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Place Value in Very Large and Very Small Numbers

Place value explains how a digit gains meaning from its position in a number. The same digit can represent a very large amount or a tiny fraction of one. Open Full Article...

Negative Numbers in Real-Life Contexts

A temperature of -3°C is warmer than -8°C because -3 is higher on the number line. Open Full Article...

Converting Recurring Decimals into Fractions

If 0.333333... never ends, how can it be exactly equal to the simple fraction 1/3? Open Full Article...

Ratio in Maps, Recipes and Scale Drawings

What connects a recipe, a map and a drawing of a room? Each changes quantities while preserving a relationship between corresponding parts. Open Full Article...

Direct and Inverse Proportion: Understanding How Quantities Change Together

If 3 cinema tickets cost £18, would 6 tickets cost £36? If 4 people take 6 hours to complete a job, would 8 people necessarily take 12 hours? Open Full Article...

Reverse Percentages Explained: Finding the Original Value

If a jumper costs £80 after a 20% discount, why is the original price not £100 simply because we add 20% back? Open Full Article...

Percentage Increase and Decrease: Understanding How Values Change

Why does a 10% rise in a £50 price not add £10? The answer depends on the value used as the reference whole. Open Full Article...

Fractions Inside Reverse Calculations: Finding the Original Amount

If 1/4 of a number is 6, how can we work backwards to discover the whole number? Open Full Article...