Measurement, Units & Experimental Evidence — Print · Grade 11 Science
Chapter: Investigating MatterMeasurement, Units & Experimental Evidence
Learning goals
- I can convert units, track significant figures, and distinguish precision from accuracy.
- I can interpret a graph or repeated measurements with stated uncertainty.
Readings for this unit
Before this unit
Division, scientific notation, and a ratio equal to one.
Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.
Start with something to explain
Can a very repeatable result still be wrong?
Illustrative evidence case. Repeated densities cluster at 2.02 g/mL while an appropriate reference is 2.50 g/mL.
Notice and wonder
Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.
Can a very repeatable result still be wrong?
Your first model
Sketch separate ideas for repeat spread and reference offset.
Build the language from the idea
- density
- Mass per unit volume, usually g/mL for liquids or g/cm³ for solids.
- systematic error
- A recurring offset caused by a method or instrument.
- significant figures
- Digits used to communicate the precision of a measurement.
Chemistry links observable measurements to particle models. A useful record identifies the substance, temperature, equipment, units, and method, so another person can repeat the work. Mass measures inertia and amount of material; volume measures occupied space; density is mass divided by volume. An intensive property such as density can help identify a material without depending on sample size.
SI prefixes rescale units: kilo means 1000, centi 0.01, milli 0.001, and micro 0.000001. One milliliter is one cubic centimeter; 1000 mL is one liter. In dimensional analysis multiply by a ratio equal to one, such as 1 L/1000 mL. Arrange it so unwanted units cancel. Never change a measured amount merely by changing its unit.
Read a scale with an appropriate last estimated digit and record its resolution. Accuracy describes agreement with a reference; precision describes repeatability. Repeated measurements can be close together but all offset by a poorly calibrated balance. A mean alone hides spread: report sample count and range, and explain likely systematic and random errors.
Significant figures communicate measurement precision. For multiplication or division, round a final result to the fewest significant figures in the measured inputs. For addition or subtraction, use the least precise decimal place. Counted objects and defined conversions are exact. Retain extra digits during calculation; round only at the end.
A measured density is not a proof of identity. Different substances may have similar densities; temperature and impurities affect the result. Compare multiple independent properties. Percent error = absolute(measured − reference)/reference × 100%; a low error for one reading does not establish that the method is reliable.
For a test of dissolved salt versus conductivity, vary salt concentration and measure conductivity under comparable temperature and geometry. Include pure water as a comparison, prepare independent repetitions, and specify equipment limitations. A diagram, labeled table, and evidence-based conclusion are part of scientific communication, not decoration.
Build your understanding
Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.
Part 1 · Distinguish accuracy, precision, and resolution
A measurement combines a value, unit and procedure. Precision describes repeatability; accuracy concerns agreement with an appropriate reference. Here instrument A repeatedly reports near 2.02 g/mL while B reports near the supplied 2.50 g/mL reference. A small spread cannot remove a systematic calibration offset. Keep individual readings and reference uncertainty; three selected trials illustrate the distinction rather than establish the long-term performance of either instrument.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
Which instrument is more accurate relative to 2.50 g/mL, and why does A’s small spread not settle accuracy?
Visual reasoning — after your attempt
B is closer to this reference. A is repeatable but offset; repeatability does not rule out systematic error.
Accuracy concerns agreement with a suitable reference; precision concerns agreement among repeated measurements. Resolution is the smallest change an instrument can distinguish. Consistent measurements can all be displaced from the reference by a systematic error, so repeatability alone does not establish accuracy.
A balance repeatedly reporting 10.20 g for a 10.00 g reference is precise but biased. Record reference uncertainty and instrument conditions before deciding what a difference means.
Pause and explain
Does averaging remove every measurement error?
Check your reasoning after answering
Averaging can reduce some random variation, but a consistent calibration bias remains unless identified and corrected.
Part 2 · Build conversions that cancel units
A conversion factor is a ratio of equal quantities, such as one liter per 1,000 milliliters. Multiplying by it does not change the actual amount. Arrange the ratio so the unwanted unit cancels between numerator and denominator. Defined unit relationships are exact and do not impose a measurement limit. The dot in 250. mL communicates three significant figures in this example, so the converted value is 0.250 L, rather than a new measurement with extra precision.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
Why is 250. mL multiplied by 1 L/1000 mL rather than 1000 mL/1 L?
Visual reasoning — after your attempt
The first ratio cancels mL and leaves liters; the inverted ratio would leave mL²/L and the wrong numerical scale.
A conversion factor is a ratio of equivalent quantities. Choose its orientation so the unwanted unit cancels, and retain units through the calculation. Scientific notation keeps very large or small quantities manageable; powers of ten are part of the arithmetic, not optional decoration.
Convert 250 mL using 1 L/1000 mL to obtain 0.250 L. Multiplying by the reciprocal would leave the wrong units and the wrong scale.
Pause and explain
What is the first check on a proposed conversion?
Check your reasoning after answering
Check unit cancellation before arithmetic, then check whether the magnitude is reasonable for the new unit.
Part 3 · Report precision supported by evidence
An instrument’s resolution is the smallest change it can distinguish or display; an analog scale usually supports an estimated digit beyond its marked intervals. That does not make every last digit exact. In classroom significant-figure rules, a multiplication result follows the least precise measured factor in significant figures. Addition and subtraction instead follow decimal-place precision. Keep guard digits while calculating and round once at the end; extra calculator digits cannot improve the original measurement.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
Why is the area reported as 2.9 cm² rather than 2.8800 cm²?
Visual reasoning — after your attempt
The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.
Measured quantities have limited precision. For multiplication and division, introductory significant-figure conventions usually follow the least precise measured factor; addition and subtraction follow decimal-place limits. Exact counts and defined conversions do not restrict precision. Keep guard digits during intermediate calculations.
A final density from 12.4 g and 5.0 mL is 2.5 g/mL under the two-significant-figure convention. Writing 2.480000 suggests precision not supported by the volume.
Pause and explain
Why should intermediate results not be rounded repeatedly?
Check your reasoning after answering
Repeated rounding can accumulate avoidable numerical error. Keep extra digits during working and round the reported result according to the input precision.
Part 4 · Match a claim to its uncertainty
A graph needs named variables, units and a defined comparison. For a homogeneous material at fixed conditions, mass equals density times volume, so a mass-versus-volume slope estimates density. A fitted intercept, residual pattern and uncertainty matter when actual data depart from a line. A high correlation alone does not identify a substance or prove a causal explanation. Here the invented points lie exactly on a line to isolate the unit calculation; real balances and volume readings have uncertainty.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
What are the slope units, and why is one density value insufficient to identify an unknown?
Visual reasoning — after your attempt
Slope is g/mL. Different substances can share a similar density, and temperature, purity and measurement error can alter comparisons.
A measurement supports a range rather than an infinitely exact value. Repeated trials, calibration records, and a controlled method help judge whether two results are distinguishable. A small difference comparable with uncertainty may not justify identifying a new material or a superior design.
Compare sample densities using the same temperature and procedure. If intervals overlap substantially, record an inconclusive comparison and propose a better measurement rather than forcing a ranking.
Pause and explain
What evidence would strengthen a small observed difference?
Check your reasoning after answering
Use calibrated instruments, more representative trials, and uncertainty estimates under comparable conditions to determine whether the difference is meaningful.
Apply the whole unit · Density with calibration evidence
Illustrative readings for a reference of 10.00 g are 10.20, 10.21, and 10.19 g. A separate sample has mass 12.4 g and volume 5.0 mL.
Your task
Calculate the reference mean and sample density, evaluate accuracy versus precision, report suitable digits, and propose how you would investigate the apparent balance bias without silently changing the sample measurement.
What your response should show
- Choose the appropriate chemical model or relationship and state its conditions.
- Show substitutions, units, particle or charge counts, and intermediate reasoning as relevant.
- Use supplied evidence to justify the conclusion; distinguish observation from inference.
- Identify a meaningful limitation, uncertainty, or next measurement.
Response guidance — after your attempt
Average reference readings: (10.20+10.21+10.19)/3=10.20 g.
Compare with 10.00 g: the mean is 0.20 g higher.
Calculate sample density: 12.4/5.0=2.48 g/mL before reporting precision.
Report 2.5 g/mL under the stated significant-figure convention.
The reference readings are tightly clustered but shifted upward, consistent with a systematic bias. The sample density calculation is 2.5 g/mL as reported, not a demonstrated corrected value. Verify calibration across the relevant mass range and record uncertainty before applying a correction; the supplied reference alone does not prove the same offset under every condition.
Scientific references and source-model foundations
Parent / teacher teaching notes
Check unit cancellation and sensible magnitude before significant figures. Separate raw data from any corrected data. Ask the student to explain the precision/accuracy distinction with a second example. Ask the learner to explain each particle symbol, axis, unit and arrow before calculating. Distinguish hypothetical models and calculated curves from measured records. Public OpenSciEd excerpts here are selected foundation prompts, not complete high-school teacher editions or an endorsement. All required advanced explanations and practice are provided locally.
The key idea
Units, precision, and a stated method make numerical evidence interpretable.
Worked examples
Example 1
- Write ρ = m/V.
- Substitute 24.0 g / 8.00 mL.
- Three significant figures are appropriate.
Example 2 · Worked application
- Multiply 2.40×1.2=2.88 cm².
- The width has two significant figures, limiting this product.
- Round the final result once to two significant figures.
Unit conversion and significant figures are different checks.
Example 3
- 250. mL × (1 L/1000 mL).
- The mL units cancel; the conversion is exact.
Example 4 · Find and fix the mistake
- Test the claim against the stated conditions: Unit conversion and significant figures are different checks.
- Reported precision must reflect the measurements; calculation cannot add information that was not measured.
Unit conversion and significant figures are different checks.
Example 5 · Reason from the visual model
- An instrument’s resolution is the smallest change it can distinguish or display; an analog scale usually supports an estimated digit beyond its marked intervals. That does not make every last digit exact. In classroom significant-figure rules, a multiplication result follows the least precise measured factor in significant figures. Addition and subtraction instead follow decimal-place precision. Keep guard digits while calculating and round once at the end; extra calculator digits cannot improve the original measurement.
- The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.
Original schematic ruler and independent area calculation. The marker illustrates interpolation rather than supplying the dimensions for that area problem.
Avoid these mistakes
- Precision does not guarantee accuracy, and extra calculator digits do not improve a measurement.
Check your understanding
Explain how density units arise and how you would check an unlikely result.
Discuss the answer
Divide mass by volume; g divided by mL gives g/mL. Check units, scale zero, volume subtraction, repeats, and a plausible reference.
Return to the phenomenon
Return to the initial case. Can a very repeatable result still be wrong? Revise your drawing or explanation using two named ideas and one stated limitation.
Compare explanations after your attempt
Repeatability concerns spread; agreement with a reference concerns accuracy. Calibration and conditions can introduce bias even when readings cluster.
What should we investigate next?
Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.
Investigate, calculate and revise
Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.
Activity 1 · Return to the opening case
Use the opening phenomenon, unit definitions and explained Parts 1–4.
Your task
Return to the initial case. Can a very repeatable result still be wrong? Revise your drawing or explanation using two named ideas and one stated limitation.
Success criteria
- Use the stated observations and appropriate units.
- Connect a labeled model with the chemical mechanism.
- State assumptions and an evidence limitation.
- Explain a substantive revision or next test.
