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

Odds or Sixes?

Age 7 to 11
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Odds or Sixes?

Tania and Derek are playing a game with a dice.

They roll the dice. If the number is odd, Tania wins that round.
If the number is a six, Derek wins.
(It doesn't matter who throws the die.)


Who is more likely to win the game? Why? How could you make the game fair?

 

Why do this problem?

This problem gives learners the opportunity to describe and predict outcomes, and consider the meaning of 'fair'. 

 

Possible approach

You could introduce this problem either by having two children come to the front to play it. Whichever way you choose, play the game a few times and record the outcomes on the board. Ask the class to predict what would happen if the game was played many times, for example $100$ times. Take suggestions from the children, looking out for those who justify their answer based on the few games which have already been played.

 
Suggest that the group tests out their theories. This could be done by pairs throwing dice and then collating class results. Bring pupils together to talk about their findings and ask them whether the game is fair or not and why. Listen out for explanations which compare the number of possible winning throws using appropriate vocabulary. Some children might quantify the probability of throwing a six, for example, as $1$ out of $6$ or $\frac{1}{6}$ whereas throwing an odd number is $3$ out of $6$, or $\frac{1}{2}$.

 

It would be useful to encourage children to talk in pairs about what they understand as 'fair' - there will be different, but equally as valid, ideas about how to change the game.

 

 

Key questions

 

What numbers are possible to throw on the dice?
Who would win with each number?
Can you use this to decide how to make the game fair?

 

Possible extension

 

Learners could try Odds and Evens which extends the ideas in this problem.

 

Possible support

 

Having dice available will help those children who are not familiar with them and playing the game for themselves would also be of benefit.

 

Related Collections

  • Playing with Dice

You may also like

Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

  • 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