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.

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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.

48 activities

Mathematics 7–10

  1. Mathematics 7–10 · Year 7

    A transversal on parallel lines: measuring the three angle relationships

    When a transversal crosses parallel lines, corresponding angles are equal, alternate angles are equal and co-interior angles add to 180 degrees, and none of these hold when the lines are not parallel.

    PracticalLow risk
  2. Mathematics 7–10 · Year 7

    Angle sum of a triangle: torn corners on a straight line, checked with a protractor

    The three interior angles of any triangle, placed together, make a straight angle, so they sum to 180 degrees whatever the triangle's shape.

    PracticalLow risk
  3. Mathematics 7–10 · Years 7–8

    Drawing pins: a chance experiment with no theoretical answer

    When the outcomes of a trial are not equally likely, the only way to estimate a probability is from the relative frequency of many trials, and the estimate steadies as trials accumulate.

    PracticalLow risk
  4. Mathematics 7–10 · Years 7–8

    Hand span of the class: mean, median, mode, range and the effect of one outlier

    A continuous measurement collected from everyone in the room gives a distribution whose centre and spread can be summarised, and one extreme value moves the mean and the range while moving the median by at most half the gap between the two middle values.

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

    Interlocking cube models: top, front and side views and isometric drawings

    A solid built from cubes can be represented by its top, front and side views and by an isometric drawing, each of which shows some features and hides others, and outline views alone can fail to fix how many cubes a model contains.

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

    Matchstick growing patterns: from a table of values to a linear rule

    A growing row of squares adds the same number of sticks each time, so the count follows a rule of the form M = 3n + 1 that can be read from the structure, tabulated and plotted as points on a straight line that does not pass through the origin.

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

    Measuring pi: circumference divided by diameter for real round objects

    For every circle the circumference is the same multiple of the diameter, and that multiple, measured with string and a ruler, comes out a little over 3.

    PracticalLow risk
  8. Mathematics 7–10 · Year 7

    Parallelogram and triangle area by cutting and rearranging

    A parallelogram cut along a perpendicular height and rearranged becomes a rectangle with the same base and height, so its area is base × height whatever its slant, and any triangle is half of the parallelogram made from two copies of it.

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

    Rates from timed walking: a distance-time graph from real data

    Speed is a rate, distance per unit time, and it appears as the gradient of a distance-time graph drawn from stopwatch readings taken at measured marks.

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

    Reaction time from a falling ruler: a formula, a table of values and class data

    The distance a ruler falls before it is caught converts to a reaction time through the formula t = sqrt(2d/g), and repeating the catch gives a data set whose centre and spread can be compared between people or conditions.

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

    Rolling one die: relative frequency settles towards one sixth

    The relative frequency of a face on a fair die wanders in a short run and settles towards the theoretical probability of 1/6 as the number of rolls grows, and the complement (not a six) settles towards 5/6.

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

    Scale drawing of the classroom at 1:50

    A ratio of 1:50 turns every measured length in the room into a drawn length one fiftieth as long, and every drawn length back into a real one by multiplying by 50.

    PracticalLow risk
  13. Mathematics 7–10 · Year 7

    Square numbers and square roots with tiles

    A number is a perfect square when its tiles form a square array, its square root is the side of that array, and a number with tiles left over has a square root between two whole numbers.

    PracticalLow risk
  14. Mathematics 7–10 · Years 7–8

    Volume of a rectangular prism: packing centicubes and filling with water

    The volume of a prism is the number of unit cubes in one layer times the number of layers, and 1 cubic centimetre holds 1 millilitre, so a box measured in centimetres predicts the water it holds.

    Practical, model not builtLow risk
  15. Mathematics 7–10 · Year 8

    A dripping tap: measuring a rate and scaling it to litres per day and per year

    A rate compares two quantities with different units, so a volume collected in a measured time gives millilitres per minute, which is the gradient of a straight volume-time graph and scales by unit conversion to litres per day and per year.

    Practical, model not builtLow risk
  16. Mathematics 7–10 · Year 8

    Area and perimeter of a composite outdoor space, measured with a tape and trundle wheel

    The area of an irregular site is found by dissecting it into rectangles, triangles and trapeziums whose dimensions are measured; two different dissections must give the same total, and the perimeter is measured and computed separately because area and perimeter do not change together.

    Practical, model not builtLow risk
  17. Mathematics 7–10 · Year 8

    Area of a circle: cutting sectors into a near-rectangle

    A circle cut into many equal sectors and laid alternately point up and point down forms a shape close to a rectangle with height r and base half the circumference, which is where A = πr² comes from.

    PracticalLow risk
  18. Mathematics 7–10 · Year 8

    Pythagoras by measurement: squares on dotty paper and a 3-4-5 rope

    The square on the hypotenuse has the same area as the two squares on the other sides, which can be counted on dotty paper and checked with a tape measure on a knotted rope that forms a right angle.

    Practical, model not builtLow risk
  19. Mathematics 7–10 · Year 8

    Random samples from a known population: how sample size changes the spread of sample means

    Samples drawn at random from the same population give different means, and the means of larger samples cluster more closely around the population mean, so the spread of the sample means shrinks as the sample size grows.

    Practical, model not builtLow risk
  20. Mathematics 7–10 · Year 8

    Volume of a cylinder: formula, measuring cylinder and displacement

    The volume computed from πr²h agrees with the water a cylindrical container holds and with the water an equal solid displaces, tying a formula to two independent measurements.

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

    Box plots of reaction time: dominant against non-dominant hand

    A five-number summary and a box plot let two sets of measurements be compared on centre, spread, shape and outliers in one display.

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

    Buffon's needle: estimating pi by dropping toothpicks on ruled lines

    When toothpicks as long as the line spacing are scattered at random over ruled lines, the long-run proportion that cross a line is 2/π (Buffon's 1777 result, whose proof needs calculus and is taken as given here), so the relative frequency of crossings estimates 2/π and hence pi, and the estimate tightens as drops accumulate.

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

    Climate Data Online: daily maximum temperatures for two months compared

    A public data set of daily observations can be downloaded, summarised and displayed so that two distributions are compared on centre, spread, shape and outliers with the real numbers behind them.

    PracticalLow risk
  24. Mathematics 7–10 · Year 9

    Compass constructions: bisectors and an equilateral triangle, then measured

    Constructions made with a compass and straight edge produce equal lengths and equal angles by design, and measuring the result with a ruler and protractor confirms the properties the construction guarantees.

    PracticalLow risk
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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

For tutors and administrators

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