Task 113 ... Years 2 - 8


This task might be the first time students think about the calendar and how it works. The challenge is to find a way to write digits on the cubes so that every day of any month can be displayed. For most students that's not too hard, but from here the calendar puzzles can grow.


  • Two black cubes
  • Chalk and eraser cloth


  • calendar conventions
  • logical reasoning
  • strategy: try every possible case
  • number patterns and calculations related to 7, 12, 365 & 366


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

Students seem to enjoy this task, perhaps because it relates to 'real life'; perhaps because of its tactile nature. The first thing they usually discuss is the number of days in each month. The task is perceived as non-threatening by the students because the trial and improve approach means that if something doesn't work it can simply be rubbed out and replaced.

After a while students realise that some numbers have to be on both cubes in order to make dates like 11th and 22nd. Most will continue from here by trial and improve, but some will reason that 10 digits (0 - 9) are required to make every number plus the repeats of 1 and 2. That's 12 digits in all and there are 12 faces on two cubes, so every face will be used. Another useful piece of reasoning is that 0 can't be on the same cube as 3, otherwise 30 can't be created.

One solution is:

  • Cube A ... 1, 2, 3, 4, 5, 6
  • Cube B ... 0, 1, 2, 7, 8, 9
assuming that single digit days may be shown with just one cube.

Once students have found a way to label the cubes, they usually enjoy verbalising and demonstrating their solution, which involves testing every possible case. (Hint: So that the solution is not easily revealed to the next users it may be necessary to slightly moisten the erasing cloth.)

Extensions include:

  • How many solutions are there?
  • How do you know when you have found them all?
  • Explore numbers greater than 31 that can be made with each solution.
  • The solution above requires that at least some of the single digit days are displayed with just one block. It is possible to solve the problem using two digit representations of single digit dates. That is, the first through to the ninth of the month would be shown as 01 through to 09. How can this be done? [Hint: It depends on the font face used for the digits.]
  • Is it possible to design cubes to show all possible six figure dates, for example, 3rd April 2006 would be 030406?
Other calendar questions include:
  • What day of the week is your birthday this year? What day will it be next year? When will it next be on a Saturday? Assume you live to eighty years old. How many of your birthdays will be on Saturday?
  • Use a month of a calendar to explore patterns in the grid as in Task 4, Window Frames.
Some students will enjoy making cubes creatively marked with digits and a tray as a craft exercise that becomes a gift.

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.

Many schools have lots of 2cm wooden cubes. These could be used to explore the calendar possibilities together with a view to opening the door to further calendar investigations. The whole might be part of a unit on Time. If you don't have lots of cubes, then consider Calendar as one work station in a suite of activities related to time. Others might be tasks such as Task 22, Time Together, Task 25, In Between Time, Task 26, Travelling Australia and Task 85, Time Swing.

At this stage, Calendar does not have a matching lesson on Maths300.

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 Calendar task is an integral part of:

  • MWA Space & Logic Years 7 & 8

Green Line
Follow this link to Task Centre Home page.