Money & Shopping
Math for spending, saving, and comparing prices
19 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.
Systems of EquationsPhone plans: finding the break-even point
Two plans, two lines. Where they cross, the price is the same.
PercentSale price and tax: what you really pay
30% off, then tax on top. Percent math decides the number at the register.
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.
GeometryPizza value: one large or two mediums?
Area grows with the square of the size. That changes which pizza is the deal.
Linear EquationsHourly pay and overtime: time-and-a-half
A straight line with a bend: after 40 hours, every hour pays more.
PercentPercent change: up 50%, then down 50%, and you’ve lost money
A percent is always “of something.” Change the something and the same percent means a different amount.
StatisticsMean vs. median: why one big paycheck skews the average
Add one huge salary and the average jumps. The median, the middle value, barely moves.
Exponents & LogarithmsCompound interest: money that grows on itself
Interest earns interest. Exponents explain why saving early wins.
Exponents & LogarithmsLoan payments: what a mortgage really costs
One formula sets every car, student, and home loan payment. See where the interest goes.
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.
StatisticsPoll margin of error: why about 1,000 people gives ±3%
The margin shrinks with the square root of the sample. Four times the people only halves it.
ProbabilityLottery odds: what is a ticket really worth?
Powerball is 1 in 292 million. Multiply the chance by the prize, after the lump sum, taxes, and splitting, and see what $2 buys.
Exponents & LogarithmsCredit card payoff: how many months until it’s gone?
A logarithm answers “how long?” See why minimum payments take forever.
StatisticsA/B test: is version B really better, or just lucky?
A higher conversion rate might be chance. The z-test turns the gap and the sample size into a p-value.
PolynomialsIs this investment worth it? The rate of return is a polynomial’s root
Money today and money later add up to a polynomial. The rate that makes it zero is the investment’s internal rate of return.
VectorsSolar panel tilt: how much sunlight it catches
Point one arrow at the sun and one straight out of the panel. Their dot product is the share of full sunlight the panel gets.
MatricesHow search ranks pages: links as votes (PageRank)
A link is a vote, and votes from important pages count more. Repeat until it settles and you get PageRank.