Concept Studio

See the idea. Put it to the test.

956 activities from Kindergarten to Year 12, in 13 subject areas. A practical gives the idea, what you need, the steps, what you should see and a safety card. A teacher-led demonstration 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 activity 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 demonstrations 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 activities 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 activity lists the NSW syllabus outcomes and Australian Curriculum v9 codes it supports. They are references, not a verified or complete curriculum alignment.

Find an activity

A practical is carried out at the bench, in the classroom or outdoors. A practical with its model not built stands on its own; the page says where a step mentions the model. A calculation and data activity works from published figures by hand, with a calculator or in a spreadsheet. No page includes an interactive model.

956 activities

Every subject and year · page 16 of 20

  1. Mathematics 7–10 · Years 9–10

    Enlargement on grid paper: lengths scale by k, areas by k squared

    An enlargement from a centre multiplies every length by the scale factor and every area by the square of it, and counting squares on the enlarged figure shows the square.

    PracticalLow risk
  2. Mathematics 7–10 · Year 9

    Fifty coin tosses: real randomness has long runs

    Genuine random sequences contain longer runs of the same outcome than people expect, so the length of the longest run separates real tosses from invented ones.

    Practical, model not builtLow risk
  3. Mathematics 7–10 · Years 9–10

    Galileo's ramp: a rolling ball's distance grows with the square of the time

    A ball rolling from rest down a straight incline covers a distance proportional to the square of the elapsed time, so the distance-time graph is half a parabola, distance against time squared is a straight line, and the distances in successive equal intervals go 1 : 3 : 5 : 7.

    Practical, model not builtLow risk
  4. Mathematics 7–10 · Year 9

    Gradient of a real ramp: rise over run with a spirit level, checked by angle

    The gradient of a straight ramp is its vertical rise divided by its horizontal run, the same at every point along it, and it can be written as a ratio 1 : n, as a percentage and as an angle whose tangent is the gradient.

    PracticalLow risk
  5. Mathematics 7–10 · Years 9–10

    Height and arm span: a scatterplot and a line of best fit by eye

    Two measurements taken from each person form points whose pattern shows the direction, strength and linearity of their association, and a line of best fit drawn by eye lets one be predicted from the other, with predictions outside the measured range treated as less reliable.

    Practical, model not builtLow risk
  6. Mathematics 7–10 · Year 9

    Height from shadows: similar triangles with a metre stick

    At one moment the sun makes the same angle for every vertical object, so a metre stick and a tree with their shadows form similar triangles and the tree's height follows from one ratio.

    PracticalLow risk
  7. Mathematics 7–10 · Years 9–10

    Height of a building with a clinometer: angle of elevation, distance and eye height

    The tangent ratio turns a measured angle of elevation and a measured horizontal distance into a height that cannot be measured directly, and the error in the answer depends on how well the angle was read.

    Practical, model not builtLow risk
  8. Mathematics 7–10 · Years 9–10

    Measurement error: the same desk with three instruments and what it does to the area

    Every measurement is an estimate with an absolute error of half the smallest unit on the instrument for each reading, and those errors carry through into any area or volume computed from them.

    Practical, model not builtLow risk
  9. Mathematics 7–10 · Year 9

    Solar system to scale on the oval: scientific notation and a 5.75 billion to one scale

    Dividing distances of hundreds of millions of kilometres by one scale factor turns them into paces on the oval, and writing both in scientific notation keeps the powers of ten under control.

    Practical, model not builtLow risk
  10. Mathematics 7–10 · Year 9

    Stacking cups: a linear relationship with a measured gradient and intercept

    The height of a stack of identical cups grows by the same amount for every cup added, so height against number of cups is a straight line whose gradient is the lip height and whose intercept is the cup body below the lip.

    Practical, model not builtLow risk
  11. Mathematics 7–10 · Year 9

    Sum of two dice: 36 equally likely pairs, 11 unequal totals

    A two-stage experiment has a sample space of ordered pairs; counting the pairs that give each total explains why 7 is the most frequent sum and 2 and 12 the rarest.

