Coloured SquaresTask 112 ... Years 2  10SummaryColoured tiles are arranged on a square grid so that no colour is repeated in any row, column or long diagonal.
This cameo includes two Investigation Guides. 
Materials
Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
Much of what we know about this problem is due to the work of Markus Bucher, Tasmania. According to Markus, the story behind the evolution of this activity goes something like this: My Grade 3 son came home with some homework. The challenge was to place 16 cubes (4 each of 4 different colours) on a 4x4 grid so that no row, column or major diagonal (the two diagonals of four squares) contained two or more of the same colour. That was where the activity ended. There was no follow up to this in the classroom. There had to be more to this activity than that. That weekend our family spent our idle moments playing with the grid and some of its possibilities.Most students tackle the problem by Guess & Check to find their first solution, which might be either of these:
As more solutions develop so do strategies for finding them:
As mentioned above, apart from the development of reasoning and spatial perception involved in this task, it can be extended further by asking:
And, if after all this adventure you want more, what happens if...:
Belinda Rayment, St. Francis Assisi, Calwell, chose to use this Investigation Guide with her students. 
Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.
 Visit the Home Page for more Background.
 For this specific activity click the Learners link and on that page use Ctrl F (Cmd F on Mac) to search the task name.
Whole Class InvestigationTasks 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. 
All you need to explore this problem is plenty of coloured tiles or blocks such as those available in most schools. Once the students find one solution, the problem is very open. There is no particular end point other than illustrating again the process of working like a mathematician, which is really the only reason for learning mathematics. This Recording Sheet might assist in this whole class investigation because it is designed so students don't spend an excess amount of time colouring. At this stage, Coloured Squares does not have a matching lesson on Maths300. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
The Coloured Squares task is an integral part of:
