Crossing The DesertTask 94 ... Years 4  8SummaryA message has to be taken across a desert and the messenger must return with an answer. However one person can't carry enough food for the full journey and two people can't carry enough for both to do the return journey. The card tells us they can bury food on the way out to be used on the way back, but on which day? It has to be just the right moment so that the messenger will have enough food to go the full journey and so the food carrier has just enough to get back. 
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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. 
This task is sure to generate discussion.
Students at East Devonport Primary. Their teacher has organised Mathematician Teams. There are subtle elements of the problem that must be explored. A mathematician needs to understand, in fact, in many cases clarify and refine, the problem before attempting a solution. Usually this process involves 'talking it through' with colleagues. In this sense the problem encourages justification of answers against agreed criteria, rather than production of the solution, or sequence of solutions. Discussion will identify some or all of the following aspects of the problem:
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The problem can be extended further by asking what happens if we change the key numbers? That is, suppose crossing the desert takes a different number of days and the travellers can carry a different amount of food? Can the students find another combination of numbers which also make an interesting problem? 
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. 
This task works well in groups of three or four. Use the A4 size board provided above and perhaps enlarge it to A3. One large board per group focuses discussion. You will need 24 counters per group but if you have Poly Plug, the red board immediately provides those. The travellers who carry the food can be represented by stacking the 'food' on a small piece of paper that slides across the desert from day to day, or simply by piles of counters manipulated by two students. At this stage, Crossing The Desert does not have a matching lesson on Maths300. However, for more information about this task being used as a whole class investigation in a Year 1/2 as part of a school's Working Mathematically with Infants kit, visit Shane Hoffman's story in Calculating Changes. Visit Crossing The Desert in Menu Maths Pack B. 
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 Crossing The Desert task is an integral part of:
This task is also included in the Primary Library Kit. Solutions for tasks in the latter kit can be found here. 