MathOS Registry — Transfer Packs v0.1 (3-Skin Packs by Concept + Method)

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PAGE_START
PageID: EDUKATE::MATHOS::REG_TRANSFER_PACKS_01
Slug: /mathos-registry-transfer-packs-v0-1/
Title: MathOS Registry — Transfer Packs v0.1 (3-Skin Packs by Concept + Method)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Publish canonical 3-skin packs (same structure, different skin) as stable records
  • Each pack maps to:
    ConceptNode + MethodCorridor + Skill(TR)
  • Enables: weekly TR measurement, promotion gates, cohort dashboards
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

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BLOCK_01_DEFINITION_LOCK
TransferPack :=
a set of 3 questions sharing the same underlying structure but different surface skins
(equation / words / table / graph / diagram).

PackContract:

  • PackIDs never renamed
  • Packs are minimal and reusable
  • Each pack includes:
    structure_family_tag
    skins (3)
    answer key
    method corridor link
    common errors (E1–E6)
    retest rule

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REGISTRY::TRANSFER_PACKS (CORE SET v0.1)

PACK_START
PackID: EDUKATE::MATHOS::TPACK::LINEAR_FAMILY_01
ConceptNode: CONCEPT::EQUATIONS_LINEAR_01
MethodID: METHOD::LINEAR_ISOLATE_01
SkillTarget: SKILL::TR_01
structure_family_tag: “linear_family_ax_plus_b”
Skins:
Q1_equation:
2x + 5 = 17
Q2_brackets:
3(x – 2) = 12
Q3_words:
“A number doubled and increased by 5 gives 17. Find the number.”
AnswerKey:
x=6
CommonErrors:

  • E2 (parsing signs)
  • E3 (wrong method choice)
  • E1 (word->symbol meaning drift)
    RetestRule:
  • TR pass if correct_count >= 2/3
  • P2 stable if >= 3/3 twice in a row

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::PROPORTION_UNITRATE_01
ConceptNode: CONCEPT::ARITHMETIC_OPS_01
MethodID: METHOD::RATIO_TABLE_01
SkillTarget: SKILL::TR_01
structure_family_tag: “proportion_unit_rate”
Skins:
Q1_ratio:
“3 pens cost $7.50. Cost of 8 pens?”
Q2_speed:
“A car travels 180 km in 3 hours at constant speed. Distance in 8 hours?”
Q3_recipe:
“200 g flour makes 5 muffins. Flour for 8 muffins?”
AnswerKey:
Q1: $20.00
Q2: 480 km
Q3: 320 g
CommonErrors:

  • E3 (additive thinking)
  • E1 (wrong base quantity)
    RetestRule:
  • require unit-rate line shown

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::PERCENT_OF_01
ConceptNode: CONCEPT::ARITHMETIC_OPS_01
MethodID: METHOD::PERCENT_OF_01
SkillTarget: SKILL::TR_01
structure_family_tag: “percent_of_base”
Skins:
Q1_basic:
“15% of 80”
Q2_discount:
“$120 item discounted by 25%. New price?”
Q3_increase:
“Increase 60 by 10%”
AnswerKey:
Q1: 12
Q2: 90
Q3: 66
CommonErrors:

  • E1 (percent of what)
  • E4 (divide vs multiply)
    RetestRule:
  • require “p/100 × base” written once

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::FACTOR_ZERO_01
ConceptNode: CONCEPT::EQUIVALENCE_REWRITE_01
MethodID: METHOD::FACTOR_ZERO_01
SkillTarget: SKILL::TR_01
structure_family_tag: “zero_product”
Skins:
Q1_standard:
x^2 – 5x = 0
Q2_shifted:
(x – 3)(x + 2) = 0
Q3_story:
“The product of two numbers is 0. One number is x-3 and the other is x+2. Find x.”
AnswerKey:
Q1: x=0 or x=5
Q2: x=3 or x=-2
Q3: x=3 or x=-2
CommonErrors:

  • E4 illegal cancellation
  • E2 sign drift
    RetestRule:
  • must show factorization then two cases

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::LINEAR_MODEL_YMXC_01
ConceptNode: CONCEPT::GRAPHS_MODELS_01
MethodID: METHOD::MODEL_Y_MX_C_01
SkillTarget: SKILL::TR_01
structure_family_tag: “linear_model_fixed_plus_rate”
Skins:
Q1_words:
“Gym charges $30 membership plus $5 per visit. Write cost y after x visits.”
Q2_table:
“Table shows x=0 -> y=12, x=1 -> y=15. Find y in terms of x.”
Q3_graph:
“A line crosses y-axis at 8 and rises 2 for every 1 in x. Write equation.”
AnswerKey:
Q1: y = 5x + 30
Q2: y = 3x + 12
Q3: y = 2x + 8
CommonErrors:

  • E1 axes/units drift
  • E3 wrong identification of m/c
    RetestRule:
  • must label m and c with meaning (rate, fixed)

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::EV_SIMPLE_01
ConceptNode: CONCEPT::PROBABILITY_EXPECTATION_01
MethodID: METHOD::EV_EXPECTED_VALUE_01
SkillTarget: SKILL::TR_01
structure_family_tag: “expected_value_discrete”
Skins:
Q1_coin:
“Win $2 for heads, lose $1 for tails. Fair coin. Find EV.”
Q2_die:
“Win $6 if roll a 6, otherwise win $0. Find EV.”
Q3_bag:
“Bag: 3 red win $5, 2 blue win $0. Pick one. Find EV.”
AnswerKey:
Q1: (0.52)+(0.5-1)=0.5
Q2: (1/6)6=1 Q3: (3/5)5=3
CommonErrors:

  • E1 probability not normalized
  • E4 percent vs probability mismatch
    RetestRule:
  • must list outcomes and probabilities

PACK_END

PACK_START
PackID: EDUKATE::MATHOS::TPACK::SIM_TEMPLATE_01
ConceptNode: CONCEPT::SIMULATION_STATE_TRANSITION_01
MethodID: METHOD::SIM_TEMPLATE_01
SkillTarget: SKILL::MF_01
structure_family_tag: “simulation_schema”
Skins:
Q1_city_queue:
“Model a clinic queue: arrivals, service rate, waiting.”
Q2_budget:
“Model a monthly budget: income, fixed costs, variable costs, savings.”
Q3_exam_plan:
“Model a 2-week revision plan: tasks, time constraints, buffer.”
AnswerKey:

  • must produce state variables + transitions + constraints + objective + one stress case
    CommonErrors:
  • E1 undefined state variables
  • E3 wrong model class (no objective/constraints)
    RetestRule:
  • pass if all 5 components present + 1 stress test

PACK_END

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BLOCK_02_USE (how to deploy packs)
Z0_WEEKLY_PROTOCOL:

  • choose 1 pack/day (Mon–Thu)
  • Friday: mixed mini-pack (3 different structures; method-choice drill)
  • record TR per pack + top error type (E1–E6)

Z1_COHORT_PROTOCOL:

  • every class runs same pack weekly
  • publish TR distribution
  • repair dominant failure via corridor directory

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BLOCK_03_PROMOTION RULES (P1->P2 gates)
Gate_P2_TR:

  • TR >= 0.7 on 2 different packs
  • SML stable
    Gate_Load:
  • after Gate_P2_TR, enter timed ladder

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RELATED_PAGES
Links:

  • /mathos-registry-method-corridors-v0-1/
  • /mathos-registry-concept-nodes-v0-1/
  • /mathos-registry-skill-nodes-v0-1/
  • /mathos-fenceos-threshold-table-v0-1/
  • /math-transfer-test-same-structure-different-skin/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_PROOF_PATTERNS_01
slug: /mathos-registry-proof-patterns-v0-1/
(proof skeletons as corridors + audit checklist)

PAGE_END
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