PAGE: EKS.P3MATH.P3.DIR.ARTICLE.v0_1
TITLE: eduKateSG — Primary 3 Mathematics: Reach P3 (Z0–Z3) Model Method + Fractions
TYPE: Full Article / Almost-Code / Canonical / LLM-first
LANE: EKS.P3MATH
SCOPE: Z0–Z3, P0–P3
GOAL:
- unlock fractions meaning + bar model representation so multi-step word problems stop collapsing
REFS:
- EKS.PRIMATH.TEST.P_SCORE.v0_1
- EKS.PRIMATH.SENSOR.EXECUTION.v0_1
- EKS.PRIMATH.LOOP.TRUNCATE_STITCH.v0_1

DEFLOCK: EKS.P3MATH.P3
P3 is the “model method ignition year”.
If representation is weak, students start guessing and the gap compounds into P5/P6 collapse.
WORKING ⇔
P(Z0) ≥ P3 on fractions + model method + translation
AND
Z1 loops harden representation (not templates)
AND
Z2 sequencing prevents “skip to answer” habits
AND
Z3 test stability holds on multi-step word problems

<EKS> × P3MATH × Z{0–3} × P{0–3} × Type × ID
Type = DIR | NODE | SENSOR | TEST | LOOP | TOOL | CLAIM | BIND

DIR: EKS.P3MATH.Z0.DIR.SKILL_POCKETS.v0_1
NODES (core):
- EKS.P3MATH.Z0.NODE.FRACTIONS_MEANING.v0_1
- EKS.P3MATH.Z0.NODE.FRACTIONS_EQUIVALENCE_SIMPLIFY.v0_1
- EKS.P3MATH.Z0.NODE.FRACTIONS_OF_A_WHOLE.v0_1
- EKS.P3MATH.Z0.NODE.MULT_DIV_MEANING_REINFORCE.v0_1
- EKS.P3MATH.Z0.NODE.MEASUREMENT_UNITS_TIME_LENGTH_MASS.v0_1
- EKS.P3MATH.Z0.NODE.DATA_TABLES_GRAPHS.v0_1
- EKS.P3MATH.Z0.NODE.MODEL_METHOD_BARS.v0_1
- EKS.P3MATH.Z0.NODE.WORD_PROBLEM_TRANSLATION_2TO3STEP.v0_1
- EKS.P3MATH.Z0.NODE.CHECKING_ERROR_CONTROL.v0_1
- EKS.P3MATH.Z0.NODE.SPEED_FOUNDATION.v0_1

TEST: EKS.P3MATH.Z0.TEST.P_SCORE.v0_1
REF:  EKS.PRIMATH.TEST.P_SCORE.v0_1
APPLY:
- fractions mini-set (meaning + equivalence)
- bar model set (represent first, solve second)
- 2–3 step word problems (translation)
OUTPUT:
- pocket P map + weakest 2 pockets

DIR: EKS.P3MATH.Z1.DIR.REPAIR_LOOPS.v0_1
LOOPS:
- EKS.P3MATH.Z1.LOOP.ERROR_NOTEBOOK_CHILD.v0_1
- EKS.P3MATH.Z1.LOOP.FRACTIONS_MEANING_DRILLS.v0_1
- EKS.P3MATH.Z1.LOOP.BAR_MODEL_REP_AUTOMATION.v0_1
- EKS.P3MATH.Z1.LOOP.WORD_PROBLEM_REP_BEFORE_SOLVE.v0_1
- EKS.P3MATH.Z1.LOOP.VARIATION_LADDER.v0_1

LOOP: EKS.P3MATH.Z1.LOOP.BAR_MODEL_REP_AUTOMATION.v0_1
RULE:
Bar model is not a “drawing”.
It is a translation system.
BAR_TYPES:
- part-whole
- comparison
- before-after (change)
- units (equal groups)
TRAINING:
- draw bars for 10 problems without solving
GOAL:
- representation becomes automatic

LOOP: EKS.P3MATH.Z1.LOOP.WORD_PROBLEM_REP_BEFORE_SOLVE.v0_1
RULE:
Solve is forbidden until representation exists.
STEPS:
(1) underline question
(2) label bars/units
(3) write 1 equation sentence
(4) solve
OUTPUT:
- stops guessing habits

NODE: EKS.P3MATH.Z2.NODE.DEPENDENCY_ROUTER.v0_1
DEPENDENCIES:
- fractions meaning → fractions of a whole → ratio later
- bar model types → multi-step translation → PSLE non-routine later
RULE:
If MODEL_METHOD_BARS < P2,
do not push “harder problems” yet.
ACTION:
Rebuild representation first, then climb variation ladder.

