First Down The MountainTask 87 ... Years 4  10SummaryClimbers on a mountain begin at different heights above the ground. Students roll a pair of dice and the sum shows which climber may move one space down the mountain. It's a race between climbers! Which climber is more likely to reach WIN first? 
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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 card asks only that 10 games are played and begins a discussion of the fairness of the game. If it was a fair game, what would the students expect to happen in these ten games? Is ten games enough to make decision about fairness with any certainty? How much data would be enough? If you keep a class record of the ten games played by each pair, the current pair can add their results and then discuss again whether they think the game is fair.
An indication of the reason comes by considering a race between the 2 and the 7, ignoring all other rolls, where the 2 has to go one step and the 7 has to go six steps. ^{6}/_{7} x ^{6}/_{7} x ^{6}/_{7} x ^{6}/_{7} x ^{6}/_{7} x ^{6}/_{7} = 39.6%.So in 1,000 trials we would expect Climber 7 to win 396 times which would mean Climber 2 would win 604 times. What happens if we change the mountain. For example, if to win a climber only had to reach the line one above WIN? 
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. 
Introduce students to the game. This First Down The Mountain board should be useful. Collect guesses from everyone as which climber they think will win. This will give you some idea of the students' current thinking. Students then play the game and add their results to a growing class record. Use the Iceberg Information to develop the lesson further. If your school is a Maths300 member, there is software to assist in collecting more data quickly. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 4, First Down The Mountain, which also includes three Investigation Guides. 
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 First Down The Mountain task is an integral part of:
The First Down The Mountain lesson is an integral part of:
