Red To Blue
Years 4 - 10


  • Find about ten (10) objects all the same, but they have two (2) different sides.
    The objects could be:
    Screw caps - cap up and cap down
    $1 coins - heads and tails
    Small pieces of paper with a cross on one (1) side - blank or cross
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

These girls are using Poly Plug which are Yellow on one side and Blue on the other.


They start with four (4) yellow in a line and have to change the line to all blue.
But there is a rule in this activity.

Getting Started

  • Line up your four objects so they are all same side up.
  • Record the starting position in your journal.
  • You have to change the line so all the objects are the other way up.
  • You have to do it in the minimum number of moves.
  • Rule: On each move you have to turn all the objects except one.
Your first challenge is to teach yourself how to do it.
Remember, a move is turning over all except one.

Have fun exploring Red To Blue.

The Next Challenge

When you think you can do it, you have to test yourself.
  • Give the objects to someone else and ask them to make the line.
  • Put your hands behind your back (or sit on them) and don't move them.
  • Tell the other person they are a robot and have to do exactly what you tell them.
  • Explain that they are going to turn over the plugs, but you are going to tell them which ones.
Now tell them what to do move by move.
  • If it works, that's great. Record the number of moves, then go to the next section.
  • If it doesn't work, discuss the problem with the other person and try again until it does work.


Now you know that you know how to do it and the number of moves, it's time to publish your explanation. Publishing could be:
  • in your journal with words and diagrams,
  • as a power point or photo slide show,
  • as a poster,
  • or in any other way so that other people learn from you.

Tree Diagrams
Tree diagrams are used to show how to do something if there are choices.
On every move of this activity you have to choose which object not to turn.
That choice will always be either choose a red to not turn or choose a blue to not turn.

This is the start of a tree diagram to explain Red To Blue.
Copy it into your journal and try to finish it.

These Year 6 girls made a 54 second
video to publish their explanation.
When you know how to do it,
click the photo to go to YouTube.


If you know about Flow Charts you might want to draw one of those to explain how to do Red To Blue, instead of drawing a Tree Diagram.


Digging Deeper

To dig deeper into a problem a mathematician asks "What happens if...?"
This boy has asked what happens if we keep the same rule but start with 5 objects?
  • Open this Red To Blue Starter. (You can read it on screen or print it.)
  • You have already done Question 1.
  • Explore the other questions.
    There might be a pattern that will help you answer the challenge.
If you really like Red To Blue you might also ask "What happens if we change the turning to rule?" and explore that question.

Just Before You Finish

Read your Working Like A Mathematician page again and describe how you worked like a mathematician in this activity.
There have been at least six (6) ways. Can you find them?


Answers & Discussion

These notes were originally written for teachers. We have included them to support parents to help their child learn from Red To Blue. These notes include excellent examples of journal entries about Red To Blue from secondary school students.


Send any comments or photos about this activity and we can start a gallery here.


Maths At Home is a division of Mathematics Centre