Rate and speed
A rate compares two different units; a unit rate has one in the denominator (miles per hour, dollars per pound). Speed is the most important unit rate: distance over time. Students convert between m/s and km/h, solve unit-price comparisons, and read speed from a story. The trap is average speed. It is always total distance divided by total time — never the mean of two speeds unless the times happen to be equal. Going 60 km/h for one hour and 40 km/h for two hours averages 46⅔ km/h, not 50.
Specification · for a parent or teacher
- rate-speed
- Advanced Math 6 · Unit 6
- High School Math 1
- Applied
- 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
- 5 items
Students can
unit rates; ; ↔ ; average-speed stories.
Ready when
they refuse to average 60 and 40 when the times differ, and compute .
Formulas
Not the mean of the speeds.
Watch for
60 km/h for 1 h then 40 km/h for 1 h averaged as 50 km/h (this one happens to be right because times are equal) vs 60 km/h for 1 h then 40 km/h for 2 h still called 50.