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? 		 

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
The Frog Pond

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 		   

  1. What happens if you begin with 4 frogs, or 6 frogs or 10 frogs? Which variation makes do you prefer to play and why?
  2. Whichever variation you choose, is the game fair? How do you decide?
  3. 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?
  4. What happens if one player begins with 5 frogs and the other begins with 4?
  5. What happens if you have to empty your pond exactly?
  6. What happens if one player has to miss a turn if they roll (say) 1 OUT.
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 on Poly Plug & Tasks, and also see learners at work below.

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

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From The Classroom

Prep/Year 1 at Footscray North Primary School. 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.

Students at work 1

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

Students at work 2

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