Only the real gaps — never a topic already demonstrated.

6 · Bridge flow

Current knowledge → target curriculum → gap → prerequisites → bridge topics → practice → retention check.

1. Current knowledge

   From the learner's own Learning Memory (fictional example): foundational arithmetic RETAINED · percentages RETAINED · fractions DEMONSTRATED · linear equations PRACTISING · Geometry (triangle basics) INTRODUCED.

2. Target curriculum

   Germany → Mecklenburg-Vorpommern → Gymnasium → Klasse 7 → Mathematik, under the Sekundarbereich I Rahmenplan family (see curriculum identity). One subject, not split into Algebra/Geometry — the target groups what the learner currently studies as two subjects into one.

3. Gap analysis

   Using the Compare mapping: foundational arithmetic is EQUIVALENT (no gap). Fractions, percentages and linear equations are NOT VERIFIED at the topic level — treated cautiously, not assumed safe to skip. Geometry is DIFFERENT DEPTH: MV expects it integrated within Mathematik, not as a separate subject the learner is used to studying on its own timetable line.

4. Prerequisites

   What the bridge topics below actually need: confident fraction and percentage arithmetic (already RETAINED / DEMONSTRATED — reused, not re-taught) and comfort moving between "Geometry as its own subject" and "geometry as part of one combined subject."

5. Bridge topics

   Only two real bridge items follow from the gap analysis: (1) confirm linear-equations fluency under MV's combined-subject pacing, since it is still PRACTISING, not yet DEMONSTRATED; (2) a short orientation to how Mathematik integrates geometry alongside algebra, rather than a full geometry re-teach.

   ✓ Percentages — already RETAINED, not repeated ✓ Foundational arithmetic — EQUIVALENT, not repeated

6. Practice

   The same try-yourself mechanism already live on the Mathematics demo — checked on-device by fixed rules, not a real AI grading call.

7. Retention check

   A later, separate check — not immediately after a correct practice answer — before linear equations could move from PRACTISING to DEMONSTRATED to (eventually) RETAINED. See the Learning Memory state model this pilot shares vocabulary with (concept only, not deployed here — see compatibility).

The rule this flow demonstrates concretely: a learner is never made to repeat a topic already DEMONSTRATED or RETAINED, on either curriculum.

8 · Language Bridge

One mathematical fact. Three languages. The maths never changes.

The same fraction example already live on the Mathematics demo — explained once, with the term introduced alongside in both curricula's language.

6 ÷ ½ = 12

"How many halves fit into 6 whole ones?" — the explanation can stay in the learner's preferred language while the target-curriculum term is introduced next to it:

6 ÷ ½ = 12 whether it is discussed as "дріб" or "der Bruch". Translation changes the label, never the mathematical truth underneath it.