The Frog PondTask 13 ... Years K  8SummaryThis task is a game between two players which involves an element of chance. Starting with five frogs in your pond, the dice determines the number of frogs you add in or take out. The winner is the first with an empty pond. But is it a good game? Is it too short or too long?
This cameo includes an Investigation Guide and has a From The Classroom section which shows an early years class tackling the problem with materials after acting it out in the sandpit. 
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Content

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 full of surprises for many students. Sometimes the pond is emptied quite quickly, but the very next trial might be substantially many more rolls. For example, it is possible to empty the pond in two rolls. But the very next trial might take 40 rolls. Students need to collect sufficient data about the number of rolls to empty the pond (which might be added to an ongoing class display) before they can make judgements about the most likely length of game (number of rolls to empty the pond). The class display (or other method of gathering ongoing data) helps form more valid judgements because it is not likely students will have sufficient time to carry out enough trials of their own. The further challenges related to changing the number of frogs to make a decision about a good length game require gathering more data and comparing it in an ageappropriate way. Range, mode, median and mean are all possible measures. An associated investigation relates to the minimum number of moves to empty the pond. The answer is two, but in how many ways can the dice fall to create this outcome. From this, can we calculate the probability of emptying the pond in the minimum number of moves? What happens if we run trials to test this calculation? (Note: The students only need to find out if a game will be a minimum or not, that is, as soon as the number of rolls exceeds the minimum, there is no need to complete that game.) Extensions

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. 
To convert this task to a whole class lesson so that you can work together to explore any of the questions above, you need specially marked dice. However, these can be time consuming to create with stickers and wooden cubes. An alternative is to play a variation using a standard dice and agree that:
At this stage, The Frog Pond does not have a matching lesson on Maths300. Visit The Frog Pond in Menu Maths Pack C. Also see learners at work below where the photographs suggest the value of the incontext skill practice component of the experience (and that paper plates make great ponds). 
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 Frog Pond task is an integral part of:

Footscray North Primary SchoolPrep/Year 1 
The table top game was played after acting out the game as frogs out in the yard.
Then I don't have to count.
Subitising: We just know it is 6 because we can just see it.
