EurekaTask 163 ... Years 4  8SummaryThe story shell about three prospectors finding gold nuggets stirs the imagination and is enhanced by the yellow counters. The observations made about the collection of nuggets are easy to understand and students quickly find themselves absorbed in a delightful number puzzle with many solutions. The card begs the questions:

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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. 
In total there are many solutions for Mary's nuggets. One is:
To advance this question students need to see restrictions in the problem such as:
So a further limit on the investigation is the largest number Paul's could be and the first case to test is Paul finding the four highest nuggets, (15, 16, 17, 40) = 88. A systematic list would look something like this:
Some results of continuing this systematic search are:

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 is easy to set up as a whole class lesson. Simply arrange the students in pairs and ask each one to tear a sheet of paper into six pieces. That gives the pair twelve pieces. Tell the story and write the weights of the nuggets on the board. Students copy the weights to their pieces of paper. Write the rules on the board and challenge the pairs to be first to find the solution. It is very likely that once one solution is found, another will follow in a short time and this opens the door to finding more, developing the limits of the problem and setting up a team investigation to find all the solutions. The solutions would look great collected onto poster paper as a class display. Even an incomplete set of solutions looks pretty impressive as an outcome to such an apparently simple problem. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 71, Eureka, which includes an Investigation Guide with answers & discussion. More than 30 answers are listed in the discussion. 
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 Eureka task is an integral part of:
The Eureka lesson is an integral part of:
