Canonical Gymnasium Mathematics: Sek I Data / Chance Audit
Snapshot: 2026-04-05
Purpose:
- review the current canonical
Sek I Daten / Zufallinventory before more bundeslandwise widening - use already reviewed
HBandHHSek-I evidence to test whether the current canonical cuts are pedagogically stable - define the next canonical work packages for
Sek I Daten / Zufall
Scope
In scope:
- the canonical Sek-I data/chance topic surface in
curricula/DE/Gymnasium/canonical/DE_DEU_S_GYM_CANONICAL_MATHEMATIK.de.json- the already reviewed lower-secondary source and mapping evidence from
HBHHMVSHRPSNST
Out of scope:
- full bundesland completion
- direct canonical JSON refactoring in this step
- learner-facing composition views
Reviewed source evidence
Hamburg (HH)
Reviewed lower-secondary source anchors exist in three bands:
J6 Daten und ZufallJ8 Daten und ZufallJ10 Daten und Zufall
Observed signal:
HHconfirms that data/chance is a stable, visible lane across the whole Sek-I progression- current reviewed
HHevidence is still broad; it is strong enough for package validation, but not yet for fine atomic forcing
Schleswig-Holstein (SH)
Reviewed lower-secondary source and mapping evidence is now explicit enough for package validation:
Jahrgangsband 5/6: Daten und Zufall- statistische Erhebungen
- kombinatorische Fragestellungen
-
einstufige Zufallsexperimente
-
Jahrgangsband 7/8/9: Daten und Zufall - Haeufigkeit
- Wahrscheinlichkeit
- mehrstufige Zufallsexperimente
- beschreibende Statistik
- Spannweite, Quartile und Boxplots
- Datenverteilungen vergleichen und deuten
Observed signal:
SHvalidates thatD4is not just an appendix to general probability work, but a visible later Sek-I package of its ownSHalso stabilizes the split betweenD2,D3, andD4more clearly thanHBandHHalone- the early
5/6lane still keeps combinatorics adjacent to first data/chance work, soD5should remain an explicit open decision rather than being silently absorbed
Bremen (HB)
Reviewed lower-secondary data/chance corridors already exist as broad strips:
J5/6 Stochastik- lists
- diagrams
- means
-
first random experiments
-
J7/8 Stochastik - distributions
- Laplace
-
two-stage random experiments
-
J9 Stochastik - combinatorics
- four-field tables
Observed signal:
HBsupports a progression from early data routines toward probability models and then toward structured multi-step and conditional settingsHBstrongly suggests that combinatorics / four-field-table work should not be hidden inside a diffuse broad statistics package
Sachsen (SN)
Reviewed lower-secondary source and mapping evidence is now explicit in three later Sek-I lanes:
K8 Lernbereich 2 Zufallsversuche- Ereignisse und Laplace-Wahrscheinlichkeiten
- Baumdiagramme
- Simulationen
-
Abzaehlprobleme
-
K10 Lernbereich 2 Diskrete Zufallsgroessen - Wahrscheinlichkeitsverteilungen
- Stabdiagramme und Histogramme
- Wahrscheinlichkeiten mit
genau/mindestens/hoechstens k - Pfadregeln und Abzaehlverfahren
- Verteilungsfunktion
- Erwartungswert, Varianz, Standardabweichung
-
faire und unfaire Spiele
-
K9 Lernbereich 4 Auswerten von Daten - Modalwert, Median, arithmetisches Mittel
- Spannweite, Varianz, Standardabweichung
- Klassenbildung und Histogramme
- typische Fehler und Manipulationen in der Statistik
Observed signal:
SNnow also confirms the existingD2,D3, andD5surfaces with an explicit K8 chance-experiment stripSNadds a real later Sek-I random-variable strip on top of the already frozenD1-D5surfaceSNnow also adds a real later descriptive-statistics strip that sits cleanly on the existingD4surfaceSNnow also adds an earlier K7 data-display strip that still fits the same broadD4surface- the Sachsen K10 strip is still internally mixed between later probability structure, counting bridge, and descriptive-statistics adjacency
- the Sachsen K8 strip is internally mixed between first Laplace work, tree structures, simulation, and counting
- the Sachsen K9 strip is internally mixed between descriptive-statistics routine, histogram work, and critical-reading residue
- the Sachsen K7 strip is internally mixed between diagram forms and first critical reading of statistical data
- together this is strong enough for reviewed corridor mappings, but still not clean enough to force a separate visible canonical
