Ohm's Law: voltage, current, resistance

For ages 12–13, Ohm's Law (V = IR) is taught as ONE relationship linking voltage (the push), current (the flow) and resistance (the opposition). Current is proportional to voltage only while resistance stays constant. The relationship is derived from the ratio definition R = V/I rather than memorised as a formula triangle. The core learning is seeing how current responds when you change voltage or resistance, and understanding WHY via a particle picture of charges colliding with the lattice: in a longer wire each charge meets more collisions along the way, and a thinner wire has fewer parallel lanes for charge, so both give more resistance. Activities cover an interactive sandbox for cause-and-effect exploration, a retrieval set for calculation fluency, reference supports, and a Socratic debrief. Note the UK curriculum placement: the V=IR ratio and calculation sit at KS3, while the named 'Ohm's Law' and graphical I–V treatment are KS4 extensions kept qualitative here.

• Treating V = IR as a meaningless triangle to shuffle — substituting without knowing which quantity is the push, the flow, or the opposition.
• Thinking resistance 'uses up' current — resistance REDUCES the current (everywhere in a series loop) but does not consume charge; the current is still the same all the way round, just smaller.
• Believing a thicker wire has MORE resistance — it has LESS (more lanes for charge); thickness and length pull opposite ways.
• Assuming current and voltage are always directly proportional — only when resistance is constant; a heating filament's resistance rises, so its V–I line bends (the KS4 caveat).
• Confusing which quantity changes when — e.g. expecting changing the resistor to change the battery's voltage; the cell sets V, the circuit's R then sets I.
• Mis-rearranging the equation — e.g. writing I = VR instead of I = V/R — from manipulating symbols without the proportional sense (more opposition must mean less current).
• Equating 'Ohm's Law' with all components — it describes the constant-resistance (ohmic) case; not every component obeys a single straight-line relationship.

• The ratio/relationship trio R = V/I, V = IR, I = V/R — shown as rearrangements of ONE relationship, each readable in words ('current is push divided by opposition').
• Particle model of resistance — charges colliding with a lattice; longer wire = more collisions, thicker wire = more lanes, making the factors causal.
• The V–I proportional relationship for a fixed resistor — double the voltage, double the current — introduced numerically/in words (the formal straight-line graph is the KS4 step).
• The formula triangle (V over I and R) — a calculation support, explicitly labelled a crutch to be backed by reasoning.
• A variable circuit picture — a battery slider (V) and a resistor slider (R) with a live ammeter (I) showing how changing one moves the current.

• Build V = IR FROM the ratio definition the child already met: resistance is potential difference divided by current (R = V/I), so V = IR and I = V/R are the same relationship rearranged — derive it, don't drop it as a triangle.
• Teach resistance as OPPOSITION to flow with a causal picture: charges collide with the vibrating lattice of the material; more collisions = more resistance = less current for the same voltage. This makes 'opposes current' mechanistic, not a slogan.
• Make the factors predictable from the picture: a LONGER wire = more collisions on the way = more resistance; a THICKER wire = more parallel lanes = less resistance; different MATERIALS pack the lattice differently. Have pupils predict before checking.
• Drill the proportional reasoning, not just substitution: for fixed R, doubling V doubles I; for fixed V, doubling R halves I. The relationships matter more than the arithmetic at this tier.
• Use the formula triangle ONLY as a support after meaning is secure, and warn against it as a crutch — require a sentence of reasoning ('more resistance, same push, so less current') alongside any rearrangement.
• Keep 'resistance opposes / reduces current' distinct from 'resistance uses up current' — resistance lowers the rate of flow everywhere in a series loop; it does not consume charge (the current is still the same all the way round, just smaller).
• Flag honestly that real components aren't all 'ohmic': a filament bulb's resistance rises as it heats, so V and I are not simply proportional — but the graphical I–V treatment of that is the KS4 extension, kept qualitative here.