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Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Ratio, Proportion & Rates of Change

Areas and Ratios

Age 16 to 18
Challenge Level Yellow starYellow star

Do you have enough information to work out the area of the shaded quadrilateral?

Mixing Paints

Age 11 to 14
Challenge Level Yellow starYellow star

Can you work out how to produce different shades of pink paint?

Mixing More Paints

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

Can you find an efficent way to mix paints in any ratio?

Dating Made Easier

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

If a sum invested gains 10% each year how long before it has doubled its value?

The Legacy

Age 14 to 16
Challenge Level Yellow starYellow star

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

All in a Jumble

Age 11 to 14
Challenge Level Yellow starYellow star

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Thousands and Millions

Age 11 to 14
Challenge Level Yellow starYellow star

Here's a chance to work with large numbers...

Speeding Boats

Age 14 to 16
Challenge Level Yellow star

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Mixing Lemonade

Age 11 to 14
Challenge Level Yellow star

Can you work out which drink has the stronger flavour?

Speed-time Problems at the Olympics

Age 14 to 16
Challenge Level Yellow star

Have you ever wondered what it would be like to race against Usain Bolt?

Nutrition and Cycling

Age 14 to 16
Challenge Level Yellow star

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Triathlon and Fitness

Age 11 to 14
Challenge Level Yellow starYellow star

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Olympic Measures

Age 11 to 14
Challenge Level Yellow star

These Olympic quantities have been jumbled up! Can you put them back together again?

Ratio, Proportion and Rates of Change - Short Problems

Age 11 to 16

A collection of short problems on ratio, proportion and rates of change.

Fractions Rectangle

Age 11 to 14
Challenge Level Yellow star

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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