This is a working draft for Leslie's review. The dependency edges below are a first pass — the diagram and the prerequisite table are the parts to check hardest, since they drive hold-vs-advance decisions.
The course map shows the eight units as a spine — atoms first, electrochemistry last. But the real prerequisite structure isn't a straight line: it's a directed graph. Chemistry is more strictly cumulative than most subjects — bonding needs atomic structure, stoichiometry needs bonding, equilibrium needs both energy and the mole. A weak concept early doesn't just lower one grade, it cascades into everything downstream that needs it. This page is the map a guide uses to find the concept that's actually blocking a stuck student.
An arrow means “must be mastered first.” Units 05, 06, and 08 each pull from two upstream units — those are the cascade points where one soft prerequisite quietly breaks several later units.
Prerequisite gating
A unit unlocks when its prerequisites are mastered — demonstrated, not merely seen. "Covered in class" is not the gate; a cleared rubric is. The difference matters most at the cascade points, where a soft prerequisite quietly breaks two or three later units.
| Unit | Must have mastered first |
|---|---|
| 01 Atomic Structure | — (entry point) |
| 02 Chemical Bonding | 01 (electron configuration, periodic trends) |
| 03 Stoichiometry | 02 (formulas & balanced equations depend on bonding) |
| 04 States of Matter & Gas Laws | 02 (intermolecular forces depend on bonding) |
| 05 Thermochemistry | 03 (mole/energy bookkeeping) + 04 (kinetic-molecular energy) |
| 06 Kinetics & Equilibrium | 03 (mole ratios) + 05 (energy & spontaneity) |
| 07 Acids & Bases | 06 (equilibrium — Ka/Kb are equilibria) |
| 08 Electrochemistry | 06 (equilibrium, Nernst) + 07 (redox & proton transfer) |
Gap-cascade diagnosis
When a student stalls late, the visible symptom is rarely the real problem — the broken concept is usually upstream. Trace the arrows backward. Common cascades:
| Late symptom | Upstream concept to check first |
|---|---|
| pH and buffer problems fall apart (Unit 07) | Equilibrium from Unit 06 — an acid constant is an equilibrium constant. |
| Equilibrium expressions don't balance (Unit 06) | Mole ratios and balanced equations from Unit 03 — not the equilibrium itself. |
| Cell potentials and Nernst stall (Unit 08) | Free energy / spontaneity from Unit 05 thermochemistry. |
| Enthalpy bookkeeping goes wrong (Unit 05) | Where the moles come from — Unit 03 stoichiometry. |
Using the graph to plan a re-attempt
The graph turns a "not yet" into a targeted re-attempt instead of a whole-unit re-teach. When a student fails a downstream demonstration:
- Trace backward to the upstream node the symptom points to.
- Re-attempt the upstream concept first — close the gap at its source, not where it surfaced.
- Then re-run the downstream demonstration. Often it passes without any re-teaching of the downstream unit at all, because the cascade is resolved.
This is also where the integration guide matters: some chemistry concepts depend on an applied-math idea — logarithms for pH, proportional reasoning for the mole — from another spoke. When the upstream chemistry node looks solid but the student still stalls, check the cross-disciplinary dependency before re-teaching the chemistry.