Hint
Keep species identity, material transfer and energy account distinct.
Response guidance — discuss after your attempt
Repeatability concerns spread; agreement with a reference concerns accuracy. Calibration and conditions can introduce bias even when readings cluster.
Activity 2 · Transfer to a changed case
Cover the worked answer and use the explained models, relationships and notebook.
Your task
An unknown has mass 37.5 g at volume 15.0 mL. Three repeat densities cluster near 2.50 g/mL, but the independently certified reference is 2.80 g/mL. Calculate density and explain the evidence limits.
Success criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the chemical mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.
Hint
Name known quantities and conditions, show intermediate steps and check conservation.
Response guidance — discuss after your attempt
Density is 37.5/15.0 = 2.50 g/mL. Repetition supports precision, but the difference from 2.80 suggests a method/reference comparison issue; check calibration, conditions and uncertainties rather than claim identity from one property.
Words to know
- density
- Mass per unit volume, usually g/mL for liquids or g/cm³ for solids.
- systematic error
- A recurring offset caused by a method or instrument.
- significant figures
- Digits used to communicate the precision of a measurement.
In the real world
Use the chapter investigation to connect this unit to measured evidence and a practical decision.
Exit check
Explain how density units arise and how you would check an unlikely result.
Check your explanation after answering
Divide mass by volume; g divided by mL gives g/mL. Check units, scale zero, volume subtraction, repeats, and a plausible reference.
Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.
Problem 1
Hints
Write the relationship first; substitute with consistent units.
Answer and explanation
2.8 g/mL
42.0/15.0 = 2.80.
Problem 2
Answer and explanation
Precise, but inaccurate relative to the reference; investigate calibration or consistent method bias.
Response criteria
- State a scientifically accurate conclusion.
- Show the calculation or mechanism that supports it.
- Include units, conditions, or limits where relevant.
Problem 3
Hints
List the given quantities, select a relationship, and check units before substituting.
Answer and explanation
3 g/mL
18.0/6.00=3.00.
Problem 4
Answer and explanation
Measure mass on a calibrated balance; record initial and final water volumes, subtract for displaced volume, repeat, and note trapped-air or scale-reading uncertainty.
Response criteria
- State a scientifically accurate conclusion.
- Show the calculation or mechanism that supports it.
- Include units, conditions, or limits where relevant.
Problem 5
Hints
Unit conversion and significant figures are different checks.
Answer and explanation
35.0 g; the exact conversion factor 1000 g/kg does not reduce the three significant figures.
Problem 6
Hints
State what the supplied observations or conditions establish, and separate that from any assumption.
Answer and explanation
The readings agree closely, indicating precision; their offset from the reference suggests lower accuracy or systematic error.
Problem 7
Answer and explanation
The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.
An instrument’s resolution is the smallest change it can distinguish or display; an analog scale usually supports an estimated digit beyond its marked intervals. That does not make every last digit exact. In classroom significant-figure rules, a multiplication result follows the least precise measured factor in significant figures. Addition and subtraction instead follow decimal-place precision. Keep guard digits while calculating and round once at the end; extra calculator digits cannot improve the original measurement.
The 1.2 cm input has two significant figures. The additional displayed calculator digits are unsupported measurement precision.
Response criteria
- Interpret labels, structures, axes, units and directions correctly.
- Explain the chemistry relationship or mechanism.
- Respect stated assumptions and distinguish observation from inference.
Problem 8
Answer and explanation
Density is 37.5/15.0 = 2.50 g/mL. Repetition supports precision, but the difference from 2.80 suggests a method/reference comparison issue; check calibration, conditions and uncertainties rather than claim identity from one property.
Density is 37.5/15.0 = 2.50 g/mL. Repetition supports precision, but the difference from 2.80 suggests a method/reference comparison issue; check calibration, conditions and uncertainties rather than claim identity from one property.
Response criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the chemical mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.