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, and on implicit signals like "I need to see who got it before I move on." Not a quiz, test, or practice set — a CFU is read for what it reveals, not scored, so a numbered quiz or a bare answer key is a different job. Does not create a lesson (k12-lesson-plan-creation, which brings its own exit ticket), tier one (k12-lesson-differentiation), or prepare a teacher to teach one (k12-lesson-prep).

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Adapts an existing K-12 lesson (math, ELA, science, or social studies) for students at different proficiency levels (below / at / above grade level). Load this skill BEFORE asking the teacher any clarifying question about the lesson, tiers, or student levels. Triggers on explicit asks to differentiate, tier, or scaffold a lesson, and on implicit signals like "my students are at different levels". Produces 1 teacher-facing differentiation plan + 3 student-ready tier documents as editable, printable documents in a single output turn (shared content is written once, so tiers cannot drift). Uses the Learning Commons Knowledge Graph when connected; works without it. This skill adapts a lesson the teacher brings or names. Not for creating a new lesson from scratch — a new-lesson request that asks for differentiated or leveled materials is k12-lesson-plan-creation's job, one package. Not for grading, rubrics, assessment feedback, or quizzes.

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Creates a lesson plan, student-facing materials, and observation template. Load this skill BEFORE asking the teacher any clarifying question about grade, subject, topic, standard, or timing. Use when a K-12 teacher needs a math, ELA, science, or social studies lesson built from scratch — even if grade, subject, or topic isn't yet stated. Do NOT load for grading, a rubric, assessment feedback, a quiz, or a standards lookup — answer those directly. Triggers on explicit requests (lesson plan, mini-lesson, unit plan, daily plan) and implicit teacher intent: "I'm teaching long division to 5th graders," "need to teach photosynthesis tomorrow." Core signal: teacher needs new instructional content created. A new lesson that asks for differentiated, tiered, or leveled materials is still ONE planning request — this skill produces those materials inside the lesson package; do not also invoke k12-lesson-differentiation. Not for differentiating an existing lesson (use k12-lesson-differentiation) or passage rewrites.

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