Lab
See the idea. Put it to the test.
956 practicals from Kindergarten to Year 12, in 9 subjects. A practical gives the idea, what you need, the steps, what you should see and a safety card. A teacher-led practical gives the idea and its hazards; its method is for tutors on the learning platform.
Review
Reviewed before publication (owner’s confirmation, 24 September 2026). That covers every practical here, and a practical’s page lists the sources its author read.
A safety card on every page
The risk, who supervises and the hazards. The 38 teacher-led practicals show their idea and hazards here; their materials, steps and sources, and any result, control or note that states a number or an amount, are for tutors and administrators on the learning platform.
School laboratory, not for home
207 practicals are medium or high risk. Each says so on its page: In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.
Curriculum references
Each practical lists the NSW syllabus outcomes and Australian Curriculum v9 codes it supports. They are references, not a verified or complete curriculum alignment.
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202 practicals
Mathematics · page 4 of 5
Compound interest as exponential growth, checked against Moneysmart
An amount that grows by a fixed percentage each period follows A = P(1 + r/n)^(nt), an exponential relationship whose graph curves upward, and the compounding frequency changes the outcome by a computable amount.
Calculation and dataLow riskCone and cylinder of equal base and height: three pours
A cone fills a cylinder of the same base and height exactly three times, which is the 1/3 in V = (1/3)πr²h.
PracticalLow riskLogarithmic scales: what one unit of earthquake magnitude means
On a logarithmic scale each step multiplies rather than adds, so one unit of earthquake magnitude is ten times the shaking amplitude and about 32 times the energy, and two magnitudes from a real catalogue can be compared as a ratio.
Calculation and dataLow riskMonty Hall with three cups: switching wins two times in three
When the host knows where the prize is and always reveals an empty cup, switching wins whenever the first pick was wrong, which is two times in three, and repeated trials make that visible against intuition.
Practical, model not builtLow riskNetworks from the school map: degrees, Euler trails and Euler's formula
A map of buildings and paths becomes a network of vertices and edges, and counting the vertices of odd degree decides whether every path can be walked exactly once, as Euler showed for the bridges of Königsberg.
Practical, model not builtLow riskThe angle in a semicircle: measured, traced with a paper corner and proved
Every angle subtended at the circumference by a diameter is a right angle, and conversely the corner of a right angle sliding against two fixed pins traces a semicircle on them as diameter, which a deductive proof with isosceles triangles explains.
Practical, model not builtLow riskTwo-way tables from a class survey: conditional probability in both directions
A two-way table of two categorical variables gives conditional probabilities by reading along a row or down a column, and P(A given B) is not P(B given A).
Practical, model not builtLow riskA 440 Hz tone on a phone oscilloscope: amplitude, period and transformations of sin x
A pure tone is a sine wave whose period is the reciprocal of its frequency, and changing volume, pitch or start time performs the dilations and translations the syllabus describes.
Practical, model not builtLow riskArea of the school oval from an aerial photograph by the trapezoidal rule
Slicing an irregular region into strips and treating each as a trapezium gives an area estimate that improves as the strips narrow, which is the idea behind the definite integral.
Practical, model not builtLow riskAverage speed from 20 m splits: Bolt's 9.58 s and your own 100 m
The gradient of a chord on a distance-time graph is an average speed, and shrinking the interval turns it into the instantaneous speed the derivative describes.
Practical, model not builtLow riskBeats from two close tones: a sum of sines rewritten as a product
Two tones a few hertz apart add to a tone whose loudness swells and fades, and the sum and difference expansions rewrite the sum as a product that predicts the beat rate exactly.
Practical, model not builtLow riskCooling curve of a cup of hot water: Newton's law of cooling
The rate at which a hot drink cools is proportional to how far its temperature sits above the room, which gives an exponential approach to room temperature.
Practical, model not builtMedium riskDistance to an inaccessible point by the sine rule
Two angles measured from the ends of a known baseline fix a triangle, and the sine rule turns that triangle into the width of a river or oval the learner never crosses.
Practical, model not builtMedium riskEarthquake magnitude: the 1989 Newcastle earthquake on a logarithmic scale
A one-unit step in earthquake magnitude multiplies the recorded wave amplitude by 10 and the energy released by about 32, which a logarithmic scale compresses into equal steps.
