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WillTeachMaths

Thinking-first maths tools

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Short, reusable ideas for when a tool mentions something useful: complex numbers, binary, graphs, proof, modelling and more.

RepetitionChangePattern

Iteration

Repeating a rule and watching what happens next.

Start with 2. Multiply by 2 and add 1 each time.

Open idea
RepetitionPattern

Recursion

Building the next case from earlier cases.

Make a sequence where each term is double the previous term.

Open idea
TransformationRepresentationRepetition

Complex numbers

Numbers with a real part and an imaginary part.

The number 3 + 2i means 3 steps across and 2 steps up.

Open idea
PatternRepresentation

Binary

A way to represent numbers using only 0 and 1.

In binary, 1011 means 8 + 0 + 2 + 1.

Open idea
ConnectionQEDReasoningOptimisation

Graph theory

Studying dots and the connections between them.

Draw four dots. Join A to B, B to C and C to D.

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ConnectionOptimisationQEDReasoning

Algorithms

Clear step-by-step methods for solving a problem.

Look through a list and keep track of the smallest number seen so far.

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ChanceRepresentationQEDReasoning

Probability

Measuring how likely an outcome is.

A fair coin has two equally likely outcomes.

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ChanceRepresentation

Sampling

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?

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TransformationRepresentation

Matrices

Number grids that can transform vectors and shapes.

Imagine every point of a square being moved by the same matrix rule.

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ChangeTransformationRepresentation

Vectors

Quantities with size and direction.

The vector (3, 2) means move 3 right and 2 up.

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ChangeRepresentationTransformation

Functions and graphs

Rules and pictures for relationships between quantities.

For the rule y = 2x + 1, try x = 0, 1, 2.

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ChangeChanceOptimisationRepresentation

Modelling

Using mathematics to represent part of the world.

Distance = speed x time models a journey at constant speed.

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OptimisationConnectionChange

Optimisation

Finding the best option under constraints.

One route is shorter, another is quieter. Which is best?

Open idea
PatternTransformationQEDReasoning

Symmetry

Structure that survives a movement or change.

Turn a square through 90 degrees around its centre.

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RepresentationTransformationChange

Coordinates

A way to describe position using numbers.

The point (4, 2) means 4 across and 2 up.

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QEDReasoningPatternConnection

Proof

An argument showing why something must be true.

Try 3 + 5, 7 + 9 and 11 + 13.

Open idea