Investigating Earth — Chapter review · Earth & Space Science, Grade 9

Use measurements, models, maps, and reference tools to build explanations from evidence.

Review the key ideas

Measurements, Models & Evidence

A scientific explanation links measured evidence to a model while making assumptions and limitations explicit.

Topographic Maps & Gradients

Contour spacing shows relative steepness; gradient measures average elevation change per horizontal distance.

Problem 1

A map averages rainfall over 100 km². Why might a school gauge differ from the map value?
Answer and explanation

The gauge samples one location while the map represents an area average; rainfall varies spatially and measurements have uncertainty.

Problem 2

Chapter review: A balance repeatedly reads 19.7 g for a 20.0 g reference. A student reports their average as accurate because the readings agree. Explain the error and propose a correction check.
Answer and explanation

The readings are precise but 0.3 g below the reference. Their average is still 19.7 g. Check calibration with suitable reference masses over the working range and repeat the measurement; do not assume repeatability proves accuracy.

Compare the repeated values with the independent 20.0 g reference.

Find the bias: 19.7−20.0 = −0.3 g.

Use calibration checks to distinguish a systematic offset from random spread.

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.

Problem 3

A 1:25,000 map shows two points 4 cm apart. Their elevations differ by 50 m. Calculate ground distance and gradient.
Answer and explanation

4 × 25,000 = 100,000 cm = 1 km. Gradient = 50 m/km.

Problem 4

Chapter review: 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.
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