Measurements, Models & Evidence — Practice · Grade 9 Science

Chapter: Investigating Earth

What this practice covers

By the end of Measurements, Models & Evidence you should be able to:

8 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: observation, inference, uncertainty.

Problem 1

Three readings are 8, 10, and 12 mm. Find their mean.
Answer and explanation

10 mm

(8 + 10 + 12) ÷ 3 = 10.

Problem 2

Which is an inference?
  1. The gauge reads 10 mm.
  2. The thermometer reads 18°C.
  3. The storm likely caused the river rise.
  4. The sample has mass 20 g.
Answer and explanation

The storm likely caused the river rise.

The statement interprets a cause rather than reporting a measurement.

Problem 3

Why can repeated readings all be similar yet inaccurate?
Answer and explanation

A consistent calibration error can shift every reading in the same direction.

Problem 4

Three rain measurements are 18, 20 and 22 mm. Report their mean and range, and describe a limitation. Explain the reasoning in your own words.
Answer and explanation

Mean 20 mm; range 18–22 mm; these values do not establish long-term rainfall.

Mean=(18+20+22)/3=20 mm.

Observed range is 18–22 mm; only three measurements and possible instrument bias limit the result.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 5

Measurements cluster at 20.0 cm but a reference is 21.0 cm. What kind of problem is suggested? Show the reasoning, not just the conclusion.
Hints

A miscalibrated instrument can give consistent wrong readings.

Answer and explanation

A systematic offset or calibration problem is plausible; small spread does not remove the 1.0 cm discrepancy.

Problem 6

A model predicts a trend that one new measurement contradicts. What should happen next?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Check methods and uncertainty, repeat the measurement and test the model's assumptions before revising the explanation.

Problem 7

Compare a model prediction with the measured outcomeCompare a model prediction with the measured outcomeRunoff collected (mL)04080120050100150Rain supplied (mL)Model: 80% runs offObserved comparison: 40%
Both lines are deliberately supplied model/test records rather than field observations. An 80% runoff assumption is compared with a 40% outcome over the same rainfall range. Connecting the points expresses those specified constant fractions; an actual landscape may respond nonlinearly.
Interpret the supplied visual model. At 150 mL supplied, what is the runoff mismatch and what measurement could test an explanation?
Answer and explanation

The model gives 120 mL and the comparison gives 60 mL, a 60 mL mismatch. Measure infiltration, surface storage and collection losses under matched conditions to test the assumed runoff fraction.

Read model and observation at the same horizontal rain value. The vertical gap is a difference in collected runoff, not a difference in the original rain supplied.

The model gives 120 mL and the comparison gives 60 mL, a 60 mL mismatch. Measure infiltration, surface storage and collection losses under matched conditions to test the assumed runoff fraction.

Response criteria

  • Read the labeled quantities, reference frame or objects correctly.
  • Explain the relation between the visual evidence and the mechanism.
  • Keep the drawing’s stated assumptions and limits in the conclusion.

Problem 8

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.

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