PAGE: EKS.P5MATH.P3.DIR.ARTICLE.v0_1
TITLE: eduKateSG — Primary 5 Mathematics: Reach P3 (Z0–Z3) Ratio + Percentage + Non-Routine Ramp
TYPE: Full Article / Almost-Code / Canonical / LLM-first
LANE: EKS.P5MATH
SCOPE: Z0–Z3, P0–P3
GOAL:
- lock ratio + percentage + speed so PSLE non-routine does not cause time-tail collapse
- upgrade model method from “draw bars” → “choose correct model under disguise”
REFS:
- EKS.PRIMATH.TEST.P_SCORE.v0_1
- EKS.PRIMATH.SENSOR.EXECUTION.v0_1
- EKS.PRIMATH.LOOP.TRUNCATE_STITCH.v0_1

DEFLOCK: EKS.P5MATH.P3
P5 is where many students “snap”.
The syllabus becomes non-routine: ratio/percent/speed + multi-step models under disguise.
WORKING ⇔
P(Z0) ≥ P3 on ratio + percentage + speed + model method transfer
AND
Z1 loops eliminate recurring translation and unit errors
AND
Z2 routing prevents time-sink collapse (skip/stitch training begins)
AND
Z3 mixed-topic stability holds on non-routine sets

<EKS> × P5MATH × Z{0–3} × P{0–3} × Type × ID
Type = DIR | NODE | SENSOR | TEST | LOOP | TOOL | CLAIM | BIND

DIR: EKS.P5MATH.Z0.DIR.SKILL_POCKETS.v0_1
NODES (core):
- EKS.P5MATH.Z0.NODE.RATIO_CONCEPT.v0_1
- EKS.P5MATH.Z0.NODE.RATIO_EQUIVALENCE_SCALING.v0_1
- EKS.P5MATH.Z0.NODE.PERCENTAGE_CONCEPT.v0_1
- EKS.P5MATH.Z0.NODE.PERCENTAGE_OF_QUANTITY.v0_1
- EKS.P5MATH.Z0.NODE.INCREASE_DECREASE_PERCENT.v0_1
- EKS.P5MATH.Z0.NODE.SPEED_DISTANCE_TIME.v0_1
- EKS.P5MATH.Z0.NODE.AVERAGE_RATE_CONTEXTS.v0_1
- EKS.P5MATH.Z0.NODE.WORD_PROBLEM_TRANSLATION_NONROUTINE.v0_1
- EKS.P5MATH.Z0.NODE.MODEL_METHOD_SELECTION.v0_1
- EKS.P5MATH.Z0.NODE.UNITS_CONVERSION_STABILITY.v0_1
- EKS.P5MATH.Z0.NODE.CHECKING_ERROR_CONTROL.v0_1
- EKS.P5MATH.Z0.NODE.SPEED_UNDER_TIME.v0_1

TEST: EKS.P5MATH.Z0.TEST.P_SCORE.v0_1
REF:  EKS.PRIMATH.TEST.P_SCORE.v0_1
APPLY:
- ratio/percent topical sets
- speed topical + unit conversion set
- 8 non-routine word problems (must include disguise)
OUTPUT:
- pocket P map + weakest 2 pockets

DIR: EKS.P5MATH.Z1.DIR.REPAIR_LOOPS.v0_1
LOOPS:
- EKS.P5MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1
- EKS.P5MATH.Z1.LOOP.RATIO_MASTERY_LADDER.v0_1
- EKS.P5MATH.Z1.LOOP.PERCENT_MASTERY_LADDER.v0_1
- EKS.P5MATH.Z1.LOOP.SPEED_CONTEXT_LADDER.v0_1
- EKS.P5MATH.Z1.LOOP.NONROUTINE_TRANSLATION.v0_1
- EKS.P5MATH.Z1.LOOP.TIMED_MICROSETS.v0_1
- EKS.P5MATH.Z1.LOOP.MIXED_TOPIC_ROTATION.v0_1

LOOP: EKS.P5MATH.Z1.LOOP.RATIO_MASTERY_LADDER.v0_1
LADDER:
L0: write ratio correctly
L1: simplify/scale
L2: part-to-whole and whole-to-part
L3: ratio with change (before/after)
L4: ratio hidden in word problems
GOAL:
Ratio becomes a reflex, not a mystery.

LOOP: EKS.P5MATH.Z1.LOOP.NONROUTINE_TRANSLATION.v0_1
RULE:
Non-routine means translation is the skill.
STEPS (forced):
(1) identify topic candidates (ratio/percent/speed/geometry/data)
(2) choose representation (bars/table/unit rate)
(3) write one equation sentence
(4) solve
FAILURE:
If student guesses operation → truncation + rebuild representation.

DIR: EKS.P5MATH.Z2.DIR.ROUTING.v0_1
NODES:
- EKS.P5MATH.Z2.NODE.PROBLEM_ROUTER.v0_1
- EKS.P5MATH.Z2.NODE.TIME_SINK_TRUNCATION.v0_1
- EKS.P5MATH.Z2.NODE.RETURN_PASS_STITCH.v0_1

NODE: EKS.P5MATH.Z2.NODE.TIME_SINK_TRUNCATION.v0_1
RULE:
If stuck beyond TIME_CAP,
TRUNCATE (skip) and move on.
GOAL:
Protect total paper score; stop one question collapse.

NODE: EKS.P5MATH.Z2.NODE.RETURN_PASS_STITCH.v0_1
STITCH:
Return to skipped questions after full first pass.
ORDER:
(1) easiest partial-mark wins
(2) medium
(3) hardest last

NODE: EKS.P5MATH.Z2.NODE.DEPENDENCY_ROUTER.v0_1
DEPENDENCIES:
- fractions/decimals conversion → percentage accuracy
- model method representation → non-routine success
- unit conversion → speed contexts
RULE:
If percent errors persist, check P4 conversion pockets immediately.
ACTION:
Back-sequence until conversion stability returns.

NODE: EKS.P5MATH.Z3.P3.NODE.P5_NONROUTINE_LOCK.v0_1
REQUIRES:
- ratio + percent pockets P3
- non-routine translation stable
- routing prevents time-sink collapse
OUTPUT:
- P6 + PSLE becomes an upgrade, not a panic event

SENSOR: EKS.P5MATH.Z3.SENSOR.TEST_STABILITY.v0_1
MEASURES:
- non-routine solve rate
- time tail events
- unit/conversion error rate
- representation correctness rate

DIR: EKS.P5MATH.DIR.STUDENT_TYPES.v0_1
TYPES:
- EKS.P5MATH.TYPE.COLLAPSING.P0P1.v0_1
- EKS.P5MATH.TYPE.UNSTABLE.P1P2.v0_1
- EKS.P5MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1

NODE: EKS.P5MATH.TYPE.COLLAPSING.P0P1.v0_1
SIGNALS:
- non-routine blanks
- ratio/percent feels impossible
- speed questions always wrong units
DIAG:
- representation + conversions P0/P1
PLAN:
- rebuild conversions, rebuild representation, rebuild ratio/percent ladders
TARGET:
- reach P2 fast → then P3

NODE: EKS.P5MATH.TYPE.UNSTABLE.P1P2.v0_1
SIGNALS:
- can do topical, fails on mixed and disguised problems
DIAG:
- pockets P2; transfer P1
PLAN:
- mixed topic rotation + non-routine translation loop + timed routing
TARGET:
- stable transfer under disguise → P3

NODE: EKS.P5MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1
SIGNALS:
- strong, wants A* trajectory
PLAN:
- higher-difficulty non-routine sets + tighter pacing + deeper explanation
TARGET:
- PSLE-ready robustness (low volatility)

TOOL: EKS.P5MATH.Z2.TOOL.REPAIR_ROUTER.v0_1
INPUT:
- pocket P map
- student_type
OUTPUT:
WEEKLY_PLAN:
(1) ratio ladder drills
(2) percent ladder drills
(3) speed contexts + units drill
(4) non-routine translation set (forced representation)
(5) timed mixed set with skip/stitch
RULES:
- conversion errors → back-sequence to P4 conversions
- guessing → truncation + rebuild representation

DIR: EKS.P5MATH.DIR.BINDS.v0_1
BINDS:
- EKS.P5MATH.BIND.P6_INTEGRATION.v0_1    TO: EKS.P6MATH.DIR.LANE.v0_1
- EKS.P5MATH.BIND.PSLE_MODE.v0_1         TO: EKS.PSLE.MATH.DIR.LANE.v0_1
- EKS.P5MATH.BIND.EDU_OS.v0_1            TO: EDU.Z3.P3.NODE.CAPABILITY_STABILITY.v0_1
- EKS.P5MATH.BIND.FAMILY_LOAD.v0_1       TO: FAM.Z0.NODE.HOMEWORK_SUPPORT.v0_1
CLAIM:
P5 is the main PSLE ramp; stability here prevents P6 panic collapse.

CLAIM: EKS.P5MATH.CLAIM.CANONICAL.v0_1
Primary 5 Math reaches P3 when ratio, percentage, and non-routine translation become stable under time,
and routing prevents time-tail collapse from one difficult question.

END: EKS.P5MATH.P3.DIR.ARTICLE.v0_1
NEXT:
- EKS.P6MATH.P3.DIR.ARTICLE.v0_1