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

Baked Bean Cans

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

Baked Bean Cans


cans 1

This challenge is all about cans or tins - the kind in which you might buy baked beans or soup.

Is there a best way to stack cans?

What do different supermarkets do? Can you explain why they might stack cans in that way?

How high can you safely stack the cans?

Investigate the different ways in which cans roll.

Does it make a difference if the can is empty compared with when it is full? How about a partially-filled can?


Why do this problem?

This activity gives pupils the opportunity to explore ways of problem solving in a familiar context. It provides a great opportunity for learners to compare ways of approaching an investigation, and to compare outcomes.

Possible approach

Ideally, this activity would be pre-empted by a visit to a local grocery shop or supermarket. If that is not possible, you could introduce the investigation by showing a selection of pictures or photos of various shops, illustrating some ways of stacking cans. Invite children to describe what they see in the photos, drawing on their own experiences too.

You can then set up the challenge and encourage pairs or small groups of learners to work together. To begin with, invite them to suggest reasons why cans are stacked in different ways. You could write these up on the board before setting them off on the problem. You may want to limit each stack to a certain number of cans to start with, or perhaps you would prefer the learners themselves to come up with that 'fair' way of testing. Having a good supply of washed-out/unopened tins or other cylindrical objects will be vital so that the children can have a hands-on experience.

Try to hold back while the children work and observe how they are approaching the task. As you go round the room, you may want to pick up on things that particular pairs have said/done and you could warn them that you'd like them to tell everyone about that later. Watch out for pairs that are approaching the task in a systematic way (for example increasing the number of cans by one and testing the effect) and for those who find a helpful way to record what they're doing, perhaps in the form of pictures, numbers or symbols.

The plenary will be a time for those pairs to share their ideas with the whole group. This work would make an engaging classroom display.

Key questions

What have you tried?
Can you tell me about what you have found?
What do you think is best? Why?

Possible extension

Children could investigate other grocery packages and/or bigger numbers of cans.

Possible support

Having lots of cans/packages and opportunities to be listened to will help all children access this problem.

  • 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