The Quiz That Says Two Different Things
Mr. Alvarez teaches four sections of seventh-grade mathematics (26 students each) and has just finished a 12-item quiz on proportional reasoning. Eight items require setting up and solving a proportion from given numbers; four are short word problems in which students must first decide that a proportion applies. Class results: 78% overall, but 41% on the four word problems. Three students - Jayden (92%), Priya (88%), and Marcus (75%) - each missed three of the four word problems. Elena, a recently arrived multilingual learner, scored 50% but 83% when the same items were read aloud to her. The next unit, scale drawings, assumes students can build proportions from context. Department policy requires a common summative assessment in nine days.
1. What does the item-level pattern tell you about whether the class is ready for the scale drawings unit, and what should happen in the nine days before the common assessment?
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Run the arithmetic before drawing a conclusion. Average items correct per student = 0.78 × 12 = 9.4. Average correct on the four application items = 0.41 × 4 = 1.6. That leaves 9.4 − 1.6 = 7.8 out of 8 procedural items - roughly 97%.
- The 78% is a blend of near-ceiling procedural fluency and weak transfer. It is not a class at 78% mastery of the standard.
- Jayden, Priya, and Marcus show the same signature: they execute an algorithm when told to use it, but do not recognize when a proportional relationship applies.
- Scale drawings requires exactly the missing skill - building a proportion from a context. The gap is a prerequisite, not enrichment.
Implication: do not simply move on, and do not re-teach the algorithm. Spend the nine days on recognizing and representing proportional relationships.
Caveat before you act: 12 items is a small sample. Check whether the four word problems share a feature (for example, all require distinguishing additive from multiplicative reasoning) before concluding the class has a general transfer problem rather than one item-type problem.
2. How should Elena's two scores be used, and what must be verified before either score affects her grade or placement?
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The pattern - 50% under standard administration, 83% with read-aloud - is a reading-demand signal, not evidence that her proportional reasoning is weak.
What it can support right now: instruction. If she solves the problems when the text is read to her, the barrier is English text, and she should get read-aloud during practice and small-group work.
What must be verified before grades or placement:
- Is read-aloud a documented accommodation on a 504 plan, IEP, or EL plan? If yes, administer and grade with it and record the accommodation on the answer document.
- Is read-aloud permitted on the district's common assessment? If not, her score on that instrument measures reading as well as mathematics and must be interpreted, not used alone to place her.
- Is the barrier English proficiency or a disability? One administration in each condition is not enough. Gather a second parallel set, confirm her language of instruction, and consult the EL coordinator before anyone labels the pattern.
Documentation rule: record both scores with the condition of administration. Never average them, and never report only the higher one.
3. Design the three highest-leverage instructional moves for the nine days and state what evidence would tell you they worked.
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Prioritize tasks that force students to decide, not compute.
- Classification sets (Days 1–2). Pairs of situations, some proportional and some additive; students sort and justify. Exit ticket: three situations, identify the proportional one and explain. Criterion: 80% of students justify at least 2 of 3 correctly.
- Faded worked examples with double number lines and ratio tables (Days 3–5). Show a fully worked model, then a partially completed one, then a bare problem. Track Jayden, Priya, and Marcus at each stage - they need the represent-then-solve sequence, not more drill.
- Error analysis of the most common wrong answer (Days 6–7). Take the four application items, give the class the most frequent incorrect response, and ask what reasoning would produce it.
Evidence of success: on a 4-item parallel set, at least 75% of students set up the proportion correctly on 3 of 4 items, and each of the three target students sets up at least 2 of 4 without prompting.
If the threshold is missed by Day 7: still administer the common assessment on schedule, but plan a post-assessment reteach and bring the parallel-set data to the next team meeting rather than declaring the unit finished.