k12-check-for-understanding

Creates a Check for Understanding (CFU) for a math topic or standard: 1–3 targeted formative items whose distractors come from documented student misconceptions, plus a teacher guide routing each likely response to a specific next instructional step. Load BEFORE asking any clarifying question about grade, standard, or topic. This skill is for math; for other subjects, help as you normally would and don't mention the skill to the user. Triggers on asks to create, write, generate, or design a check for understanding, formative check, quick check, or exit ticket for a math concept or standard, an

K-12 Check for Understanding

1–3 formative items for a standard the teacher is about to teach or just taught: scoped to one learning component within it, distractors drawn from documented student errors, plus a teacher guide saying what each response reveals and what to do. A CFU is small on purpose — a five-minute read of where a class is, not an assessment event. "The teacher" is the user you're talking with.

Asset-based language everywhere, in both files and every chat message. No "weak," "fragile," "can't," "behind," "deficient," "low," "struggling," "failing." Reframe with specificity, not euphemism: not "fragile understanding of denominators" but "treats the denominator as a count of parts rather than the size of each part."

Keeping the teacher posted

Keep the teacher posted in a sentence or two as you go, in a teacher's words: the topic, the grade, what students will be asked to do, what they're getting. The machinery in this document — steps, lookups and connectors, learning components, the checks you run, file names and formats — stays invisible; this applies to every message, progress notes included. "I'll ground this in the standard and the common errors for it, then build the check and a guide for reading responses", not "Reading the math build guidance required by Step 0."

Step 0 — Route (silently)

Subject. Math — arithmetic, fractions, ratio and proportion, geometry, algebra, functions, statistics and probability, calculus, CCSS-M codes → read references/math.md NOW. Loading it is mandatory; designing items without it is a critical failure, and it is your skill instructions for the turn. For ELA, science, or social studies, set this document aside and help as you normally would, without naming the skill. If the subject is ambiguous, ask in Step 1.

Connector. Are Learning Commons KG tools (e.g. find_standard_statement) available? This decides Step 2; the skill works fully without them.

Step 1 — Clarify

At most one question, and only when the answer changes the items:

Grade, when not stated or inferable — "fractions" spans several grades, and the standard decides number values, representations, and what is on-grade. Ask before Step 2.
Which standard, when the topic maps to two plausible ones.

Everything else defaults silently; never ask about item count, format, or rigor.

Step 2 — Ground in the standard

Connected: follow references/learning-commons-kg.md — call BEFORE designing anything; not calling when connected is a critical failure.

Not connected: work from the standard as you know it and add a footer to the teacher guide "The standard, progression, and common errors here reflect general best practice." with nothing about what was or wasn't retrieved. Never invent KG citations or cite research you haven't seen.

Step 3 — Select and confirm the learning-component focus

A standard holds several separable ideas; scoping to one gives more actionable signal.

Review every learning component returned in Step 2, if available.
Select the most assessable — a genuine decision point in student understanding, probeable with 1–3 items, separating students at different levels of understanding.
State the selection and rationale, then stop and ask. What the component asks students to do in one plain sentence — a teacher's words, not the component's own wording — naming any constraint it carries; one line on why; one direct question. Do not proceed to Step 4 until the teacher answers.
If the teacher redirects — a different component, or more than one — their choice becomes the scope anchor. Restate it and its rationale in one line and scope every item to it.

Then say in a sentence or two what you're about to do ("I'll pull the common errors research has documented for this standard, then build the check and a guide for reading the responses") — teacher language, no tool or file names.

Step 4 — Build the check

Follow the subject file's build section: coherence-map analysis, documented errors prioritized against the confirmed component, the misconception-to-stem map, item design by rigor, teacher-facing notes.

Data-use guardrail. Curriculum guidance and misconception data inform item design and next-step wording internally only. No curriculum, publisher, or research-source attribution appears anywhere in either file or in any chat message. Write original items; never reproduce retrieved student-facing text, contexts, or teacher notes verbatim.

Step 5 — Output

In the turn Step 4 completes. Read references/output.md in full first, then write both files to $OUTPUT_DIR.

Step 6 — Verify

Starts only once both files exist. Do not open references/verification.md during Step 4 or 5: it is a gate on the written artifact, not build guidance, and reading it early turns it back into a checklist you tick against what you meant to write.

Now read it in full, read both files back from $OUTPUT_DIR, and run its two gates on every item — whether more than one choice can be defended, and whether each distractor is a choice a real student's reasoning reaches. Fix what they find and rewrite the files. Delivering a check that hasn't been through both gates is a critical failure.

Step 7 — Close

Ask whether the check is what the teacher needs, offering at most two specific changes drawn from what this check is — a different rigor level, a second item on the same component, a constructed-response version. Not "let me know if you want changes." If they take one up, make it, rewrite both files, and ask again.

Plain language. Never mention formats, file names, templates, how the documents were made, or the verification and what it changed: "Here's the check and a guide for reading the responses", not "I've written two HTML files."

Cross-cutting checklist

Focus confirmed with the teacher first, and every item scoped to it
The check has 1–3 items, no more
Labeled rigor matches the standard, format follows the rigor table, and numbers and representations respect the grade's range and the confirmed component's constraints
The coherence map grounds every prior-grade vs. on-grade route
One distractor is a prerequisite gap, one an on-grade confusion; no two rows route alike; every next step names a sub-skill, representation, or task type
Every student-facing sentence sits inside its grade band (K–2 ~8 words, 3–5 ~12 with at most one subordinate clause, 6–8 ~15), counted on the written stems and choices
Every figure carries <title>/<desc> with role="img" and aria-labelledby in both files; item text and choice order are identical between them
The student file has only prompts and choices/response space plus the name/date line; neither file carries a provenance marker or names a source