Interactive maths tools

Every tool here is free, needs no account, and works on a phone. They are built around the ideas students get stuck on most, and each one shows the working rather than just the answer.

Algebra and calculation

Working with letters, fractions and powers: the machinery every later chapter leans on.

• Ages 11 to 13Adding fractionsSee with bars why fractions need a common denominator, and what goes wrong without one.→
• Ages 12 to 14Solving equationsSolve with the balance method and see why the same move goes on both sides.→
• Ages 13 to 15Solving inequalitiesSee the answer on the number line and why the sign flips with a negative.→
• Ages 13 to 15Binomial squaresSee (a+b)², (a-b)² and a²-b² as areas, and why that 2ab is really there.→
• Ages 14 to 16Factoring quadraticsSee with a rectangle why sum and product works, method included.→
• Ages 13 to 15System of equationsTwo lines, one crossing point, with the opening steps of all three solving methods.→

Geometry and triangles

Lengths, angles and shape, from Pythagoras through to trigonometry in any triangle.

• Ages 13 to 15Pythagoras theoremDrag the triangle and watch the two small squares always fill the big one.→
• Ages 14 to 18Unit circleDrag the angle and see sin, cos and tan as lengths, with the exact values.→
• Ages 15 to 17Sine and cosine ruleDrag a triangle and watch both rules keep up, with Pythagoras as the special case.→

Functions and analysis

Graphs and what they do: straight lines, parabolas, waves, logarithms, derivatives and integrals.

• Ages 14 to 16Slope of a lineDrag two points and see Δy/Δx as a staircase, with the equation and the perpendicular alongside.→
• Ages 14 to 16Discriminant and parabolaSlide a, b and c and see D decide whether the parabola cuts, touches or misses the axis.→
• Ages 16 to 18LogarithmsSee a logarithm as an exponent, with the log rules read off as differences in height.→
• Ages 16 to 18Sine functionSlide a and b to see amplitude and period change, with the equation right beside it.→
• Ages 16 to 18Derivative and tangentDrag the point and watch the tangent tilt, with the secant closing in on it.→
• Ages 17 to 18Integral and Riemann sumPush the rectangle count up and watch the sum close in on the exact area.→

Statistics and probability

Reading a set of numbers, and working out how likely something is before it happens.

• Ages 14 to 16Probability treeClick a path and see how you multiply along branches and add across them.→
• Ages 15 to 18Boxplot and spreadType in your own numbers and watch the boxplot, the quartiles and both standard deviations move live.→
• Ages 17 to 18Binomial distributionSet n, p and k to see the bars and the formula, with the normal approximation alongside.→
• Ages 16 to 18Normal distributionDrag the bounds across the bell curve and read probability and z-scores straight off.→

Teachers, use these freely

You are welcome to use these in class, project them, or link to them from your school site. No account, no ads, nothing to install. A link back is appreciated but never required.