# Measurement tools for IB Mathematics experiments

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Choose equipment purposefullyMeasurement tools for IB Mathematics experiments
Measuring equipment does not automatically make an IA strong. The measured quantity must match the research question, the data must be reproducible, and you must explain resolution, accuracy, uncertainty and limitations. This guide connects common devices with mathematical methods and possible topic directions.
Basic measurementsTemperature, light and environmentElectrical, mechanical and acousticPhone, camera and trackingSensors and school laboratoryModelling, software and data
Start with the quantity
Which variable actually answers your question?
Separate resolution and accuracy
A display in 0.1 increments does not automatically prove ±0.1 accuracy.
Calibrate and pilot
Run a short pilot before collecting the full series.
Repeat
Multiple trials reveal variation, outliers and uncertainty.
Preserve raw data
Keep original files, settings and timestamps traceable.
Safety and privacy
Heat, electricity, sport, personal or health data require additional safeguards.
From device to research questionPlan the variable, sampling interval and analysis together.
Question: Which relationship or model will be investigated?
Measurement plan: Which values, intervals, controls and repetitions are needed?
Mathematics: Which functions, regressions, distributions or optimisations answer the question?
Reflection: How do measurement error and model assumptions affect the result?
See a complete practical example
The hibiscus-tea IA shows how temperature measurements, exponential models, regression and model criticism work together, including a detailed review.
Open the IA sample
Basic measurementsBasic measurements
↔Ruler, tape measure, calliper and protractor
What you can do with it
Use these tools to measure length, diameter, thickness, angle and geometric distance. A calliper is valuable when millimetres or tenths of a millimetre matter; a protractor supports projectile, light, solar and slope experiments.
Typical data
Length, angle, area, volume, ratio, measurement error
Mathematics
Geometry · Trigonometry · Regression · uncertainty
Example topics
Paper-aeroplane trajectory at different launch angles
Volume of irregular or solids-of-revolution objects
Solar-cell output as a function of incidence angle
Practical and safety notesRecord resolution and measurement method. Repeat readings and keep the same reference points.
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gScale and precision balance
What you can do with it
A kitchen scale is sufficient for gram-level readings; a precision balance is better for evaporation, filter residue, electrodes or small material samples. Mass time series can be analysed with linear, exponential or piecewise models.
Typical data
Mass, mass change, density, loss rate
Mathematics
Regression · calculus · statistics · uncertainty
Example topics
Evaporation rate of different liquids
Density of wood, plastics or solutions
Mass gained by filters or water absorbed by materials
Practical and safety notesUse the same container, tare before each run, and protect the balance from draughts and splashes.
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mLMeasuring cylinder, pipette and lab vessels
What you can do with it
Measuring cylinders provide reproducible volumes; pipettes are useful for small, accurately dispensed quantities. They support concentration series, density measurements and controlled flow or mixing experiments.
Typical data
Volume, concentration, flow, density
Mathematics
Proportionality · regression · differential equations · uncertainty
Example topics
Drainage time for different outlet areas
Density of water–ethanol mixtures
Effect of sugar concentration on flow rate
Practical and safety notesRead the meniscus at eye level. Chemicals and hot liquids require appropriate school-lab supervision and protection.
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⏱Stopwatch, timer and light gate
What you can do with it
Time measurement is central to motion, reaction, cooling, oscillation, flow and decay. A phone timer is enough for slow processes; video or a light gate is much better for short intervals.
Typical data
Time, period, travel time, reaction time
Mathematics
Kinematics · regression · statistics · periodicity
Example topics
Pendulum period as a function of length
Flow or drainage times
Learning curves and reaction-time distributions
Practical and safety notesSeparate device resolution from human reaction delay. Manual timing requires many repetitions.
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Temperature, light and environmentTemperature, light and environment
°CContact thermometer and temperature data logger
What you can do with it
A contact probe measures the temperature of an object, liquid or the air at the sensor. Data loggers record at fixed intervals, making them ideal for cooling, conduction, insulation and daily cycles.
Typical data
Temperature, temperature difference, rate of change, time constant
Mathematics
Exponentials · differential equations · regression · residual analysis
Example topics
Newton cooling of drinks
Insulation performance of cup materials
Temperature profiles in rooms or soil samples
Practical and safety notesCheck immersion depth, response time and calibration. A liquid probe should not touch the vessel wall.
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IRIR thermometer and thermal camera
What you can do with it
An IR thermometer measures surface temperature at a point without contact. A thermal camera produces spatial temperature fields for profiles, area means, cooling curves and image analysis.