D6package for discrete random variables or a separate visible critical-statistics package
Sachsen-Anhalt (ST)
Observed signal:
STnow contributes a first reviewed early lower-secondary data lane throughJG 5/6- the lane is still broad and splits only into data-display work and measures-of-data work
- both strips fit the existing descriptive-statistics surface
- this confirms that early Sachsen-Anhalt data work does not currently force a separate visible early diagram-reading or measures package
Mecklenburg-Vorpommern (MV)
Observed signal:
MVnow contributes a first reviewed early lower-secondary data/chance corridor on the explicitKlassen 5/6lane- the Mecklenburg-Vorpommern source separates
Statistische Erhebungeneinstufige Zufallsexperimente- this makes
MVa useful pressure test for whether the visible early data/chance surface can absorb both survey/display work and first Laplace-style probability work without forcing a separate early diagram or early-probability package MVnow contributes a first reviewed lower-secondary data/chance corridor on the explicitKlasse 9lane- the Mecklenburg-Vorpommern source separates
Haeufigkeiten, Mittelwerte und Streumassestatistische Erhebungen- this makes
MVa useful pressure test for whether the visibleD4descriptive-statistics surface can absorb both summary measures and survey-design/evaluation residue without forcing a separate survey or critical-statistics package MVnow also contributes a first reviewed later-probability corridor on the explicitKlasse 10lane- the Mecklenburg-Vorpommern source separates
Zufallsexperimente mit und ohne ZuruecklegenZufallsgroessen und Binomialverteilung- this confirms that the visible
D3surface can coexist with the frozen broadD1-D5surface for later random-variable residue without forcing a separate visibleD6package
Thueringen (TH)
Observed signal:
THnow contributes a first reviewed lower-secondary data/chance corridor on the explicitKlassenstufen 5/6lane- the Thueringen source separates
Daten erfassen und darstellenstatistische Kenngroessen und mit Zufall experimentieren- this makes
THa useful pressure test for whether the early data surface can coexist with a still-mixed early statistics/chance strip on the broad Sek-I data/chance surface without forcing either a separate early diagram package or a separate early-probability package THnow also contributes a first reviewed broadKlassenstufen 7/8data/chance corridor- the archived
7/8source still exposes only one sharedStochastikstrip - this confirms that the shared broad Sek-I data/chance surface can absorb a reviewed wide
7/8lane without forcing a sharper canonical split from source granularity alone THnow also contributes a first reviewed broadKlassenstufen 9/10data/chance corridor- the archived
9/10source still exposes only one sharedStochastikstrip - this confirms that the same shared broad later Sek-I data/chance surface can absorb a reviewed wide
9/10lane without forcing a sharper canonical split from source granularity alone
Current canonical data/chance inventory
The canonical graph is already materially seeded here.
Important existing package handles:
- early package
-
Fruehe Daten-, Zufalls- und Zaehlvorstellungen (Sek I) -
later package
-
Spaetere Daten-, Wahrscheinlichkeits- und Statistikvorstellungen (Sek I) -
descriptive-statistics package
Kenngroessen von Daten bestimmen und interpretieren-
Beschreibende Statistik mit Quartilen, Boxplots und Verteilungen (Sek I) -
probability / experiment packages
Laplace-Wahrscheinlichkeiten und relative HaeufigkeitenZusammengesetzte Zufallsexperimente modellieren und simulieren-
atoms for
Baumdiagramme,Pfadregeln, simulation -
top-level package
Daten und Zufall (Sek I)
Audit judgment
The canonical data/chance topic is not missing a foundation.
The main packaging decision is now materially stabilized: HB, HH, and especially SH support D1-D4 as a workable nationwide cut.
Main problem:
- the current top-level topic mixes
- early data routines,
- later probability,
- multi-stage experiment structure,
- and descriptive statistics without exposing the package boundaries clearly enough for state-by-state validation
This is therefore primarily a packaging-and-cut problem, not first a missing-content problem.
