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

Compare the Cups

Age 5 to 7
Challenge Level Yellow star
Primary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Compare the Cups

For this challenge, you will need lots of different cups. This picture shows some:



Which might you choose if you wanted a lot to drink? Why?
Which one would you choose if you did not want a lot to drink? Why?
Can you arrange the cups in a line from the one that holds the most liquid to the one that holds the least liquid? 
How will you test whether you are right?
 

Why do this problem?

This practical activity offers a context in which children can develop their conceptual understanding of capacity.


Possible approach

For this activity, have a collection of cups/glasses/mugs available for the children to explore themselves.  You may want to offer a context for the activity to link in with a current theme or story.

Pose some questions orally to the group, as in the problem, and encourage them to think about the answers by estimating and by eye at first.  You could discuss their thinking and then give them the opportunity to test out their ideas, perhaps with water or sand.

In the plenary, you could pose a final challenge, such as how many of the smallest cup will be needed to fill the largest cup?  Again, encourage estimation first before trying it out practically.
 

Key questions

Tell me about your thinking.
How will you test out your ideas?
 

Possible extension

You could introduce a much, much smaller container, for example a spoon, and observe what the children do with it.
 

Possible support

Some learners might need help with awkward pouring.

You may also like

I'm Eight

Find a great variety of ways of asking questions which make 8.

Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Noah

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

  • 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