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

Sumo

Age 7 to 11
Challenge Level Yellow star
  • Game

This game was invented by Tony Reeves who teaches at Christ's College in Brecon.

When Push Comes to Shove

  1. Sumo is a one dimensional representation of a Sumo wrestling bout.
  2. Each bout lasts a maximum of 6 turns.
  3. The ring is represented by a linear track seventeen spaces long.
  4. A counter is placed on the central space of the track at the start of the bout and is moved to the left or right depending on the outcome of each round.
  5. If the counter is pushed beyond the end of the track then the bout is over as one contestant has pushed his opponent out of the ring.
  6. Each player begins the game with 6 cards values 1 to 6 inclusive.
  7. Players simultaneously reveal their choice of card.
  8. If the cards are equal, no movement occurs.
  9. If the cards are not equal, the player selecting the larger value card pushes the token a number of spaces equal to:

    THE DIFFERENCE BETWEEN the two card values MULTIPLIED BY THE LOWER of the two card values.

Examples:

 Higher Card   Lower Card   Movement
6 4  (6 - 4) x 4 = 8 
5 2  (5 - 2) x 2 = 6 
4 3  (4 - 3) x 3 = 3 


A player wins a bout by either:
Pushing the counter off the opponent's end of the track.
Ending the six turns with the counter in the opponent's half of the track.

An interesting variant is the introduction of a zero card to the initial allocation.

You may also like

Traffic Lights

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

Daisy

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

Jumping Reindeer

A game for 1 person to develop stategy and shape and space awareness. 12 counters are placed on a board. Counters are removed one at a time. The aim is to be left with only 1 counter.

  • 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