Findings
1. Early data routines are present but not visibly separated enough from later probability
The canonical graph already has:
- absolute / relative frequencies
- diagrams
- arithmetic mean
- first random experiments
This is good. But for topic-first steering, these should become a visibly own package:
- collecting, displaying, and interpreting data
- first random situations
2. Laplace / relative-frequency work is pedagogically real and should remain explicit
HB J7/8 clearly supports a package around:
- distributions
- Laplace
- first probability reasoning
The canonical graph already contains this material, but it sits partly spread across the early and later mixed package handles.
3. Multi-stage experiments are already a strong canonical unit
This part looks healthier:
Zusammengesetzte Zufallsexperimente modellieren und simulierenBaumdiagramme und Pfadregeln- simulation
This should stay an explicit later package.
4. Descriptive statistics is present, but its relation to the rest is too implicit
The canonical graph already includes:
- median
- quartiles
- boxplots
- comparing distributions
That is strong. But at the package level it is still not clear enough whether descriptive statistics is:
- just an appendix to probability
- or a full own later Sek-I subpackage
The reviewed state evidence points to the second reading.
5. Combinatorics / four-field-table work deserves an explicit decision
HB J9 gives an important signal:
- combinatorics
- four-field tables
This does not yet force a large new canonical wave, but it does require a packaging decision:
- either these stay inside the multi-stage / conditional package
- or they become a visible subpackage of later probability structure
That decision should be made explicitly, not by drift.
Proposed canonical work packages
For Sek I Daten / Zufall, use these work packages:
D1 Early data routines and first random experiments- collecting data
- tables / diagrams
- absolute / relative frequencies
- arithmetic mean
-
first simple random situations
-
D2 Laplace ideas and probability from frequencies - probability notions
- relative frequency as empirical bridge
-
Laplace settings
-
D3 Multi-stage experiments, tree diagrams, conditional structure - tree diagrams
- path rules
- simulations
-
four-field-table adjacency
-
D4 Descriptive statistics and data comparison - median
- quartiles
- boxplots
-
compare distributions
-
D5 Combinatorics / structured counting bridge - only if the reviewed state evidence shows this repeatedly enough
- otherwise keep it attached to
D3
Recommendation
Do not widen more bundesland mappings on Sek-I data/chance before one canonical pass answers these questions:
- Should
D1become a clearly visible own canonical subcluster? - Should
D4 descriptive statisticsbecome a more explicit later subcluster? - Should combinatorics / four-field-table work remain inside
D3, or should there be a visibleD5bridge package?
Recommended next concrete step
Run one canonical design step only on:
Sachsen K10 random-variable and K9 descriptive-statistics corridors connected (2026-04-03)
SN K10 Lernbereich 2 Diskrete Zufallsgroessennow points to the broad visibleDaten und Zufall (Sek I)surface- the split Sachsen source strips there now separate
- distributions of discrete random variables,
- event probabilities with path rules / counting procedures / distribution function,
- expected value / variance / standard deviation / fair games
SN K9 Lernbereich 4 Auswerten von Datennow also points to the visibleD4descriptive-statistics surfaceSN K7 Lernbereich 4 Vernetzung: Darstellen von Datennow also points to the visibleD4descriptive-statistics surface- the split Sachsen source strips there now separate
- Lageparameter,
- Streuungsmasse und Histogramme,
- kritische Beurteilung statistischer Darstellungen
- the earlier Sachsen K7 strip intentionally stays broad on the same
D4surface instead of forcing a separate visible diagram-reading package - the later probability strips intentionally stay on broad existing
D3andD4-adjacent package targets - the later descriptive-statistics strips intentionally stay on broad existing
D4targets instead of forcing a new visible histogram or manipulation package -
together this confirms reviewed late-Sek-I residue, but still does not justify a new visible canonical random-variable package beyond
D1-D5 -
D1 Early data routines and first random experiments D2 Laplace ideas and probability from frequenciesD3 Multi-stage experiments, tree diagrams, conditional structureD4 Descriptive statistics and data comparison
Why this cut:
HBandHHalready provide enough reviewed evidence for the broad progression- the package decision matters more right now than adding lots of new atoms
- it keeps combinatorics / four-field-table work open as an explicit follow-up decision instead of forcing it too early
Exit criteria for this audit
This topic audit is complete when:
- the canonical subpackage boundaries above are either accepted or revised
- the canonical graph has a stable Sek-I data/chance packaging
- reviewed
HBandHHevidence can be described as aligned to the revised packaging or intentionally broader because of source granularity - it is clear whether combinatorics / four-field-table work stays inside
D3or deserves a visibleD5package - at least one reviewed third-state lane beyond
HBandHHconfirms whetherD4really behaves like an explicit later package
Design step executed (2026-04-01)
The canonical packaging step for Sek I Daten / Zufall is now executed.
