The Pacing Guide vs. the Item Analysis
Mr. Alvarez teaches fourth grade in a K–5 building of 520 students. He has 26 students. On the end-of-unit quiz on multi-digit multiplication, 9 students scored 90% or higher, 10 scored between 60% and 79%, and 7 scored below 50%. Item analysis shows that 6 of the 7 lowest scorers made the same error: when regrouping across a zero, they misalign partial products and shift place value by one column. The district pacing guide allots one reteach day before the next unit-division-begins Monday. At Thursday's grade-level team meeting, colleagues plan to move ahead on schedule, and the principal has said unit tests must stay on the district calendar.
1. What should Mr. Alvarez teach on Monday, and what evidence justifies that choice over a whole-class reteach day?
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A whole-class reteach misallocates time in both directions. The 9 high scorers do not need the lesson, and one day is not enough for the 7 students who hold a place-value misconception. The item analysis is the key evidence: 6 of 7 low scorers made the same alignment error, which signals a conceptual gap (partial products represent hundreds, tens, and ones), not carelessness.
A defensible plan:
- Whole-class mini-lesson (10–15 min): compare a correct and an incorrect partial-products model using an area model or base-ten blocks, so all students see why the second partial product shifts left.
- Small group, 2–3 days: the 7 students work with the area model, then connect it to the algorithm; exit ticket each day with items that include a zero in the multiplier.
- Independent task: the 10 middle students do mixed practice with a few zero-regrouping items plus error analysis.
- Enrichment: the 9 high scorers apply multiplication to multi-step problems.
One day of reteach for 26 students addresses no group well; differentiated days match the data.
2. The principal insists the district calendar be honored. How can Mr. Alvarez respond to legitimate pacing pressure without abandoning the data?
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Pacing addresses sequence, not uniform time for every student on every day. Mr. Alvarez can honor the calendar while still responding to the data:
- Compacting: keep the Monday start of division for the class, and embed the multiplication remediation inside the warm-up and small-group slot, since division depends on the same place-value and partial-product reasoning.
- Bring data, not preferences, to the team meeting: present the item analysis and the six matched error patterns. A shared error pattern is a strong argument for a brief, targeted adjustment rather than an open-ended delay.
- Set a reviewable checkpoint: promise that the 7 students will be re-probed on zero-regrouping items by Wednesday, so the adjustment is bounded and the team can see results.
- Document the decision: note the adjustment, rationale, and outcome so the choice is transparent if the principal or a coach asks.
This keeps the required test dates intact-the unit test still occurs on the district date-while changing what happens inside the days.
3. What formative evidence should Mr. Alvarez have in hand by Thursday's team meeting, and what would make him change course?
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He needs item-level, error-specific evidence, not an average. By Thursday he should have:
- A 3-item exit ticket containing one problem with a zero in the ones place of the multiplier, one with a zero in the tens place, and one standard problem, so he can separate alignment errors from general multiplication errors.
- Student work samples from the area-model group showing whether students can explain why the second partial product shifts.
- A quick oral check with 2–3 students: ask them to explain what 20 × 34 means in the model.
Change course if: the low group's errors persist on the same items after the area-model work (the misconception is deeper than one lesson); or if the middle group's errors also cluster on zero-regrouping (the problem is class-wide and a whole-class lesson is warranted after all).
Do not change course merely because students finish worksheets quickly; speed is not evidence of understanding of place value.