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

Red Balloons, Blue Balloons

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

Why do this problem?

This problem would be a good one when doing calculations with fractions. It also requires logical thinking and organising of results. Different strategies and approaches can be taken: knowledge of addition, or multiples, or an understanding of fractions can be used to arrive at a solution.

Key questions

What do you think is a good way to start?
How big was Katie's balloon after the second (third, fourth etc.) puff?
How big was Will's balloon after the second (third, fourth etc.) puff?

Possible extension

Learners could make up a similar problem of their own for a friend to try.

Possible support

Breaking the problem down step by step will help learners reach a solution. It might be useful to have each subsequent piece of information written on a separate card so that they can be given to children when ready, rather than presenting all the information at once.

You may also like

Pizza Portions

My friends and I love pizza. Can you help us share these pizzas equally?

Doughnut

How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

Pies

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

  • 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