Accepted package cut:
D1=Fruehe Datenroutinen, Haeufigkeiten und Datendeutung (Sek I)D2=Laplace-Vorstellungen und Wahrscheinlichkeit aus Haeufigkeiten (Sek I)D3=Mehrstufige Zufallsexperimente, Baumdiagramme und bedingte Struktur (Sek I)D4=Beschreibende Statistik und Datenvergleich (Sek I)
What changed in the canonical decision:
- the broad mixed
J6 Prozentrechnung und Datencorridor is no longer pulled wholesale into the top-level data/chance package - instead, the data-facing early atoms now sit in an explicit
D1package D2is now a visible probability bridge from frequencies to Laplace settingsD3explicitly carries tree diagrams, simulation, and for now also the adjacency to combined events / four-field structuresD4is now an explicit descriptive-statistics package instead of an implicit appendix
Explicit non-decision kept open:
D5(Zaehlen / Kombinatorikas its own visible package) is still intentionally open- reviewed
HB J9evidence is strong enough to keep that question alive, but not yet strong enough to force a separate package in this step
Resulting next step:
- realign reviewed
HBandHHlower-secondary data/chance mappings toD1-D4 - only after that decide whether later reviewed state evidence forces an explicit
D5
Third-state validation executed (2026-04-01)
SH now serves as the first external validation lane beyond HB and HH.
What SH confirms:
D1remains a legitimate early package, even when simple combinatorics sits adjacent to first data/chance workD2andD3can stay separated from later descriptive-statistics workD4is pedagogically real as a visible later package because the source lane exposesbeschreibende StatistikSpannweite, Quartile und BoxplotsDatenverteilungen vergleichen und deuten
Resulting topic status:
D1-D4are now not only canonical design decisions but also externally validated by a third reviewed state lane- the last package decision
D5(Zaehlen / Kombinatorikas a separate visible bridge) is now executed
Recommended next step after this validation:
- treat
Sek I Daten / Zufallas canonically stable enough to freeze further package churn - use additional state lanes only for mapping and residue control, not to reopen the
D1-D5cut without strong contrary evidence
D5 decision executed (2026-04-01)
The open D5 question is now resolved in favour of a visible package.
Why this decision is now justified:
HBcontributes a reviewed later Sek-I signal viaJ9 Stochastik: Kombinatorik und VierfeldertafelnSHkeeps combinatorial questions explicitly adjacent to early data/chance work inJahrgangsband 5/6- the Hessen lower-secondary source lane contributes an explicit later atom
Abzaehlstrategien nutzenwith direct probability use
Canonical consequence:
D5is now visible asZaehlen, Kombinatorik und Wahrscheinlichkeitsbruecken (Sek I)- the package currently bundles
- the existing early atom for simple counting principles
- one later bridge atom for combinatorial reasoning in probability situations
D3keeps four-field tables, conditional structure, and multi-step random experimentsD5does not absorb thoseD3structures; it stays a counting/probability bridge
Result:
Sek I Daten / Zufallnow has a stable visibleD1-D5package surface- the topic should now be treated as materially packaged, with later work focused on mapping quality rather than package invention
Sachsen-Anhalt JG 5/6 data corridor connected (2026-04-03)
- the ST
JG 5/6stripsErfassen, Darstellen und Auswerten von DatenandKenngroessen von Datennow both point to the existing descriptive-statistics surface - the reviewed ST lane therefore confirms the broad early
D4packaging without reopening the current Sek-I data/chance cut
Sachsen-Anhalt JG 7/8 chance corridor connected (2026-04-03)
- the ST
JG 7/8stripZufaellige Ereignisse, Haeufigkeiten, Wahrscheinlichkeitennow points to the existing Laplace / frequency bridge - the ST
JG 7/8stripMehrstufige Zufallsversuche und Wahrscheinlichkeitennow points to the visible multi-step random-experiment surface - the reviewed ST lane therefore confirms the current
D2/D3split without forcing a new mixed early-probability package
Sachsen-Anhalt JG 10 random-variables corridor connected (2026-04-03)
- the ST
JG10stripZufallsgroessennow points to the broad visibleDaten und Zufall (Sek I)surface - the reviewed ST lane therefore confirms that later Sek-I random-variable residue can stay on the frozen
D1-D5package surface without forcing a separate visibleD6package
Sachsen-Anhalt JG 9 frequency-distributions corridor connected (2026-04-03)
- the ST
JG9stripHaeufigkeitsverteilungennow points to the visibleD4descriptive-statistics surface - the reviewed ST lane therefore confirms that later Sek-I distribution-comparison residue can stay on the frozen descriptive-statistics package without forcing a separate visible histogram or frequency-distribution package
Rheinland-Pfalz Klassenstufen 9 und 10 data/chance corridor connected (2026-04-03)
- the broad RP
Klassenstufen 9 und 10: Daten und Zufallanchor now carries a reviewed split intoVierfeldertafeln, zweistufige ZufallsexperimenteandWahrscheinlichkeiten durch Simulationen - the first strip points to the visible multi-stage-experiment surface
- the second strip points to the visible probability-from-frequencies bridge
- the RP lane therefore confirms the visible Sek-I chance surface without forcing a new visible later random-variable package
Saarland Klassenstufe 7 data/chance corridor connected (2026-04-04)
- the broad SL
Klassenstufe 7: Daten und Zufallanchor now carries a first reviewed corridor on the shared Sek-I data/chance surface - the current Saarland grade-7 source still exposes only one shared data/chance strip
- this confirms that the shared broad Sek-I data/chance surface can absorb an explicit reviewed class-7 lane without forcing a sharper state-local split from source granularity alone
Saarland Klassenstufe 8 data/chance corridor connected (2026-04-04)
- the broad SL
Klassenstufe 8: Daten und Zufallanchor now carries a first reviewed corridor on the shared Sek-I data/chance surface - the current Saarland grade-8 source still exposes only one shared data/chance strip
- this confirms the shared broad Sek-I data/chance surface can absorb an explicit reviewed class-8 lane without forcing a sharper state-local split
Saarland Klassenstufe 9 data/chance corridor connected (2026-04-04)
- the broad SL
Klassenstufe 9: Daten und Zufallanchor now carries a first reviewed corridor on the shared Sek-I data/chance surface - the current Saarland grade-9 source still exposes only one shared data/chance strip
- this confirms the shared broad Sek-I data/chance surface can absorb an explicit reviewed class-9 lane without forcing a sharper state-local split
Saarland Klassenstufe 10 data/chance corridor connected (2026-04-04)
- the broad SL
Klassenstufe 10: Daten und Zufallanchor now carries a first reviewed corridor on the shared Sek-I data/chance surface - the current Saarland grade-10 source still exposes only one shared data/chance strip
- this confirms the shared Sek-I data/chance surface can absorb an explicit reviewed grade-10 lane without forcing a sharper state-local split
Additional reviewed nationwide evidence (BW, BY, SH)
Baden-Wuerttemberg (BW)
Observed signal:
- the reviewed Baden-Wuerttemberg lower-secondary lane already carries explicit
3.1.5,3.2.5, and3.3.5widening steps on the shared Sek-I data/chance spine 3.1.5 Daten und Zufallnow bridges reviewed early data leaves for frequencies, arithmetic mean, and critical diagram reading3.2.5 Daten und Zufallnow bridges reviewed later descriptive-statistics and Laplace work3.3.5 Daten und Zufallnow bridges reviewed later conditional-probability, four-field, stochastic-independence, random-variable, and binomial surfaces- together this confirms that the visible
D1-D5surface can absorb the Baden-Wuerttemberg lane without forcing another package split
Bayern (BY)
Observed signal:
- the reviewed Bavaria retained gymnasium lane now already reaches the visible Sek-I data/chance surface across
M5-M10 - the active BY mappings now cover simple counting, frequencies, arithmetic mean, descriptive statistics with quartiles and boxplots, Laplace situations, linked events with Vierfelderstrukturen, tree diagrams, simulation, and conditional-structure work
- together this keeps Bavaria on the current
D1-D5package surface instead of forcing a new nationwide data/chance pass
Schleswig-Holstein (SH)
Observed signal:
- Schleswig-Holstein no longer only serves as the original third-state validation lane; the lower-secondary source snapshot is now fully refined across
5/6and7/8/9onDaten und Zufall - the active SH mappings now cover early statistical surveys, simple combinatorics, one-stage random experiments, frequencies, probability, multi-stage random experiments, quartiles / boxplots, and data-comparison work
- there are now no remaining unmapped SH Sek-I source atoms or source clusters in the active data/chance-owning lane; the remaining mismatch is broad-source residue, not a missing canonical package
Nordrhein-Westfalen lower-secondary data/chance corridor connected (2026-04-05)
Observed signal:
- the active Nordrhein-Westfalen lower-secondary source snapshot now also carries explicit reviewed data/chance corridors from
2.3,2.4.1, and2.4.2 - the mapped NRW lower-secondary lane now covers early statistical data collection and representation, first measures of data, one- and two-stage random experiments, Laplace-based probability, simulation, critical reading of statistical representations, conditional probability, stochastic independence, and combinatorics
- the compiled canonical applicability now keeps
DE-NWon the sharedDaten und Zufall (Sek I)root together with the visibleD1,D2,D3,D4, andD5package handles - the Nordrhein-Westfalen data/chance cell can therefore now be treated as resolved on topic level
Berlin / Brandenburg lower-secondary data/chance corridors connected (2026-04-05)
Observed signal:
- the active shared BE/BB lower-secondary source snapshots now also carry explicit reviewed data/chance corridors from the Sek-I
Daten und Zufallsurface on NiveaustufenE-H - the mapped Berlin and Brandenburg lower-secondary lanes now cover statistical surveys and samples, diagram work with frequencies and simple data measures, boxplots / histograms / descriptive-statistics reading, survey critique and manipulation detection, Laplace-oriented probability reasoning, tree/vierfelder-based conditional structure, and explicit combinatorial probability bridges
- the compiled canonical applicability can therefore keep both
DE-BEandDE-BBon the sharedDaten und Zufall (Sek I)root together with the visibleD1,D2,D3,D4, andD5package handles - the Berlin and Brandenburg data/chance cells can therefore now be treated as resolved on topic level
Niedersachsen lower-secondary data/chance corridor connected (2026-04-05)
Observed signal:
- the active Niedersachsen lower-secondary source snapshot now also carries an explicit reviewed data/chance corridor from the five real Lernbereiche
Planung und Durchfuehrung statistischer Erhebungen,Masszahlen statistischer Erhebungen,Wahrscheinlichkeit,Ein- und mehrstufige Zufallsversuche, andBaumdiagramme und Vierfeldertafeln - the mapped Niedersachsen lower-secondary lane now covers survey planning and data preparation, chart/frequency work, simple descriptive-statistics measures, probability as a model of relative frequencies, Laplace reasoning, simulation, multi-stage tree-diagram work, and vierfelder-linked-event interpretation
- the compiled canonical applicability can therefore keep
DE-NIon the sharedDaten und Zufall (Sek I)root together with the visibleD1,D2,D3, andD4package handles, while the NI source still does not force a separate new canonical package beyond the frozenD1-D5cut - the Niedersachsen data/chance cell can therefore now be treated as resolved on topic level
Coverage checkpoint (2026-04-05)
NInow joinsBE,BB,BW,BY,NW, andSHtogether with the already reviewedHB,HH,HE,MV,RP,SL,SN,ST, andTHlanes as resolved against the frozenD1-D5package surface- the nationwide data/chance row is therefore fully resolved once across all
16states and is no longer blocked by package design or by state-lane breadth debt - the next nationwide math move should therefore no longer be another Sek-I data/chance sweep; it should shift to applicability, learner-facing scope stabilization, and the broader
P6/F6cutover work