Fay's Nines

Task 54 ... Years 4 - 10


Easy to state and easy to start. Arrange the nine digits 1 to 9 in the spaces to make three 3-digit numbers whose sum is 999.

This cameo includes an Investigation Guide.



  • 9 number tiles 1 - 9


  • basic arithmetic skills
  • problem solving strategies
  • number patterns
  • connection between addition and subtraction
  • place vlaue
  • symmetry and combination theory properties
  • symbolic representation
  • concept of proof
Fay's Nines


A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

The task only asks for the first solution and then five more, but this opens the door to the mathematician's questions:

  • How many solutions are there?
  • How will I know I have found them all?
The six solutions provide only a little data, so students should be encouraged to seek more.
As a mathematician you need to look beyond what the task card says. I want you to collect data about this task until you can see links between the solutions you find.
Nichola Brandon, St. Benedict's Primary School, Narrabundah, has supplied this Investigation Guide to help take the investigation further. It could also be used in a whole class investigation approach to this task. Observations which allow the task to be taken further include:
  • You can't do it without carrying.
  • The last column has to add to 19.
  • All the big numbers seem to be in the last two columns.
From here there are several strategies possible, for example:
  • Given the last (or ones) column adds to 19, one strategy is to find all the groups that add to 19. Systematically listed these are:
    982     973     964     874     865     ...
  • These 5 groups all lead to solutions, and then there are systematic place value combinations or variations within each. Indeed there are 36 variations of each, hence the 5 'families' with 36 variations of each leads to the 180 different solutions.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

This task can easily be converted to a whole class investigation by asking students to tear a piece of scrap paper into nine pieces and write the numbers 1 to 9. The challenge is to arrange them as three 3-digit numbers so that the total is 999.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 31, Fay's Nines, which includes additional challenges with nines in the answer line.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Fay's Nines task is an integral part of:

  • MWA Number & Computation Years 9 & 10

The Fay's Nines lesson is an integral part of:

  • MWA Number & Computation Years 9 & 10

Green Line
Follow this link to Task Centre Home page.