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Short, reusable ideas for when a tool mentions something useful: complex numbers, binary, graphs, proof, modelling and more.
Iteration
Repeating a rule and watching what happens next.
Start with 2. Multiply by 2 and add 1 each time.
Open ideaRecursion
Building the next case from earlier cases.
Make a sequence where each term is double the previous term.
Open ideaComplex numbers
Numbers with a real part and an imaginary part.
The number 3 + 2i means 3 steps across and 2 steps up.
Open ideaBinary
A way to represent numbers using only 0 and 1.
In binary, 1011 means 8 + 0 + 2 + 1.
Open ideaGraph theory
Studying dots and the connections between them.
Draw four dots. Join A to B, B to C and C to D.
Open ideaAlgorithms
Clear step-by-step methods for solving a problem.
Look through a list and keep track of the smallest number seen so far.
Open ideaProbability
Measuring how likely an outcome is.
A fair coin has two equally likely outcomes.
Open ideaSampling
Using part of a population to learn about the whole.
If you ask ten friends about a school issue, is that enough to know what the whole school thinks?
Open ideaMatrices
Number grids that can transform vectors and shapes.
Imagine every point of a square being moved by the same matrix rule.
Open ideaVectors
Quantities with size and direction.
The vector (3, 2) means move 3 right and 2 up.
Open ideaFunctions and graphs
Rules and pictures for relationships between quantities.
For the rule y = 2x + 1, try x = 0, 1, 2.
Open ideaModelling
Using mathematics to represent part of the world.
Distance = speed x time models a journey at constant speed.
Open ideaOptimisation
Finding the best option under constraints.
One route is shorter, another is quieter. Which is best?
Open ideaSymmetry
Structure that survives a movement or change.
Turn a square through 90 degrees around its centre.
Open ideaCoordinates
A way to describe position using numbers.
The point (4, 2) means 4 across and 2 up.
Open ideaProof
An argument showing why something must be true.
Try 3 + 5, 7 + 9 and 11 + 13.
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