Teaching-mechanic library

balance_chamber · math · balance.equation

Concept: Solving linear equations

Player does: Apply the same operation to both pans until x stands alone

Breaks: You can move a term across without changing its sign

Moving a term to the other side is really applying the same operation to both sides, which flips its sign.

mean_median_seesaw · math · balance.torque

Concept: Mean vs median

Player does: Add an outlier; move the fulcrum (mean) while the median marker stays put

Breaks: Mean and median always move together

The mean is pulled toward outliers while the median resists them, so the two can move very differently as data changes.

energy_converter · physics · balance.ledger

Concept: Energy conservation

Player does: Route energy among potential, kinetic, and spring meters

Breaks: Energy gets used up

Energy is conserved and converts between forms like potential and kinetic; it is never simply used up.

lever_door · physics · balance.torque

Concept: Torque

Player does: Place the weight at the distance that opens the lever door

Breaks: Only the force matters, not where it's applied

Torque depends on both the force and its distance from the pivot, so where a force is applied matters as much as its size.

balance_builder · physics · balance.torque

Concept: Center of mass

Player does: Stack cargo so the center of mass stays over the base

Breaks: Center of mass is always the geometric center

Center of mass depends on how mass is distributed, so an unevenly loaded object's center of mass shifts off its geometric center.

flow_network · physics · balance.ledger

Concept: Current

Player does: Fill each branch's current so every junction balances

Breaks: Current is used up by bulbs

Current is conserved through a circuit; a bulb converts electrical energy to light and heat, but the current itself is not consumed.

atom_conservation · chemistry · balance.chem_equation

Concept: Balancing equations

Player does: Set coefficients until every atom token balances and the reactor starts

Breaks: Change subscripts to balance

Balancing an equation means adjusting coefficients, since changing a subscript would change the substance itself.

reaction_factory · chemistry · balance.ratio

Concept: Stoichiometry

Player does: Feed reactants in the required ratio; leftovers pile up

Breaks: Reactants combine 1:1 by mass

Reactants combine in the mole ratios set by the balanced equation, not in equal masses.

production_bottleneck · chemistry · balance.ratio

Concept: Limiting reagent

Player does: Predict which feed runs out first and how much product ships

Breaks: The reactant with less mass is limiting

The limiting reagent is decided by mole ratio needed, not by which reactant has the smaller mass.

current_junction · engineering · balance.ledger

Concept: KCL

Player does: Balance every junction: current in = current out

Breaks: Current gets used up at junctions

Kirchhoff's current law says current in equals current out at every junction; none of it is consumed there.

voltage_loop · engineering · balance.ledger

Concept: KVL

Player does: Make rises and drops around the loop sum to zero

Breaks: Voltage is the same everywhere in series

Kirchhoff's voltage law says the rises and drops around a loop sum to zero, so voltage drops across each series element.

electoral_math · civics · balance.ledger

Concept: Electoral systems

Player does: Allocate electoral votes to reach the threshold

Breaks: Winning the national popular vote guarantees the presidency

The presidency is decided by a majority of electoral votes, which can diverge from the national popular vote.

budget_balance · finance · balance.ledger

Concept: Budgeting

Player does: Balance income against expenses and savings goals

Breaks: Budgets only need to track big purchases

A budget only balances when every regular expense, not just the big ones, is tracked against income.

accounting_equation · business · balance.ledger

Concept: Accounting equation

Player does: Post each transaction so assets = liabilities + equity

Breaks: Revenue is the same as cash

Revenue is recognized when earned, which is not always the moment cash changes hands.