Crazy AnimalsTask 102 ... Years 2  10SummaryThis investigation began when a child in the first year of school brought along a book that allowed the reader to connect the head of one animal with the body of another with the legs of another. Talk about Crazy Animals! Over the years it has become a favourite at all levels. Everyone seems to want to make and name the animals and work out how many there are? But there is much more to the task than that.Materials

Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
Using only two animals, there are 8 crazy possibilities, including the 'normal' animal. For three animals there are 27 possibilities. But how do you know? There are several strategies children could use to work this out.
The second part of the card explores probabilities related to making a crazy animal at random. In this case the animal identified as the student's favourite. Each animal has an equal chance of being made, ie: in the two animal case  1 in 8, and in the three animal case  1 in 27. So, in the long run we would expect, respectively, an average of 8 or 27 rolls to make the chosen favourite. Here is an opportunity to experience the concept of short term variability and compare it with a long term average. It may be that in a given trial a student makes their favourite the first roll. However, it may be that it takes 200 rolls for the favourite to appear.

Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.
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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. 
Question 4 on the card can be an introduction to a whole class lesson. It actually takes many experiments to be able to get a clear idea of the expected number of rolls to make a favourite. More than any pair is likely to do. So the instruction to 'keep a tally' can be reinterpreted in the whole class environment. Over time each pair explores the task and records their 'trials to make the favourite' results on a class chart (or spreadsheet). Discussion develops on a regular basis as the data is viewed and reviewed. Alternatively, if you make your own Crazy Animal books or cards, the investigation can be compressed into a couple of lessons with each pair (or person) carrying out as many 'trials to favourite' experiments in, say, 10 minutes as possible. This approach, and several other directions for the investigation, are explored in the companion Maths300 lesson, which includes software. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 57, Crazy Animals, which includes an Investigation Guide and companion software. This lesson is also available in the Free Tour section of Maths300, so all aspects of the lesson are available to nonMembers, including the software. 
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 Crazy Animals task is an integral part of:
The Crazy Animals lesson is an integral part of:
Crazy Animals task is also included in the Task Centre Kit for Aboriginal Students and the Primary Library Kit. Solutions for tasks in the latter kit can be found here. 