TOOL: EKS.P3MATH.Z2.TOOL.MASTERY_SEQUENCE.v0_1
INPUT:
- pocket P map
OUTPUT:
- weekly plan:
  (a) fractions meaning pocket
  (b) bar model pocket
  (c) translation pocket
STOP-LOSS:
- if student guesses without representation → immediate truncation + rebuild

NODE: EKS.P3MATH.Z3.P3.NODE.MODEL_METHOD_LOCK.v0_1
REQUIRES:
- representation-first habit
- stable fractions meaning
- ability to handle unfamiliar story contexts
OUTPUT:
- smooth P4 ramp; fewer “sudden collapses”

SENSOR: EKS.P3MATH.Z3.SENSOR.TEST_STABILITY.v0_1
MEASURES:
- % problems with correct representation
- fraction errors trend
- multi-step translation success
- time stuck events

DIR: EKS.P3MATH.DIR.STUDENT_TYPES.v0_1
TYPES:
- EKS.P3MATH.TYPE.COLLAPSING.P0P1.v0_1
- EKS.P3MATH.TYPE.UNSTABLE.P1P2.v0_1
- EKS.P3MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1

NODE: EKS.P3MATH.TYPE.COLLAPSING.P0P1.v0_1
SIGNALS:
- cannot start word problems
- fractions feel “random”
- guesses operations
DIAG:
- fractions meaning P0/P1
- model method P0/P1
PLAN:
- rebuild fractions meaning using visual parts
- train bar model representation-only sets
TARGET:
- reach P2 fast → then P3

NODE: EKS.P3MATH.TYPE.UNSTABLE.P1P2.v0_1
SIGNALS:
- can do textbook examples, fails on new story
DIAG:
- bar model exists but not stable across types (transfer fails)
PLAN:
- variation ladder across bar types + representation-first enforcement
TARGET:
- stable transfer to unfamiliar contexts → P3

NODE: EKS.P3MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1
SIGNALS:
- good fundamentals, wants harder challenges
PLAN:
- non-routine bar models + mixed-topic sets
TARGET:
- P3 robustness without reliance on memorized templates

TOOL: EKS.P3MATH.Z2.TOOL.REPAIR_ROUTER.v0_1
INPUT:
- pocket P map
- student_type
OUTPUT:
WEEKLY_PLAN:
(1) fractions meaning drills
(2) bar model representation-only sets
(3) translation 2–3 step sets
(4) variation ladder across bar types
RULES:
- representation before solve
- guessing triggers truncation + rebuild

DIR: EKS.P3MATH.DIR.BINDS.v0_1
BINDS:
- EKS.P3MATH.BIND.P5_RATIO.v0_1      TO: EKS.PRIMATH.Z0.NODE.RATIO.v0_1
- EKS.P3MATH.BIND.PSLE_NONROUTINE.v0_1 TO: EKS.PSLE.MATH.DIR.LANE.v0_1
- EKS.P3MATH.BIND.EDU_OS.v0_1        TO: EDU.Z3.P3.NODE.CAPABILITY_STABILITY.v0_1
- EKS.P3MATH.BIND.FAMILY_LOAD.v0_1   TO: FAM.Z0.NODE.HOMEWORK_SUPPORT.v0_1
CLAIM:
Model method stability in P3 prevents later non-routine collapse.

CLAIM: EKS.P3MATH.CLAIM.CANONICAL.v0_1
Primary 3 Math reaches P3 when fractions meaning and bar model representation become stable habits,
so multi-step word problems are translated—not guessed.

END: EKS.P3MATH.P3.DIR.ARTICLE.v0_1
NEXT:
- EKS.P4MATH.P3.DIR.ARTICLE.v0_1