Making MonumentsTask 180 ... Years 4  8SummarySet in a story shell resembling real life, the students build tower monuments in the middle of a park and construct pathways leading to the monument from the four arms of the compass. These monuments and paths are special though because:
If I tell you any height of a tower can you tell me how many tiles are needed to surface the paths and the monument? This cameo has a From The Classroom section which shows how it can lead into an area of the Year 11 curriculum. 
Materials
Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
Answers are:
The iceberg begins to open with the Challenge section which asks students to explain how they worked out these results, then pushes the communication aspect of a mathematician's work further by challenging the students to explain in another way. Students might reason in the following ways:
Extend Making Monuments further with questions such as:

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. 
If you intend to have every pair or group in a position to build towers with matching paths, then you will need cubes and tiles of the same size, for example, 2cm squares as in the task. However, 2cm cubes are reasonably easy to obtain, but 2cm tiles are not  which is why the tiles in the task have been specially made. So an alternative approach to developing the whole class lesson is to use the task equipment in a fish bowl situation to set up the problem. Most students can visualise the structure of the problem from here. Perhaps set up the Size 2 situation as on the card with student assistance first. Then use your electronic whiteboard to show how this can be recorded on isometric paper. Handing out the Recording Sheet at this stage and asking students to make their own copy of Size 2 will help to confirm the structure. Encourage drawing Sizes 1 and 3 to discover (or confirm) the number of tiles. The model is always in the fish bowl to check. From here, develop the lesson along the lines suggested above. At this stage, Making Monuments 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 4 Arm Shapes task is an integral part of:

Mackillop College
Damian Howison 
Damian asked the question: What happens if the monument is placed at a specific place inside a courtyard walled on three sides?. The mathematical model which develops is perhaps more connected to real life, since the task assumes the area of the park is infinite, whereas in real life such a park must be bounded. 
G'day Doug, 
Damian's slides are a very clear development of the thoughts opposite. They are highly recommended, especially to teachers of senior high school and university.
Damian's Slides 