Litres and minutes, kilometres and hours, rupees and kilograms: a rate puts two different kinds of quantity side by side and asks how much of one goes with a single unit of the other. This unit starts with the unit rate and what makes a fair comparison, then uses it for speed, distance and time, for changing one unit or currency into another, and for the straight-line graph that a steady rate leaves behind.
Every idea is something you can move: litres poured into equal minutes, two taps set against each other, a journey along a road, a ruler with two scales, a price compared across two currencies, and a line whose steepness is the rate. No lesson needs a calculator.
The lessons, in order
- Lesson 1 · Rates and unit rates A rate as two different units compared, the unit rate found by dividing, its unit (litres per minute), comparing and adding rates. Slide the litres and the minutes of a tap and see the same amount in every minute; then set a second tap against a fixed one. No calculator
- Lesson 2 · Speed, distance and time Speed as distance per time, finding distance, time or speed from the other two, minutes to hours, and average speed over a whole journey. Set a speed and a time and see the distance along a road; then set two legs of a trip and compare the true average speed with the mean of the speeds. No calculator
- Lesson 3 · Converting units Metric length, mass and capacity conversions, inches to centimetres, a conversion factor as a rate, and kilometres per hour to metres per second. Choose a pair of units and an amount and see the same length on two scales; then change kilometres per hour to metres per second in two steps. No calculator
- Lesson 4 · Exchange rates and fair comparisons An exchange rate as a conversion factor, changing currency in both directions, and comparing prices across currencies and pack sizes. Set the exchange rate and see which of two prices is cheaper once both are in rupees, and where the answer flips. No calculator
- Lesson 5 · Graphs of a constant rate A steady rate as a straight-line graph, the rate as rise over run with its units, comparing steepness, and finding values from a graph. Set the rate of two lines and slide the second point along the first: the rise changes, the rise over run does not. No calculator
- Lesson 6 · Start values and falling rates A straight line with a start value, the rate between any two points, falling quantities with a negative rate, and when a falling quantity reaches zero. Set a start value and a rate from negative to positive and watch the value after 5 hours and where the line crosses zero. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.