
2. How should the team handle scoring and the intervention placement for the students who answered 6.4?
Read the worked answer
Do not place any student on the basis of this item.
- Score it as correct or void it. Both 6.4 and 6.5 reflect a defensible convention, so marking 6.4 wrong would punish students for a rule they were taught and would be indefensible if a parent appealed.
- Keep it out of the placement decision. Tier 2 rosters should rest on the remaining items and on other evidence (prior unit work, error patterns on non-tie rounding items). A single flawed item should not move 49 students into intervention.
- Audit the rest of the benchmark. If the item bank contains a tie-at-the-midpoint item, it likely contains others. Ask the assessment office how the key was set and whether the tie rule is stated in the item specifications.
- Document and escalate. Note the decision in the team minutes and send it to the district assessment coordinator before rosters are finalized, so the item is retired for next year rather than rediscovered.
- Preserve the instructional value. The disagreement is a usable discussion: have students argue from a number line which of 6.4 and 6.5 is closer, and surface that neither is.
3. Write one replacement item that assesses the same standard without depending on a tie-breaking convention, and justify the design.
Read the worked answer
Replacement (short answer, with explanation):
A number rounds to 6.5 when rounded to the nearest tenth. Give two different numbers that could be that number, and explain how you know there are more.
Why it works:
- The correct response set (anything from 6.45 up to but not including 6.55, under round-half-up) can only be produced by reasoning about the interval between tenths. Memorized digits do not generate it.
- It reports on the standard's actual demand (place value to any place) and yields diagnostic information: a student who answers 6.4 or 6.6 has a specific, addressable gap.
- It does not require the student to guess a rule at the midpoint, so it is fair to students taught either convention.
Acceptable alternatives:
- "Round 6.47 and 6.42 to the nearest tenth and explain how you decided." (Removes the tie, keeps procedural plus justification.)
- "A student says 6.45 is closer to 6.5 than to 6.4. Do you agree? Use a number line." (Turns the flaw into the assessed reasoning.)
Design rule for the item bank: never place an exact midpoint in a rounding stem unless the tie rule is printed in the stem.