Learning target: I can calculate a rate of change from measurements, graph it, convert rates to a common unit so that processes at different scales can be compared, and explain what a rate can and cannot tell me about a sudden event.
This sheet has three parts. Parts A and B use teaching datasets; the numbers were invented to be realistic, not measured at a real place. Part C compares rates. Graph carefully with a ruler. Show every calculation with units, and write the unit on every answer. A rate is a change divided by the time it took: meters per year, millimeters per year, centimeters per year. Keep track of which one you are using.
You will need: This worksheet, Pencil, Ruler, Calculator
A park ranger drove a steel post into the ground on a grassy bluff and, once a year, measured the distance from the post to the edge of the sea cliff. Waves undercut the cliff, and chunks of it fall to the beach. The ranger's six measurements are below.
| Year | Distance from post to cliff edge (m) |
|---|---|
| 0 | 24.0 |
| 1 | 23.4 |
| 2 | 22.9 |
| 3 | 22.1 |
| 4 | 21.6 |
| 5 | 21.0 |
A satellite-positioning station bolted to bedrock records its position to the nearest millimeter. Each year, the station's eastward position is compared with where it started. The movement is the whole plate, carrying the station and the continent with it.
| Year | Eastward movement since year 0 (mm) |
|---|---|
| 0 | 0 |
| 1 | 24 |
| 2 | 51 |
| 3 | 74 |
| 4 | 101 |
| 5 | 125 |
Rates are hard to compare when they use different units. Convert each rate below to millimeters per year so they can be lined up. Two of the rates come from your own answers above.
| Process | Rate as measured |
|---|---|
| Cave formation (stalactite) growing | 0.1 mm per year |
| Continent moving (your Part B answer) | ? cm per year |
| Sea cliff retreating (your Part A answer) | ? m per year |
| Dune crest moving downwind | 12 cm per month |
| Glacier front flowing | 0.5 m per day |
| Landslide (moved 300 m, then stopped) | 300 m in 2 minutes |
| Rate in mm per year | Show the conversion |
|---|---|
| Stalactite | |
| Continent | |
| Sea cliff | |
| Dune crest | |
| Glacier front | |
| Landslide |
Write every rate calculation in three lines: (1) the total change with its unit, (2) the total time with its unit, (3) change ÷ time = rate, with the unit written as 'per' (for example, 3.0 m ÷ 5 years = 0.6 m per year). To convert a rate, change one unit at a time and write the new unit after each step: 0.5 m per day → 0.5 × 365 = 182.5 m per year → 182.5 × 1,000 = 182,500 mm per year. To find a time from a rate, divide the distance by the rate and check that the distance units cancel.
The cliff lost 0.8 m in year 3 but only 0.5 m in years 2 and 4. Suppose that from now on a big storm like year 3's hits once every five years and ordinary years lose 0.5 m. Recalculate how long the cliff will take to reach the post under this pattern, compare it with your q2 answer, and write two sentences about why planners who build near cliffs should use the storm pattern rather than a single average. Then find out how scientists measure present-day plate movement to the millimeter, and write one sentence on why a five-year record is enough to measure a rate that will run for millions of years.