Highest Number 2Task 128 ... Years 2  10SummaryThis task is a variation on Task 127, Highest Number 1. By using digits 1 to 9 and a tensided dice, it extends the place value component and challenges students to reconsider the higher order thinking involved when faced with the question of choosing a strategy for placing cards. 
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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
The first part of the task is a game, so has not specific answers. It is Question 2 that focuses attention on strategy for placing the cards. The following example indicates the type of reasoning that the task is encouraging students to employ. 5 is rolled first so place it in the centre position because it is in the middle of 19.Having analysed several (if not all) situations like this, students can be challenged to put their reasoning to work. Ask them to play a game composed of five rounds each. The winner is the person with the higher total score at the end of the five rounds, rather than the number of rounds an individual wins. This can be taken further by suggesting that there is the opportunity for the game to be used at the school fair. Players would pay $1 to play a five round game. If they achieved above a certain total the would win $5. The challenge is to decided what that certain total would be. To come to this decision students would need to play many more 5round games and record their data (perhaps as a stemandleaf plot). The investigation can be taken as deeply as you wish, for example by asking what happens if the amount to play and/or the prize are changed. See the Investigation Guides in Highest Number 1 for ideas. Another aspect of the task is its place value component. Especially in younger classes teachers might use the task primarily for this purpose. If so, the task can be varied by:

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. 
Tasks have three lives:

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 Highest Number 2 task is an integral part of:
This task is also included in the Task Centre Kit for Aboriginal Students and the Secondary Library Kit. Solutions for tasks in the latter kit can be found here. 