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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...

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...

Finding Rules for Number Sequences

If a sequence continued for a thousand terms, could its thousandth term be identified without writing out the other 999? Open Full Article...

Straight-Line Graphs and Their Equations

Why can points that look almost identical belong to different graphs? Open Full Article...

Expanding and Factorising Algebraic Expressions

How can 3(x + 4) and 3x + 12 look different yet represent the same value? Open Full Article...

Solving Equations by Balancing Both Sides

If two sides have the same value, what does the equals sign actually tell us? Open Full Article...

How Variables Represent Unknown Values in Algebra

A number is hidden in the statement □ + 3 = 8, yet the relationship is already clear. Open Full Article...