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

Folding

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

Folding


Take an A4 piece of paper ...
How small can you make it by folding?
How many different sorts of triangle can you produce by folding?
Can you produce four identical triangles?

What is the quickest way to produce a square?
Can you make other quadrilaterals by folding?

Or by folding a long sheet of paper ...

What can you produce?
Other shapes?
More folds?


Why do this problem?

This exploratory task is accessible to all and therefore good for boosting children's confidence. It would make a good introductory activity for work on shape.

Key questions

Tell me about what you have done.
How many folds have you made?
What shape/s have you made?

Possible extension

Some learners will enjoy this activity about folding a sheet of paper to make an equilateral triangle.

Possible support

Pupils could start by folding into a rectangle.
 

You may also like

Tangrams

Can you make five differently sized squares from the interactive tangram pieces?

Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

  • 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