Calculation and dataLow riskEstimating 30 seconds: z-scores and the empirical rule on a class dataset
A class of time estimates gives a real dataset whose mean, median and mode can be compared, whose values convert to z-scores, and whose spread can be tested against the 68-95-99.7 rule.
Practical, model not builtLow riskFree fall on video: displacement, velocity and acceleration from frames
Velocity is the derivative of displacement and acceleration the derivative of velocity, and a dropped ball filmed at a known frame rate gives all three from real positions.
Practical, model not builtLow riskGalton board: ten left-or-right bounces, Pascal's triangle and the binomial distribution
A ball that goes left or right with equal chance at each of ten rows lands in bin k in C(10, k) ways out of 1024, so the bins fill in the proportions of Pascal's triangle.
Practical, model not builtLow riskGradient of a tangent as the limit of secant gradients
The derivative at a point is the limit of the gradient of a chord as the second point slides towards the first, which the learner sees both on a drawn curve and in a table.
Practical, model not builtLow riskHeight of a flagpole with a phone clinometer and a tape
An angle of elevation and a measured distance fix the height of an object the learner cannot reach, and the sensitivity of tan to an angle error decides how carefully to measure.
Practical, model not builtLow riskHeight of a tower from two ground stations: trigonometry in three dimensions
Two vertical right triangles sharing the tower and a horizontal triangle on the ground fit together in three dimensions, so an elevation from one station and the ground distances predict the elevation at the other.
Practical, model not builtLow riskHow much rain falls on the school roof: area from a scaled aerial photo and V = Ah
A depth of rain spread over a measured area is a volume, so 1 mm of rain on 1 square metre is 1 litre, and a roof's yearly catch follows from its scaled area and the local rainfall record.
Practical, model not builtLow riskIncome tax and the Medicare levy with the 2026-27 resident tax rates
Australian income tax is progressive: each rate applies only to the part of taxable income inside its bracket, so the average rate always sits below the top marginal rate.
Calculation and dataLow riskPendulum: period against length and rearranging T = 2 pi sqrt(L/g)
A formula becomes a relationship the learner tests by measurement: doubling the length does not double the period, and plotting L against T^2 gives a straight line whose gradient contains g.
Practical, model not builtLow riskProjectile motion: a marble off the table and a thrown ball on video
Horizontal motion at constant velocity and vertical motion under constant gravity combine into a parabola whose range and flight time follow from the launch speed and angle.
Practical, model not builtLow riskReaction times from the ruler drop: a class dataset for centre, spread and outliers
A variable measured by every learner becomes a real distribution whose mean, median, standard deviation, quartiles and outliers mean something because the learners produced it.
Practical, model not builtLow riskShared birthdays in a class: counting with permutations
The chance that nobody in a group shares a birthday is an ordered selection of distinct days divided by all possible selections, and it falls below one half at only 23 people.
Practical, model not builtLow riskSolar noon from a shadow: longitude, 15 degrees per hour and standard time
The sun is highest when it crosses the local meridian, so the clock time of solar noon, found halfway between two equal shadow lengths either side of it, shows how far the observer sits from the standard-time meridian, at 15 degrees of longitude per hour.
Practical, model not builtLow riskSound level against distance: the inverse-square law on a decibel scale
Sound intensity from a small source falls with the square of distance, and on the logarithmic decibel scale that appears as a fixed drop of about 6 dB for every doubling.
Practical, model not builtLow riskSun elevation from a shadow: inverse tan checked against Geoscience Australia
The ratio of a stick's height to its shadow passes through the inverse tangent to give the sun's elevation, and Geoscience Australia's calculator gives the same angle from astronomy.
Practical, model not builtLow riskThe open box: cut squares from a sheet and find the largest volume
A cubic volume function built from a real sheet has a maximum that calculus locates and a measured fill of rice confirms.
Practical, model not builtLow riskThe school grounds as a network: minimum spanning tree and shortest path from measured paths
Buildings joined by measured paths form a weighted network, in which a minimum spanning tree connects every building with the least total length and a shortest path may use edges the tree does not include.
