Sphinx Sizes
Years 3 - 10


  • Print four copies of this Sphinx Sheet and, for now, cut out just five (5) shapes.
  • Print this Triangle Dot Paper to record the shapes you make.
  • You will need some sticky tape too.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.
When the activity is over your recording sheet should be put into your journal beside any other notes you make.

Drawing Sphinxes

  • The triangle dot paper will guide you. Your first challenge is to join dots on the paper to draw the smallest sphinx shape you can.
    When you get it right, it will look exactly like the same as the shapes you cut and there will be no dots inside your drawing.
  • Pick up two of your sphinx shapes. Put them together so the long sides match exactly.
  • Draw this 2 sphinx shape on your dot paper.
    If you are right this time, the drawing will be the same shape as your model and there will be only two inside dots. They will be along the join line.
  • Check with someone else.

Four Sphinx Challenge

  • It is possible to put four (4) sphinx shapes together to make a new, bigger sphinx.
  • Your first challenge is to...

Use 4 of these...


Have fun exploring Sphinx Shapes.

When you find the the solution record it on your Triangle Dot Paper.

...to make this.

Talk Me Through It

  • Remove all your clues:
    - turn off the screen,
    - turn over your recording sheet,
    - flip some of your sphinxes and mess them around on the table.
  • Now try to make it again.
  • When you are quite confident that you can do it, mess it up again and ask someone else to be your partner.
  • Ask the person to sit in front of the pieces and say to them:
    I think I know how to do this sphinx puzzle. I am going to test myself by teaching you.
    You are like a robot and I am going to give you instructions.
  • Now you tell them what to do BUT you must NOT use your hands.
    You must sit on your hands, or hold them together behind your back.
Congratulate each other. It takes a good talker and a good listener to make this work.
They will probably want to try it for themselves now. That's okay. They can cut some more sphinxes.
  • Hold your solution together with sticky tape (not too much) and keep it on your table.
  • Discuss with each other the language you used and if there could be a better way to say the instructions.
  • Record something in your journal about what you both learnt when you were talking them through it.

But Wait ... There's More!

You have proved that four sphinxes make a sphinx.

Size 1

Two (2) Size 1 fit along the bottom of Size 2.
That's why it's called Size 2.

Size 2

  • But wait! Size 2 is a sphinx. And ... four sphinxes make a sphinx ... so ... four Size 2 sphinxes will make a Size __.
  • Make four more Size 2 sphinxes and turn them into a Size __ sphinx.
    How many Size 1 Sphinxes will you need?
    Start cutting. Let's see if you can do it. Your partner might want to help.

Finding The Numbers

Now you have proved that four Size 2 sphinxes make a...

Size 4

...and the Size 4 is a sphinx so four Size 4 sphinxes will make a Size __ ... and after that? ... and after that? ...

It looks like we better organise our data before we get to infinity!

  • There are pairs of numbers in this challenge: (1, 1), (2, 4), (4, 16), (8, __), (__, __)
  • Copy these pairs into your journal and fill in the gaps.
  • Number pairs can also be shown in a table.
    Print this Square Line Paper and use it to make a table like this near the top of it.

Size 1 2 4 8 16 and it keeps going --->
No. of Size 1 1 4 16

  • If you know how to draw a graph from ordered pairs of numbers use the rest of the paper to plot the points from the table.

Meet Michael & Tyler

Years ago, when they were in Year 5, Michael and Tyler were working on Sphinx Sizes and they noticed something.
They asked their teacher, What happened to Size 3 sir?
Their teacher had never thought of that and said so.
Can it be made? they asked.
Their teacher didn't know that either and the boys asked, Can we try?

We're very glad their teacher said yes, because, as far as we know, they were the first people to ever ask that question. And guess what. It took them quite a long time, but they did it. And they handed it in coloured like the Aboriginal flag. Can you see it at the top of the page?

  • Your turn. Try to make the Size 3 sphinx.
  • How many Size 1 Sphinxes might you need?
  • It might not be easy, but at least you know it can be done.
    Michael and Tyler didn't.

Meet More Mathematicians

Michael and Tyler started other people thinking.
If we can make Sizes 1, 2, 3, 4, ... 8, ... 16, ..., then what about the other missing ones??
Is it really possible to make every size sphinx?

Nick and his friends made this Size 16 Christmas Sphinx
when they were in Year 1.


Amy and Emma built this Size 13 in Year 7.

Chris Collet built this Size 19 after he finished the Size 17.
You can see when he showed it to his teachers.

Then he left the school and went off to do his Year 12 exams.

Now you go off and get a drink and a snack.
Bring it back and watch this 8min 40sec video made by a Year 8 class about their Adventure of the Sphinx.

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • Look at your notes for this activity. Think back through what you did.
  • Draw an oval in your journal.
    • Change it into a face that shows how you feel about Sphinx Sizes.
    • Add a speech bubble if you wish.
  • How did you work like a mathematician? Record at least 2 ways.
  • What do you know now that you didn't know when you started Sphinx Sizes?


A Final Conversation

Hey, I just thought.
You know that Size 1 sphinx?
Well it's a sphinx right?
Yeah. So.
So what's it made from...?


Answers & Discussion

These notes were originally written for teachers. We have included them to support parents to help their child learn from Sphinx Shapes.

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


Maths At Home is a division of Mathematics Centre