Cap-turing Mathematics
Years K - 10

This is a smörgåsbord of ideas for a wide range of ages. Dip in and out as you please. The ideas have come from learners, parents and teachers. Explore what is suggested or let these ideas stimulate new ideas of your own. When you create and try out something new send it to us for the Gallery.


  • You need a mixed collection of at least fifty (50) plastic screw caps to start. You can get them from milk, water, soft drink, fruit juice and other products. Collect as many as you can. They will be useful in several other activities too.
  • Remember to keep a journal record of the ideas you use and what you learn.

Getting Started

Now that you have sorted, what questions can you ask?

Even if it is just to check your guess by counting, you can ask the mathematician's question: Can we check that another way?.

Perhaps you can sort and display a different way.

You could check your guess by sorting.


They started with this Investigation Guide.
Click the image to open a PDF file that you can print.
Column graphs are good for quickly seeing which is biggest and smallest.
  • They also make it easy to count how much bigger or smaller.

Scroll down to find the idea that's right for you today, or you could start the way this dad and daughter did.


Have fun exploring the ideas in Cap-turing Mathematics.

Making Pictures

Making cap pictures provides opportunity to ask mathematical questions. For example:
1st Photo
How many of each colour do you need to make 3 flowers like this?
How did you work that out?
Can you check it another way?
2nd Photo
The gardener made more flowers like this. Twenty-five white caps were used.
How many flowers were made?
How did you work that out?
Can you check it another way?

More Ideas


Picture with patterns that go along ... or ... patterns that go up.
What questions would you ask the people who made these patterns?






For Year 9 and higher: If I tell you any level,
can you tell me the number of caps in that level
...the total number of caps to get to that level?

What can you do if you use dice (or calculators,
or playing cards) with caps?


Add Town

Welcome to Add Town where all the street names are numbers.
On Sunday afternoon there is no traffic in town and the people all go out for a walk.
Exactly at 2pm the people gather in the intersections to show the total when the left street sign is added to the top street sign.
  • Why are there 7 people in the top left?
  • Why are there 7 people in the bottom right?
  • Explain the other numbers of people on the grid.
  • Copy the grid into your journal and show the number of people in every intersection.
  • Make up your own Add Town puzzles.

What happens if it's Times Town where the people stand in equal rows on each intersection to make the answer? (Product is the answer to a multiplication.)


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


Maths At Home is a division of Mathematics Centre