calculation trainer

Model solution graphs and student steps

Represent the canonical Kp calculation path, structured student work, example tracing, and model tracing as separate inspectable objects.

120 minSaved locally

Read with a clear lens

solution graph nodes and dependencies
structured student steps
example tracing versus model tracing
separate mathematical and chemistry-model correctness

Pause and write

Which facts belong to the problem, the canonical solution, the student's attempt, and the evaluator trace?

Inline chapter

From a worked answer to an inspectable solution graph

A calculation coach cannot diagnose a path if it stores only the question and the final answer. It needs separate records for what the problem fixes, what the canonical method requires, what the learner actually enters, and what the evaluator concludes. This chapter builds that model around the first bounded Kp archetype.

Keep four records separate

The CalculationProblem is the frozen task: prompt, givens, balanced equation, answer requirements, source evidence, and review state. The SolutionGraph is the canonical dependency path for that exact problem version. A StudentStep is one piece of structured learner work. An evaluator trace records how each student step aligned to a graph node and why a check passed, failed, or required review.

Source Data model (AI_DRAFT)

These records answer different questions. The problem says what is authoritative input. The graph says what must be derived and in which dependency order. The attempt says what the learner supplied. The trace says what the deterministic checks observed. Combining them into one mutable object makes it impossible to reproduce a diagnosis or tell whether a value came from the source, the canonical method, or the learner.

Sources Calculation domain schema (AI_DRAFT) · Data model (AI_DRAFT)

Pause in the chapter

A learner uses the wrong total number of moles, then carries that value into every mole fraction. Which facts belong in the StudentStep records, and which conclusions belong only in the evaluator trace?Source Data model (AI_DRAFT)

Trace the ten-node Kp path

For KP_FROM_EQUILIBRIUM_MOLES, the graph makes the familiar worked method explicit. Each node produces a named value or expression, and every edge states which earlier result the next node depends on. The sequence below traces the repository's versioned draft fixture; it demonstrates the data shape but does not claim chemistry or curriculum review.

Sources Calculation domain schema (AI_DRAFT) · Original Day 2 guide (INTERNAL_SYNTHESIS) · Kp calculation fixture (AI_DRAFT)

Worked example

Worked draft: calculate Kp from equilibrium moles

Fixture CAIE9701-KP-EQM-001@1.0.0 gives 0.40 mol PCl5, 0.30 mol PCl3, 0.30 mol Cl2, and a total equilibrium pressure of 2.00 × 10^5 Pa. Its provenance is INTERNAL_AUTHORED_DRAFT and its review status is AI_DRAFT, so use it to inspect the calculation path—not as an approved CAIE question or mark scheme.

Balanced equationPCl5(g) ⇌ PCl3(g) + Cl2(g). All three species are gases, and the 1:1:1 coefficients define the pressure powers in Kp.
Equilibrium molesRecord n(PCl5) = 0.40 mol, n(PCl3) = 0.30 mol, and n(Cl2) = 0.30 mol as the frozen equilibrium givens.
Total molesn(total) = 0.40 + 0.30 + 0.30 = 1.00 mol. This value is the common denominator for every mole fraction.
Mole fractionsx(PCl5) = 0.40 / 1.00 = 0.40; x(PCl3) = 0.30; x(Cl2) = 0.30. The fractions sum to 1.00.
Partial pressuresUsing p(i) = x(i) × 2.00 × 10^5 Pa gives p(PCl5) = 80 000 Pa, p(PCl3) = 60 000 Pa, and p(Cl2) = 60 000 Pa.
Kp expressionKp = p(PCl3) × p(Cl2) / p(PCl5). The equation fixes the participating species, numerator, denominator, and exponents.
SubstitutionKp = (60 000 Pa × 60 000 Pa) / 80 000 Pa. The substitution preserves the canonical expression structure.
Numerical resultThe unrounded evaluated result is 45 000. This numerical node is downstream of both the partial pressures and the Kp expression.
UnitThe net pressure power is 2 − 1 = 1, so this draft fixture requires the unit Pa.
Significant figuresReport Kp = 4.5 × 10^4 Pa to the fixture's required two significant figures.

Takeaway The edges are as important as the nodes. If a StudentStep reports 1.30 mol at total moles, an evaluator trace can mark N03 as the first invalid node and inspect N04, N05, N07, and N08 as dependent consequences. N06 remains an independent chemistry-model check: a correct carried calculation cannot repair a wrong Kp expression.

Sources Calculation domain schema (AI_DRAFT) · Data model (AI_DRAFT) · Kp calculation fixture (AI_DRAFT)

Pause in the chapter

If every arithmetic operation is correct but the learner includes a solid in the Kp expression, which node is first invalid and which correctness dimension should report it?Sources Calculation domain schema (AI_DRAFT) · Data model (AI_DRAFT)

Distinguish example tracing from model tracing

Example tracing follows one frozen problem and one learner attempt through concrete node values: which step aligned, what value was produced, and where the first invalid dependency appeared. It is the fastest way to see whether the current graph explains a real calculation path.

Sources Original Day 2 guide (INTERNAL_SYNTHESIS) · Data model (AI_DRAFT)

Model tracing checks the reusable archetype instead. It asks whether every allowed variation still maps to the declared node kinds, whether every edge remains valid, and whether unsupported variations fail closed. A single worked example can pass while the reusable model is still incomplete, so the two traces are related evidence, not substitutes.

Sources Calculation domain schema (AI_DRAFT) · Original Day 2 guide (INTERNAL_SYNTHESIS)

Pause in the chapter

A proposed variation sets n(Cl2) = 0 exactly at equilibrium but still expects a finite, non-zero Kp for the same PCl5(g) ⇌ PCl3(g) + Cl2(g) system with non-zero PCl5 and PCl3. What inconsistency should an example trace expose, and why should model tracing reject this unsupported variation?Sources Original Day 2 guide (INTERNAL_SYNTHESIS) · Calculation domain schema (AI_DRAFT)

Sources and further reading

Original Day 2 guideINTERNAL_SYNTHESISOpen Calculation domain schemaAI_DRAFTOpen Data modelAI_DRAFTOpen Kp calculation fixtureAI_DRAFTOpen

After reading

Trace one Kp example through the ten canonical nodes and identify the data produced at each node.

Knowledge check

Why are a list of final answers and a solution graph not equivalent?

Write an answer to unlock the reference

A solution graph records node meaning, dependencies, expected transformations, and provenance. That structure lets the evaluator align student steps, locate the first invalid dependency, and distinguish a carried-forward consequence from a new error.

AI_DRAFT · The domain model is frozen for engineering work but awaits chemistry and curriculum review.

Study information and required outputs

Item information

Stable ID: sprint.domain-model
Version: 2.1.0
Content status: ready
Kind: mental model

Dependencies

Orient to the calculation-path coach

Required repository outputs

docs/architecture/DATA_MODEL.md

Typed separation of problems, graphs, attempts, checks, and traces

docs/content/CALCULATION_DOMAIN_SCHEMA.md

Canonical calculation content contract

Done criteria

Can trace every canonical Kp node
Can distinguish example and model tracing
Can explain why student input remains structured in V0

Finish the session

Record where your understanding stands

Confidence