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

Make Your Own Pencil Case

Age 11 to 14
Challenge Level Yellow star
  • Project
  • Teachers' Resources

  • Warm-up
  • Try this next
  • Think higher
  • Read: mathematics
  • Read: design technology
  • Explore further

Would you like a personalised pencil case which is exactly the right size for the number of pens, pencils, etc, you generally carry around?  Then make your own!

You'll need to think through some initial questions before you start planning your design:

  • How long is the longest pen, pencil, ruler or other object you might want to carry in it?
  • How many pens, pencils, etc, do you want to carry about?
  • If you bunch then all together, and measure round them with a piece of string, what diameter pencil case do you need?

When you've decided on the dimensions of your pencil case, have a think about what shape would be a good idea.  You may well decide that a cylinder, cuboid or triangular, hexagonal or octagonal prism would work well.

What does the net of the shape you want look like?  

  • How many separate pieces do you need?  
  • What shape is each piece?
  • Which sides need to fit together?

Try modelling the net of your pencil case with scrap paper, folding the paper net into shape and sticking it together with sellotape.  Does it work?  Is it the right size for your pens and pencils?

Once you're happy with your paper prototype, you need to decide what materials you will use for the real thing:

  • Does it need to be a rigid material or could you use recycled fabric?
  • Will you need to alter the measurements in your design to use the chosen material?
  • Do you want the same material for all the pieces, or could the ends be made of something different from the rest?
  • How will you stick or fasten the pieces together?
  • How will you do up the pencil case?
  • Do you want to put a design on any of the pieces before making up the pencil case?
  • How will you ensure your pencil case stays shut?

You may also like

Which Solid?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Witch's Hat

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Gym Bag

Can Jo make a gym bag for her trainers from the piece of fabric she has?

  • 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