Typical data
Surface temperature, temperature field, hotspots, spatial gradient
Mathematics
Regression · area analysis · interpolation · calculus
Example topics
Heat distribution around bearings after motion
Cooling of different cup surfaces
Comparison of insulation materials or windows
Practical and safety notesEmissivity, reflections and distance affect readings. Do not infer medical diagnoses from skin images; anonymise any personal imagery.
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RHHumidity, material-moisture and weather instruments
What you can do with it
Hygrometers, moisture sensors, anemometers, rain gauges and pressure sensors create environmental time series suitable for multiple regression, seasonal patterns and controlled comparisons.
Typical data
Relative humidity, wind, precipitation, pressure, material moisture
Mathematics
Time series · multiple regression · statistics · periodicity
Example topics
Humidity and evaporation rate
Local wind and heat loss
Material moisture and Wi-Fi attenuation
Practical and safety notesDo not expose sensors to sun or rain unless rated for it. Document a constant location and measurement height.
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lxLux meter, light sensor and solar sensor
What you can do with it
Lux meters measure illuminance; suitable solar sensors or multimeters can measure electrical output. They support inverse-distance models, angle of incidence, shading and daily cycles.
Typical data
Lux, irradiance, voltage, power, angle
Mathematics
Trigonometry · power models · regression · optimisation
Example topics
Solar-cell output at different angles
Light intensity and plant response
Illuminance distribution in classrooms
Practical and safety notesLux is weighted to human vision and is not identical to radiant power. Control sensor orientation and ambient light.
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Electrical, mechanical and acousticElectrical, mechanical and acoustic
VΩMultimeter and electrical meters
What you can do with it
A multimeter measures voltage, current and resistance. With a defined load it can support battery-discharge, internal-resistance, solar-cell and sensor-response investigations.
Typical data
Voltage, current, resistance, power, energy
Mathematics
Functions · regression · integration · optimisation
Example topics
Battery discharge curves
Internal resistance versus temperature
Solar-cell power versus light angle and distance
Practical and safety notesUse only safe low-voltage circuits. Connect current ranges correctly; mains electricity is not suitable for a student experiment.
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NForce sensor, spring balance and torque sensor
What you can do with it
These devices measure tension, compression, spring force and sometimes torque. Typical uses include Hooke’s law, friction, failure load, levers and optimisation of mechanical models.
Typical data
Force, extension, friction, breaking load, torque
Mathematics
Linear regression · optimisation · mechanics · uncertainty
Example topics
Spring constant and working range
Friction coefficient of different materials
Bending or breaking load of standard samples
Practical and safety notesDo not exceed rated loads. Fracture tests need eye protection, containment and competent supervision.
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dBMicrophone, sound-level meter and audio analysis
What you can do with it
Microphones provide waveforms and spectra; sound-level meters report levels in decibels. Software supports Fourier analysis, resonance, attenuation and reverberation time.
Typical data
Frequency, amplitude, decibels, spectrum, reverberation time
Mathematics
Sinusoids · Fourier analysis · logarithmic models · regression
Example topics
Resonance frequency of tubes
Sound attenuation by materials
Overtones of musical instruments
Practical and safety notesKeep microphone position and gain fixed. Protect hearing and avoid unnecessary sound levels.
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Phone, camera and trackingPhone, camera and tracking
fpsCamera and smartphone for photo/video analysis
What you can do with it
Video makes position, angle and time measurable frame by frame. Photographs support area fractions, symmetry, fractals, perspective and spatial interpolation. Include a calibration length in the image.
Typical data
Pixel coordinates, distance, velocity, angle, area
Mathematics
Kinematics · regression · geometry · image analysis
Example topics
Trajectory of a ball or paper aeroplane
Rotational motion in sport
Bubble fraction, leaf area or filter area from images
Practical and safety notesFix the camera, control perspective and record the frame rate. Obtain consent before recording people.
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a⃗Phone sensors: accelerometer, gyroscope and magnetometer
What you can do with it
Many phones record acceleration, angular velocity and magnetic field. This supports oscillation, rotation, travel, inclination and relative field measurements.
Typical data
Acceleration, angular velocity, orientation, magnetic field
Mathematics
Vectors · periodicity · integration · power models
Example topics
Damping of a pendulum or vehicle
Magnetic field strength versus distance
Acceleration profiles during motion
Practical and safety notesDocument sensor axes and sampling rate, subtract background values and secure the phone safely.
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GPSGPS device and fitness tracker
What you can do with it
GPS and trackers provide position, distance, speed, elevation, time and sometimes heart rate. They support real motion datasets, routes, elevation profiles and statistical comparisons.
Typical data
Coordinates, distance, speed, elevation, time series
Mathematics
Vectors · geometry · regression · statistics
Example topics
Cycling speed and gradient
Route optimisation to school
Pacing and performance variation in running
Practical and safety notesGPS errors increase indoors and near tall buildings. Protect privacy and do not publish precise home or health data.
