Why take the Making the Most Challenge?

In this challenge, you and your team need to make the most efficient use of a limited number of resources to build small plant enclosures.This challenge will help you understand optimisation, which is when we look for the most efficient way to do something.

Can you make the most of a set of limited resources to make the most number of different shapes?


Watch Shane introduce the Making the Most Challenge.

Connections to real life

At the Centre for Education and Research in Environmental Strategies (CERES), maths helps to inform decisions around resource use everyday. Data is collected via a distributed metering system for electricity and water use. Waste and biodiversity are tracked via simple counting and recording.

1. Setting the Scene

As a planet, we have a limited number of resources for the people who live here. We need to make sure that we are using resources in the most efficient way. We call this optimisation.

In this challenge you and your family need to think about how you can best optimise your use of scarce resources when planning to build imaginary plant enclosures. You will use your knowledge of shapes to find the best solutions.

Links to the Curriculum

Measurement and Geometry, Levels 4-10

Maths Words

optimisation – finding the best solution for any given situation.

Find more maths words in the Glossary.

2. The Challenge

Using 19 equal lengths, make as many different shapes as possible.

  1. Each person should gather 19 items which are straight and have the same length. These could be 19 toothpicks, matchsticks or pens. These 19 straight items will represent pieces of fence to build your plant enclosures. If you don’t have 19 for each person, team up.
  2. Find a flat surface to try out the different shape combinations. 
  3. Build the maximum number of different shape enclosures using your 19 ‘fences’. They may not share any edges. That means there must be a gap between each enclosure. How many different enclosures can you make? Take a photo to share.
  4. Try again but this time build your enclosures so that they share common edges. Can you build 4, 5 or maybe even 6 different shaped enclosures?

See the image below for an example of what ‘sharing a common edge’ means.


If you are stuck, here are some questions and suggestions that might help.

Make a list of all of the different two dimensional shapes you could use. Remember that there are many quadrilaterals (four sided shapes) you can build. Have a look at this website to explore quadrilaterals further.

Can you name a shape with more than four sides which would use fewer fence lengths than a rectangle?

3. Keep Going

Take 11 of your equal straight lengths. 

How many squares can you make? You may lay lengths on top of one another. Can you make 8, 10 or even 15 squares?