Painted RodsTask 152 ... Years 4  10SummaryThe story shell is that a company produces rods like those shown in the photo and has to paint them all over. The square cross section is the unit. The challenge is:

Materials
Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
Some students might need the experience of stamping the square end of one rod along the length of another. For some it might be appropriate to reinforce the concept of area (surface area too) as they do so. The solutions to the questions on the card are:
By exploring the rods and examining this table, students will begin to see a generalisation. Encourage them to express how they 'see' the rods in order to calculate the number or painted squares. Here are some sample ways to explain the generalisation:
Generalisations such as these are what students will use to calculate the result for 10 and 100, however each visualisation will lead to a different calculation:
Extensions

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. 
Note that there is no suggestion here of drawing a table or choosing symbols for length and squares painted. The students are learning to work like a mathematician, so they have to learn to make those decisions for themselves.
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 39, Painted Rods, which also includes an Investigation Guide. 
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 Painted Rods task is an integral part of:
The Painted Rods lesson is an integral part of:
