This is a phrase to capture the full potential and flexibility of open-ended investigative or problem solving tasks such as are available within the Task Centre Project. Teachers say they like using them in three distinct way:

1. as a short term (10-20 minute) challenge for two students
2. as a whole class lesson involving all students
3. as an extended investigation or project

The first of these involves just the 'tip of the iceberg' of each task, but nonetheless does provide a worthwhile problem solving challenge, and one which 'demands' concrete materials in its solution. The task does provide for a level of success and accomplishment in this short time period.

The second use involves using simple materials and engaging the whole class in the task in order to develop key outcomes or specific content knowledge. This involves particular pedagogical additions or adjustments to make the task 'fit' the whole class environment.

The extended investigation or project challenges students to explore the 'rest of the iceberg'. That is, to probe all aspects and extensions of the task. Typically this involves providing an investigation worksheet to pupils, perhaps with suggestions for the direction the investigation might take. Students hand in the 'story' of their work for 'portfolio assessment'. The criteria for assessment are typically the recognisable stages of the investigative process.

Some tasks which have been documented to illustrate these three different uses are:

• Greedy Pig
• Highest Number
• Win At The Fair
• Duelling Dice
• Number Tiles/Fay's Nines/Addition Totals/Truth Tiles
• Crazy Animals
• Jumping Kangaroos
• Crossing The River

Many of these have been incorporated into Replacement Unit packages. These are detailed three week unit structures which combine the Three Lives Of A Task. The term 'Replacement' is used because teachers are invited to replace their existing three weeks of work on any of the available topics with one of these units. In this sense, the package has a 100% professional development purpose as teachers trial and reflect on a possibly different approach to planning, classroom delivery and assessment.

Mathematics Task Centre Project products and prices (includes details for ordering).