Practical, model not builtLow riskThe sum of two dice: sample space, relative frequency and expected value
Thirty-six equally likely outcomes give the sum of two dice a triangular distribution, and relative frequencies from hundreds of real rolls settle towards it as the number of rolls grows.
Practical, model not builtLow riskThree cups and a coin: conditional probability and the stick-or-switch game
When a host who knows where the prize is always reveals an empty cup, switching wins two times in three, which a tree diagram predicts and 60 real trials confirm.
Practical, model not builtLow riskTide heights from Bureau of Meteorology predictions modelled by a cosine curve
Tide predictions for a harbour rise and fall close to a cosine curve whose period, amplitude and centre line the learner reads from real data, and whose equation then predicts later high waters.
Practical, model not builtLow riskWalking pace as a linear model, and time against speed as a reciprocal one
Steady walking gives distance in direct variation with time, the gradient is the speed, and the time for a fixed distance varies inversely with that speed.
Practical, model not builtLow riskWhat an appliance costs to run: measured energy in kilowatt-hours and the household bill
Power is a rate of energy use, so kilowatts multiplied by hours gives kilowatt-hours, and a measured kilowatt-hour figure multiplied by the tariff on a bill gives a running cost.
Practical, model not builtMedium riskWhy A4 is 210 by 297: the surd sqrt 2 and index laws in the A-series paper sizes
A sheet that keeps its shape when folded in half must have sides in the ratio sqrt 2 : 1, and fixing A0 at one square metre makes every A-size an exact power of 2 that the index laws predict.
Practical, model not builtLow riskA lift ride: integrating measured acceleration to find speed and height
The area under an acceleration-time graph is the change in velocity and the area under the velocity-time graph is the change in height, which a phone in a lift measures directly.
Practical, model not builtLow riskA reducing balance home loan and a credit card balance at current RBA rates
Each month a loan balance grows by interest and falls by the repayment, so a spreadsheet of the reducing balance shows why early repayments are mostly interest and why extra repayments save so much.
Calculation and dataLow riskA thrown ball as a vector-parametrised curve, with skew lines measured in the room
A position vector that depends on a parameter traces a curve, while a point and a direction vector describe a straight line, and the scalar product then settles how far a point lies from a line and whether two lines in three dimensions meet or pass each other.
Practical, model not builtLow riskA vector walk: adding displacements on bearings
Two legs walked on bearings add as vectors, and the resultant displacement the learner tapes back to the start is the vector sum, not the sum of the leg lengths.
Practical, model not builtLow riskBouncing ball: bounce heights as a geometric sequence with a limiting sum
Each bounce returns a fixed fraction of the previous height, so the heights form a geometric sequence and the total distance travelled is a finite limiting sum.
Practical, model not builtLow riskDice decay: exponential decay and half-life with 100 dice
When every item has the same chance of being removed each round, the number left falls by a constant fraction per round and halves after a fixed number of rounds.
Practical, model not builtLow riskDraining a funnel: related rates and Torricelli's law
When water drains from a cone through a small hole, the depth falls at a rate linked to the volume rate by the chain rule, and the link changes as the surface shrinks.
Practical, model not builtLow riskDrop height against bounce height: scatterplot, correlation and least-squares line
Two measured variables with a physical link give a scatterplot whose strength and direction a correlation coefficient measures and whose trend a least-squares line predicts, within the measured range only.
Practical, model not builtLow riskFilling vessels at a steady rate: height-time graphs for a cylinder and a cone
The same steady inflow gives a straight height-time graph in a cylinder and a curved one in a cone, because the rate of rise depends on the surface area at the current height.
Practical, model not builtLow riskHow fast does a car lose value: declining balance depreciation from advertised prices
A car loses a roughly constant fraction of its value each year, so real advertised prices by age follow a declining-balance curve rather than a straight line.
Practical, model not builtLow riskHow many people can leave per minute: network flow through measured doorways
The largest flow through a network of doorways and corridors is limited by its narrowest cut, so widening the wrong doorway changes nothing.
Practical, model not builtLow risk
For tutors and administrators
The materials and steps of every teacher-led practical are on the learning platform, with the safety card first. Sign in with a tutor or administrator account to read them.