Gradient — Science definition
Change in elevation divided by horizontal distance.
Where it is taught
- Topographic Maps & Gradients — Investigating Earth, Earth & Space Science, Grade 9
Questions using gradient
Problem 1
Elevation rises 60 m over a horizontal distance of 3 km. Find gradient.
Answer and explanation
20 m/km
60 ÷ 3 = 20.
Problem 2
Elevation rises from 120 m to 300 m over a horizontal distance of 3 km. Find gradient. Explain the reasoning in your own words.
Answer and explanation
60 meters of elevation change per kilometer horizontally.
Elevation change=300−120=180 m.
Gradient=180 m/3 km=60 m/km.
Response criteria
- Use the stated conditions.
- Show the evidence or calculation.
- Explain the conclusion and any stated limitation.
Problem 3
Elevation rises 60 m over 300 m horizontally. Find gradient. Show the reasoning, not just the conclusion.
Hints
Use horizontal ground distance and actual elevations, not contour-line count alone.
Answer and explanation
60/300=0.20 m/m, or 20%.
Problem 4
A map scale is 1 cm = 0.4 km. Two points 3 cm apart along a stated map line rise from 220 to 280 m. Calculate average gradient and explain why it does not establish every local slope.
Answer and explanation
Ground distance is 1.2 km and rise is 60 m, so average gradient is 50 m/km. Local segments can be steeper or flatter; additional contour crossings or survey points are needed.
Convert 3×0.4 = 1.2 km.
Subtract 280−220 = 60 m.
Divide 60/1.2 = 50 m/km and distinguish the average from local values.
Response criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the physical mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.