MATHS300 Lesson 57

Overview

Summary:

One day a young child brought a new book into class for her 'show and tell'. It was a book which mixed up the heads, middle and legs of a set of animals to make a whole collection of 'crazy animals'. The teacher had an idea about investigating how many different animals could be made. Another teacher thought of including a dice to explore the possibility of making these animals. Another thought of naming the animals to add interest and to make recording and publication easier. Yet another realised the algebra possibilities. This lesson is truly the composite of creative teachers sharing and learning from each other.

Resources required:

• Master sheet for Animal Book
• Master sheet for Draw Your Own Animal Book
• One dice for each student
• Investigation Sheet (Years 1 - 3)

Content Outcomes\Links To Curriculum Documents

• using everyday language to describe chance events
• recognising and describing more and less likely events
• making predictions based on informal probability assumptions
• systematically collecting and organising data
• physical graphing
• number
  • powers
  • clever counting
    (also known as selections & arrangements or permutations & combinations)
  • pattern
• algebra
  • symbolic representation
  • generalising
  • expanding brackets and collecting like terms
  • expansion of (n + 1)³

Lesson Stages

1. Introduction
2. Designing and drawing two animals
3. Making up different animals
4. Some dice games
5. Computer simulation
6. Predicting whole and part giraffes
7. Adding a third animal
8. Analysis of secondhand data
9. Writing a story
10. Consolidation

Issues or Discussion Points

• This lesson could be presented as a pencil and paper style of question about combinations and arrangements which is usually reserved for Year 11. The tweak of providing animal booklets which can produce images of the crazy animals has opened the mathematics to children as young as Year 1, who deal with it quite satisfactorily at their level.
  • Is mathematics truly as 'hard' as we make out?
  • Would it be easier for the Year 11 students if we also used structured materials at that level?
• The synthesis of this lesson into the rich whole that it is, has occurred because teachers have been provided with time to share, discuss and explore as professionals on a journey to learn how to teach. What provision do we make within our faculty/school/district/system to regularly grow together in this way?

Straw Vote

After teaching the lesson, please rate each of the following features (out of 10) as to its contribution to the overall quality of the learning experience. This exercise will provide a basis for staff discussion of curriculum development.

Acknowledgements:

This lesson derives from Task 102, Crazy Animals, of the Mathematics Task Centre Project. This professional development project is resourced with over 200 hands-on mathematical tasks packed with equipment for two students. A large amount of information about this project can be found at the Problem Solving Task Centre web site. Follow the Curriculum Corporation link from the opening screen.

The project can supply:

• multiple copies of the the task (card and materials for two students), or in some cases,
• materials in bulk packs so teachers can use this task with the whole class simultaneously.

Offering this service allows teachers to devote more time to the professional issues of planning and executing the use of the materials and to evaluating the learning. Click here to order materials.

Software: Contributions To Learning

The many options of this software extend and enhance the problem solving.

Many students find the process of making Crazy Animals becomes even more enjoyable on the computer. The first option is, in fact, a simulation of the hands-on game, and it creates crazy animals in the same way as the cards:

The students need to realise that the computer really does follow the same construction rules as they did because in the other options a very large number of trials happen very quickly and only the results show.

This, of course, demonstrates the power of the computer as a tool. It can do in real time what the students could never do in a life time. As a result students begin to use the computer in the same way as a mathematician does - as an analysis tool.

Features

Group work: When children work together to solve problems there are benefits which derive from the mathematical conversation. Students challenge and learn from each other (something mathematicians have done forever) as they refine and develop the problem. Mathematics becomes something you do, and succeed at, in community. For many, to the degree that this adds to their self-esteem, the lesson is uplifting.

Materials: are important in the challenge to find all possible crazy animals. They provide the gateway through which all may enter the problem. If presented in the context of traditional mathematics education the problem would likely be reduced to a pencil and paper exercise with animals represented by letters - an algebraic presentation. Certainly, this is a valid objective in the learning program, but as a starting point, it can become the finishing point for many students. It seems fairer, and more likely to allow more students to exhibit their preferred intelligence, if the materials are used.

Working Mathematically connections: One of the key aspects of this lesson is to discover how many crazy animals can be made. This challenge is introduced through two key questions which are central to the Working Mathematically process:

• How many solutions (animals) are there?
• How can you convince me that you have found them all?

Other links to the process are:

• collecting and organising data
• seeing a pattern and making and testing hypotheses based on it
• publishing a story related to the problem solving

First hand data: Because the students use their own animals to produce their own data, many teachers have reported an added interest in the problem.