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

Which Spinners?

Age 14 to 18
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Which Spinners? printable sheet - bar graphs


In the interactivity below there are two spinners.
When you press "One spin", the computer spins them once and adds (or finds the difference between) the numbers.

You can also spin 100 or 500 times at once. The interactivity records the results in the relative frequency chart.
Warning - the computer needs a little bit of thinking time to do 500 spins!



 

Experiment with different pairs of spinners.

What features do you notice on the bar charts that you produce?

Can you come up with ways of predicting what a chart will look like before you produce it?
 

The challenge

The bar charts below were generated on the interactivity using different combinations of spinners.

Can you deduce which spinners were used to create each bar chart?

Can you explain how you used the information provided by the bar charts to work it out?

(You can download all eight bar charts here, or click on each chart to see a bigger version)

A  B
C  D
E  F
G  H


Final challenge

Imagine you had 1-20 and 1-30 spinners. Describe in as much detail as you can what the relative frequency bar charts would look like for:

  • The sum of two 1-30 spinners
  • The difference between two 1-20 spinners
  • The sum of a 1-20 and a 1-30 spinner
  • The difference between a 1-20 and a 1-30 spinner

Try to provide a good explanation to convince us that your descriptions of the bar charts are correct.
 

This resource is part of the collection Statistics - Maths of Real Life

You may also like

Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Squash

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

In a Box

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

  • 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