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

Short problems for Starters, Homework and Assessment


The links below take you to a selection of short problems based on UKMT junior and intermediate mathematical challenge questions. We have chosen these problems because they are ideal for consolidating and assessing subject knowledge, mathematical thinking and problem-solving skills. You may wish to use these as lesson starters, homework tasks, or as part of internal assessment exercises.

Longer NRICH problems can be found on the Secondary Curriculum page.
Age 11 to 16

Number - Short Problems

A collection of short Stage 3 and 4 problems on number.

Age 11 to 16

Algebra - Short Problems

A collection of short Stage 3 and 4 problems on algebra.

Age 11 to 16

Geometry and Measure - Short Problems

A collection of short Stage 3 and 4 problems on geometry and measure.

Age 11 to 16

Handling Data - Short Problems

A collection of short Stage 3 and 4 problems on handling data.

Age 11 to 16

Working Mathematically - Short Problems

A collection of short Stage 3 and 4 problems on Working Mathematically.

  • 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