    Practical, model not builtLow risk
  12. Mathematics 7–10 · Year 9

    Surface area of a cylinder: peeling the label off a tin

    The curved surface of a cylinder unrolls into a rectangle whose length is the circumference and whose height is the cylinder's height, so the surface area is 2πr² + 2πrh.

    PracticalLow risk
  13. Mathematics 7–10 · Year 9

    Two draws from a bag: with and without replacement, tree diagram against 100 trials

    Whether the first marble goes back changes the probabilities on the second branch of the tree, and the difference shows up in the relative frequencies of a hundred real draws.

    Practical, model not builtLow risk
  14. Mathematics 7–10 · Year 9

    Which three measurements fix a triangle: congruence tests by construction

    Triangles constructed from three sides, two sides and the included angle, two angles and a side, or a right angle with the hypotenuse and a side always match when overlaid, while three angles fix only the shape and two sides with a non-included angle can give two different triangles; the same tests explain why a diagonal splits a parallelogram into two congruent triangles.

    Practical, model not builtLow risk
  15. Mathematics 7–10 · Year 9

    Why the trigonometric ratios are constant: measuring similar right-angled triangles

    Right-angled triangles that share one acute angle are similar, so the ratio opposite over adjacent is the same for all of them, and that shared number is the tangent of the angle.

    Practical, model not builtLow risk
  16. Mathematics 7–10 · Year 10

    Bouncing ball: rebound heights as an exponential decay

    Each bounce returns a fixed fraction of the height it fell from, so successive rebound heights form a geometric sequence and the graph of height against bounce number is an exponential decay rather than a straight line.

    Practical, model not builtLow risk
  17. Mathematics 7–10 · Year 10

    Catch-up walkers: when and where two measured walks draw level

    Two steady walks are two linear equations in time and distance, and the time and place at which the walkers draw level is their simultaneous solution, found algebraically or as the intersection of their graphs and then tested on the track.

    Practical, model not builtLow risk
  18. Mathematics 7–10 · Year 10

    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 risk
  19. Mathematics 7–10 · Year 10

    Cone 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 risk
  20. Mathematics 7–10 · Year 10

    Logarithmic 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 risk
  21. Mathematics 7–10 · Year 10

    Monty 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 risk
  22. Mathematics 7–10 · Year 10

    Networks 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 risk
  23. Mathematics 7–10 · Year 10

    The 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 risk
  24. Mathematics 7–10 · Year 10

    Two-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 risk
  25. Mathematics 11–12 · Years 11–12

    A 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 risk
  26. Mathematics 11–12 · Years 11–12

    Area 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 risk
  27. Mathematics 11–12 · Years 11–12

    Average 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 risk
  28. Mathematics 11–12 · Years 11–12

    Beats 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 risk
  29. Mathematics 11–12 · Years 11–12

    Cooling 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 risk
  30. Mathematics 11–12 · Years 11–12

    Distance 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 risk
  31. Mathematics 11–12 · Years 11–12

    Earthquake 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 risk
  32. Mathematics 11–12 · Years 11–12

    Estimating 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 risk
  33. Mathematics 11–12 · Years 11–12

    Free 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 risk
  34. Mathematics 11–12 · Years 11–12

    Galton 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 risk
  35. Mathematics 11–12 · Year 11

    Gradient 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 risk
  36. Mathematics 11–12 · Years 11–12

    Height 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 risk
  37. Mathematics 11–12 · Year 11

    Height 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 risk
  38. Mathematics 11–12 · Years 11–12

    How 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 risk
  39. Mathematics 11–12 · Year 11

    Income 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 risk
  40. Mathematics 11–12 · Year 11

    Pendulum: 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 risk
  41. Mathematics 11–12 · Years 11–12

    Projectile 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 risk
  42. Mathematics 11–12 · Year 11

    Reaction 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 risk
  43. Mathematics 11–12 · Year 11

    Shared 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 risk
  44. Mathematics 11–12 · Year 11

    Solar 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 risk
  45. Mathematics 11–12 · Years 11–12

    Sound 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 risk
  46. Mathematics 11–12 · Years 11–12

    Sun 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 risk
  47. Mathematics 11–12 · Years 11–12

    The 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 risk
  48. Mathematics 11–12 · Year 11

    The 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 risk

For tutors and administrators

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