The Life of a River

This week in our online maths clubs, in honour of World Rivers Day, we are looking at some of the maths that you might find along the course of a river and other puzzles inspired by rivers. If you would like to try these challenges in our online maths clubs, visit and book a free trial session.

All major ancient civilisations grew up near major rivers. Rivers made agriculture possible and enabled one place to support large amounts of people. We started this week’s sessions by going over what the life of a river was and what some of the important aspects of a river are.

We talked about rivers joining together to produce rivers with more water and designed a map with rivers branching and joining and becoming bigger before going to the sea. The goal of the map was to get all the rivers to the sea but also to ensure that all the settlements had adequate water. As rivers join together you can see them getting thicker.

Added to that we have a few river crossing puzzles (especially bridges).

We also introduce Leonard Euler, a Swiss mathematician who ended up solving the puzzle just above on the right. In doing so, he developed a brand new area of maths called graph theory.

Euler also introduced the notation that we use for functions, which is another area we look at in this week’s activities.

We hope that this enables discussions about bridges or rivers. We would love it if you do have any #momentsofmaths while doing this if you could share them with us. You can do this in the comments or by uploading a picture to the gallery.

Some related topics:

  • Systems for counting
  • Networks and diagrams
  • Measures
  • functions

To try this activity:

  1. Download the resource file with templates and challenges
  2. Print out the file
  3. Get coloured pencils and scissors
  4. Watch the video below
  5. This one’s aimed at KS1 activities – KS1 video

Download or share all of these challenges with this pdf and let us know how you got on with it by tweeting using #momentofmaths and start to see Every moment is a #momentofmaths. Please add any photos or videos to our gallery. Here’s the link: View and upload moments. Remember you can explore the chalenges that we post here in our online maths clubs where you get an online version that you can play with directly on your computer. To find out more about our online clubs go to

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