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

Presents

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

No one has sent in a complete solution for this problem, so please send one in if you think you have it. These two partial solutions from Joanne and Jill might get you thinking!!

Joanne, West Flegg Middle School says:

I first took your plans and developed them.

After that I thought about what didn't work in the patterns and I found that groups of 4 squares together in a square didn't work:

These shapes do not work


These shapes do work. They are nets of a cube:


I think there are 6 different ways of covering this parcel.

Task 2: To make a net for a cuboid.


These did not work.

I found that you could not have the 2 end squares on the same side.

These are the nets that did work:


I found 6 nets that will cover this parcel.

I predict that for the present that is different from a cube in 2 directions the number of nets is 3.


Jill, also from West Flegg Middle School, says:

First of all I found several different ways of the non net (reflected, upside down, sideways). Here are two that I found the most:


But then, when cutting out the card to test it, I cut it wrongly.
Then a brainwave struck me: if I move one segment over a bit it would work!

Here are some I investigated:


But then, when I came to this one which didn't work, I realised something: the squares that are moved have to be on the same side.


This led to some interesting thoughts:

  • How many other nets can be made?
  • What would happen if there weren't two squares on different sides?
  • Can we do this with other 3D shapes?

Well, the truth is there must be answers out there somewhere.



You may also like

Face Painting

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Let's Face It

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Cubic Conundrum

Which of the following cubes can be made from these nets?

  • 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