Jumping Kangaroos
Years 6 - 10

These secondary students from Coolgardie Christian Aboriginal Parent-directed School (CAPS)
are enjoying working with someone else on the floor as they investigate Jumping Kangaroos.
You might like to find a partner and do that too.


You need at least four (4) pretend kangaroos in each of two (2) colours. You need at least 9 pretend stepping stones.
In the photos the kangaroos are the yellow and blue plugs. The stepping stones are the red plugs.
  • Kangaroos could be: small plastic screw caps, pebbles from the garden, buttons, plastic cups...
  • Stepping stones could be: bits of paper, drink coasters, crosses drawn on a sheet of paper...
Send us photos of what you choose and how you use them.

Investigating Jumping Kangaroos

  • Open this Jumping Kangaroos Starter.
    You can read it on screen or print it.
  • Investigate Jumping Kangaroos using the rules on the Starter.
    If you only solve the puzzle with three (3) kangaroos on each side you have done well.
    When you do, remember to count your moves ... then record in your journal in pictures and words to show how you did it.
  • You can return to this problem and continue at another time. Or if you get 'hooked' keep on going for as long as you want to.
Have fun exploring Jumping Kangaroos.

Remember a kangaroo can only ever jump one (1) on-coming kangaroo into an empty space.
They can't jump kangaroos from their own side.


  1. Ask yourself: Which pieces could I move now?.
  2. Choose one (1), move it and keep your finger on it. Ask yourself: What could happen next?. Put it back.
  3. Choose another one from your choices in A. Repeat B.
  4. Continue with other choices from A if there are any.
  5. Decide which move in A will give you the best choice in the next move ... and do it.
Go through this sequence again for each move. When you get it, your fingers will feel like they are moving in a pattern.

A Pattern of Patterns

When your fingers and eyes and reasoning have helped you find the movement pattern, you can ask What happens if we change the number of kangaroos on each side?.
  • Try the rest of the questions on the Starter.
  • Each time you think you know the answer, ask yourself Can I check it another way?.

Time To Explain

When a mathematician eventually finds a pattern and a rule (or rules) to predict the numbers in their data, they have to explain it to their colleagues.
  • In your journal use pictures and words to explain what you found out.
After you have tried to create your own explanation, you can look at the two reports in the next link.
One is from a Year 6 student and one is from a Year 7.
No peeking. Try for yourself first. What did you learn by reading the work of your colleagues?

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • Read again what it means to work like a mathematician.
  • How did you work like a mathematician during this investigation?
  • What mathematics do you know now that you didn't know when you started this investigation?


Answers & Discussion

Once upon a time a small group of teachers sat down to investigate Jumping Kangaroos during their lunchtime. Yep. Really!

Five (5) short videos were made during the session. View them in order and share the teachers' struggles and their successes. They had just as much difficulty - and just as much fun - as you.

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


Maths At Home is a division of Mathematics Centre