Fill The Board
Years K - 6

This is a game for two players ... for young children this should be an adult or older child.


In school this game is played with the school resource called Poly Plug. At home you can play it with your plastic screw caps from soft drink and spring water bottles on a game frame, or by using a game sheet and crossing out circles as you go.
  • Print this Poly Plug Frame if you are playing with caps or this Poly Plug Paper if you are crossing off.
    Whichever way you choose, you only need one between two.
  • One spot dice per pair.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

Have fun exploring Fill The Board

How To Play Fill The Board

The aim of the game is to fill the board with screw caps, or cross off all the circles.
The dice tells you how many to cover each turn.


  • Both players predict how many rolls of the dice it will take to fill the board.
  • Record the predictions.
  • Take turns to roll the dice and cover or cross off that many circles.
  • Keep count of the number of rolls it does take to fill the board.
  • The last throw doesn't have to exactly fill the board - there can be some 'left over'.
Each time a player has a turn, the other player asks these three (3) questions:
  • How many left?
  • How do you know?
  • Can you check it another way?


Here one player is putting in the last plug of four (4) because the dice roll was four.
The other player asks:

  • How many left?
  • How do you know?
    I can see it's five, 'cos there's five in each row.
  • Can you check it another way?

Yep. There's twenty-five (25) in the board. We've plugged in twenty (20).
Five (5) more makes twenty-five.
Play the game a few times until you get better at predicting.


Each time you play you are collecting data to help answer the question:

Year 1
What is the most likely number of rolls to fill the board?

Your challenge is to keep playing games until you think you can answer that question.
Then you explain in your journal.

  • Very young learners tell their explanation. The older player writes for them.
Another way for any age to record is to make a video.


  • The older you are, the more you should use graphs and statistics (mode, median, mean, range) in your report.
  • You could also comment about the most and least number of rolls it could take to fill the board.
Year 6

More Investigation

  • What happens if we change the number of boards?
  • What happens if we flip a coin instead of rolling a dice? Cover 1 for a head and 2 for a tail.
  • What happens if we change the number of dice?

Playing On The Computer

Cambridge University runs a project called NRICH for mathematics. They learnt about Fill The Board and created software (Adobe Flash) for the game. They call their activity All Change. They have made three variations of the game. Remember to predict the number of rolls before you play with the computer.

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • Draw an oval in your journal.
    • Change it into a face that shows how you feel about Fill The Board.
    • Add a speech bubble if you wish.
  • What do you know now that you didn't know when you started Fill The Board?


Answers & Discussion

These notes were originally written for teachers. They have been shared from the Members section of Calculating Changes, which is a division of Mathematics Centre.

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


Maths At Home is a division of Mathematics Centre