Ratios & Proportions
Where ratios and proportions show up in real life
13 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Ratios & ProportionsScaling a recipe: more people, same taste
Double the guests? Every ingredient grows by the same factor.
Arithmetic & Number SenseRoad trip math: miles, liters, and dollars
Convert once and the trip adds up: how far, how much fuel, how much money.
Ratios & ProportionsUnit price: is the big size really the better deal?
Divide price by size and the shelf tags stop lying. Bigger isn’t always cheaper.
Ratios & ProportionsE6B time and fuel: will it make it with a reserve?
Distance over groundspeed gives time; time times burn gives fuel. Then leave something in the tanks.
Ratios & ProportionsTorque: how hard to pull the wrench, and what an adapter changes
Torque is force times distance. A longer handle takes less push, and an adapter that adds length means you must set the wrench lower.
Ratios & ProportionsWire resistance: longer and thinner resist more
Resistance grows with length and shrinks with thickness. Pick the wire that keeps it low.
Linear EquationsVoltage divider: two resistors make a new voltage
The output is the input times a ratio of resistors, until you connect a load.
Exponents & LogarithmsBrightness vs. distance: the inverse-square law
Move a light twice as far and it gives a quarter of the light. Photographers call that two stops.
Ratios & ProportionsRunning pace: from your 5K to a marathon time
Pace is a ratio. Predicting a longer race takes an exponent, because you slow down.
Arithmetic & Number SenseE6B weight and balance: where the center of gravity lands
The CG is a weighted average. Load people, bags, and fuel, and watch the dot move in the envelope.
Linear EquationsHome heat loss: where does the heat go?
Heat leaks through each surface in proportion to area and temperature difference, divided by R. Windows and drafts punch far above their size.
Ratios & ProportionsInsulation payback: how long until it pays for itself?
Heat saved goes as 1/R_before − 1/R_after, so the first few inches pay back fastest.
Ratios & ProportionsLead screw vs. ball screw: turning torque into a push
A screw trades turns for force: F = 2π × efficiency × torque ÷ lead. Friction decides whether it also holds the load with the power off.