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♥Non-invasive physiology sensors
What you can do with it
Heart-rate, reaction-time or simple breathing sensors can record temporal patterns and differences between conditions. They are for low-risk observation, not diagnosis or self-intervention.
Typical data
Heart rate, reaction time, breathing period, recovery curve
Mathematics
Statistics · regression · exponentials · hypothesis tests
Example topics
Recovery after standardised light activity
Reaction time under different conditions
Periodic modelling of breathing
Practical and safety notesConsent, anonymisation and school rules are essential. Do not conduct risky exertion, medication trials or diagnoses.
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Sensors and school laboratorySensors and school laboratory
pHpH, conductivity and salinity meter
What you can do with it
These sensors quantify properties of solutions, enabling calibration curves, concentration models, temperature corrections and time-dependent mixing or reaction studies.
Typical data
pH, conductivity, salinity, concentration
Mathematics
Logarithms · regression · calibration · uncertainty
Example topics
Conductivity of rainwater samples
Salinity and sound or freezing properties
pH during dilution or neutralisation
Practical and safety notesUse only safe substances and school-appropriate concentrations. Rinse and calibrate probes and document temperature dependence.
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CO₂CO₂ sensor and indoor-air data logger
What you can do with it
A suitable NDIR CO₂ sensor records concentration, often with temperature and humidity, over time. It supports rise, decay and air-exchange models.
Typical data
CO₂ concentration, rate of change, time constant, air exchange
Mathematics
Exponentials · differential equations · multiple regression · time series
Example topics
CO₂ decay after room occupancy
Window opening and ventilation effectiveness
Light intensity and net plant CO₂ exchange
Practical and safety notesDo not deliberately enrich occupied rooms with CO₂ or seal people inside. Record warm-up time, drift and sensor position.
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LABSpecialist school-lab equipment
What you can do with it
Light gates, ultrasonic sensors, force plates, spectrometers, magnetic stirrers or precise data loggers can support demanding questions. A device is useful only when its measurement matches the research question and its operation is understood.
Typical data
Device-specific data at high temporal or spatial resolution
Mathematics
depending on experiment: calculus · statistics · differential equations · spectral analysis
Example topics
Speed of sound in water
Induced voltage from a moving magnet
Controlled thermal or flow experiments
Practical and safety notesAgree access with the teacher. Test limits, calibration, safety rules and data export before the main data collection.
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Modelling, software and dataModelling, software and data
3DPhysical model, material samples and 3D printer
What you can do with it
Models provide controlled geometry, interchangeable parameters and repeatable trials. A 3D printer can produce channels, blades, vessels, bridges, tessellations or sensor mounts.
Typical data
Geometry, dimensions, load, flow, optimisation parameters
Mathematics
Geometry · optimisation · scaling · simulation
Example topics
Channel cross-section and discharge
Bridge curvature and material use
Water-wheel blade angle
Practical and safety notesDocument print settings and dimensional error. Physical models simplify reality; those assumptions belong in the reflection.
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ƒ(x)Computer, spreadsheet, CAS, GeoGebra, Desmos and Python
What you can do with it
These tools store data, run regressions, create graphs, calculate residuals, simulate random processes and solve equations numerically. They do not replace an explanation of the mathematics.
Typical data
Tables, models, parameters, simulations, graphs
Mathematics
Regression · simulation · numerical methods · optimisation
Example topics
Nonlinear regression of a cooling curve
Monte Carlo simulation of Buffon’s needle
Comparison of sorting or graph algorithms
Practical and safety notesDocument formulas, data ranges, software version and settings. Explain central results rather than presenting black-box output.
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SSDSSD, SATA docking station and data backup
What you can do with it
The photographed device is not a sensor; it is a SATA docking station with a KingSpec SSD inserted. It is useful for securely storing, versioning and transferring large video, thermal-image, audio or sensor datasets. A traceable folder structure can be as important as the measuring device.
Typical data
Raw data, image sequences, video, audio, scripts, analysis versions
Mathematics
Data management · reproducibility · versioning · sample checking
Example topics
High-frame-rate video of a trajectory
Thermal-image time series with many frames
AI classification using a self-collected image dataset
Practical and safety notesVerify the drive model and backups before initialising or formatting. Keep at least two copies and encrypt or anonymise personal data. The exact dock model is not legible in the photograph.
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Equipment is only one partThe mathematical decision remains central.
An expensive sensor does not replace a clear research question or transparent mathematics. A ruler or phone may be enough for a strong paper when experimental design, analysis and reflection are convincing.
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Before buying or borrowing
Check data export
Check range and resolution
Test drivers and software
Confirm school safety approval