Fay's Nines

Task 54 ... Years 4 - 10

Summary

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. 		 

Materials

  • 9 number tiles 1 - 9

Content

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

Iceberg

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.
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.

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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
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