Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

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

More Low Threshold High Ceiling Tasks

Unexpected Ordering

Age 5 to 7
Challenge Level Yellow star

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

Eightness of Eight

Age 5 to 7
Challenge Level Yellow star

What do you see as you watch this video? Can you create a similar video for the number 12?

Next-door Numbers

Age 5 to 7
Challenge Level Yellow star

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Ring a Ring of Numbers

Age 5 to 7
Challenge Level Yellow starYellow star

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Digit Addition

Age 5 to 11
Challenge Level Yellow star

Try out this number trick. What happens with different starting numbers? What do you notice?

I'm Eight

Age 5 to 11
Challenge Level Yellow star

Find a great variety of ways of asking questions which make 8.

Strike it Out

Age 5 to 11
Challenge Level Yellow star

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Dotty Six

Age 5 to 11
Challenge Level Yellow star

Dotty Six is a simple dice game that you can adapt in many ways.

Seeing Squares

Age 5 to 11
Challenge Level Yellow star

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

School Fair Necklaces

Age 5 to 11
Challenge Level Yellow starYellow star

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Magic Vs

Age 7 to 11
Challenge Level Yellow star

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Number Differences

Age 7 to 11
Challenge Level Yellow star

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Surprising Split

Age 7 to 11
Challenge Level Yellow star

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Subtraction Surprise

Age 7 to 14
Challenge Level Yellow star

Try out some calculations. Are you surprised by the results?

Consecutive Numbers

Age 7 to 14
Challenge Level Yellow star

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

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.

University of Cambridge logo NRICH logo