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

Transferring

In the third stage of the problem-solving process, learners are aiming for generalisation and possibly proof.  (See the article Mastering Mathematics: The Challenge of Generalising and Proof.)  A key skill in moving towards generalisation and proof is being able to transfer your thinking from one example to another new example.  Similarities and differences between the two cases may become apparent.  Exploring further examples means that strategies might emerge which always work, which is the essence of a generalisation. 

The tasks below provide opportunities for learners to get better at transferring their thinking.

Two-digit Targets

Age 5 to 7
Challenge Level Yellow star

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Secret Number

Age 5 to 7
Challenge Level Yellow starYellow star

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Dotty Six

Age 5 to 11
Challenge Level Yellow star

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

Display Boards

Age 7 to 11
Challenge Level Yellow starYellow star

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Curious Number

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Dice in a Corner

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

  • 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