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Simplifying Problems with Diagrams and Tables

A difficult-looking problem can become easier to reason about when its information is organised differently. Open Full Article...

Proving That an Answer Must Be True

What separates an answer that looks right from one that must be right? A correct result does not, by itself, show why it cannot be different. Open Full Article...

Finding Patterns and Testing Conjectures

If a pattern has worked every time it has been checked, must it always be true? Open Full Article...

Working Backwards from a Result

If you know where a calculation finished, can you reconstruct exactly where it started? Open Full Article...

Understanding Inequalities on Number Lines

If x is greater than 4, does that mean x has one answer or infinitely many possible values? Open Full Article...

Turning Word Problems into Mathematics

A paragraph about tickets can hide several different quantities and relationships. Open Full Article...

Using Algebra to Prove a Pattern

If a pattern works for the first ten examples, how do we know it will still work for the millionth? Open Full Article...

Quadratic Equations and Their Graphs

Why does one equation involving x produce a straight line, while another produces a curve? Open Full Article...

Rearranging Formulae Without Guesswork

A formula can give speed when the quantity needed is distance, yet the relationship remains unchanged. Open Full Article...

Solving Simultaneous Equations

If two equations describe the same two unknown quantities, how can both equations help us pin down one exact pair of values? Open Full Article...