# The Frog Pond

### Task 13 ... Years K - 8

#### Summary

This 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.

#### Materials

• Objects to act as frogs and two ponds
• A specially marked dice

#### Content

• subitising and 1:1 correspondence
• addition and subtraction practice
• intuitive probability experiences
• recording and analysing data

#### Iceberg

A 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 on-going 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 on-going 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 age-appropriate 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

1. Suppose the dice was marked 1, 2, 3, 4 IN and 1, 2 OUT. Could it ever be that the pond was empty of frogs? If so, on average, how many rolls to empty the pond?
2. What happens if one player begins with 5 frogs and the other begins with 4?
3. What happens if you have to empty your pond exactly?
4. What happens if one player has to miss a turn if they roll (say) 1 OUT.
5. Use these Investigation Guides shared by Toni Pfeiffer, Good Shepherd, Amaroo - or design your own and share it here.
Investigation Guide 1
Investigation Guide 2
This task is also linked to Task 47, Red & Black Card Game, which uses a similar addition/subtraction structure, but includes negative numbers.

#### Whole Class Investigation

Tasks 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:

• a score of 1, 2, 3 means 1, 2, 3 IN
• a score of 4, 5, 6 means 1, 2, 3 OUT
If you have Poly Plug the plugs make excellent frogs.

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 in-context 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 hands-on learning kits available from Years 3-10 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:

• MWA Chance & Measurement Years 3 & 4
• MWA Chance & Measurement Years 7 & 8

## From The Classroom

#### Footscray North Primary School

Prep/Year 1
The table top game was played after acting out the game as frogs out in the yard.

Arrange your frogs so I can just walk past and see how many there are?
Then I don't have to count.

Subitising: We just know it is 6 because we can just see it.

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