Contextualization

Introduction to the topic

Negative numbers are a fundamental concept in mathematics. They are present in a wide range of areas from finance to physics and essential to solve a wide range of problems, so a good knowledge of their operation is fundamental.

Negative numbers represent the opposite concept to positive, and in physics they can represent a movement backwards, in economics a negative balance indicates that more money has been spent than earned, and a negative temperature in meteorology indicates below zero.

The operations with negative numbers follow some basic rules that must be learnt, such as multiplying and dividing two negative numbers resulting in a positive one, while adding and subtracting two negative numbers results in a negative number.

These rules, despite being simple, have great importance, and allow us to solve complex problems. To understand how they operate, the implications they have and the correct way to use them is not just a school exercise, but something that can be used in everyday situations.

Contextualization

Negative numbers have a wide range of uses in real situations. If you scrape the floor, the position of your hand is below ground level, representing a movement in a “negative” direction. Negative numbers are used to indicate economic losses too, an account in negative represents you spent more money than you earned, and in meteorology, temperatures below 0 are measured in negative numbers.

To understand the operation and functionality of these is, therefore, essential to solving everyday problems, and to better understand the world that surrounds us. The projects you are going to develop will help you to learn about this concept, and will also help you work in a team, improving communication and collaboration skills along the way.

Practical Activity

Activity Title: Not everything is negative: operations with negative numbers

Objective of the project

The objective of this project is to encourage the understanding of working with negative numbers, and the basic operations involved (adding, subtracting, multiplying and dividing), and to promote teamwork and logical reasoning, and time management.

Project description

Each group of 3 to 5 students will create a game using an operations board featuring negative numbers, the rules of play and the challenges posed should be created and designed by the student groups, with the teacher being there to offer support and advice. It is important that the game includes real life situations or topics that interest the student groups to give the experience more meaning.

Necessary materials

• Cardboard or foam board to make the board game base
• Coloured card to make the playing pieces, and cards for the game
• Felt tip pens or colouring pencils, and other decorative materials to finish the board
• Scissors without sharp points
• Glue

Step by step

1. Group Formation: The students will organise themselves into teams of 3-5 people, each group will nominate a group leader who will help with the communication and decision making

2. Planning the Game: Students will debate the content of their game, rules, board design, and game cards, amongst other things. All challenges to the game must include operations using negative numbers.

3. Challenge Creation: Each member of a group will think up a series of problems featuring operations using negative numbers, which will then be written on the game cards.

4. Board and card creation: Using the cardboard and coloured card the students will create their game boards and playing pieces, and game cards

5. Play testing and adjustments: Once the games are finished, the students should play test them and make any necessary changes

6. Project Report: The groups must put together a project report which explains the content of the game they created including the game rules and instructions, and the challenges with answers. As well as any problems encountered, and how they overcame them

Project Presentation

Once the projects are finished, each team will present a report to the rest of the class, and explain the game rules, and play one quick game

The following must be included in the report

1. Introduction: Here the students will explain their aims for the game and why they have chosen the format they have. They can also use this space to describe the real world uses of operations with negative numbers

2. Development: Here the step by step method of creating their game should be detailed, along with their game rules. Negative number operations used in the game should be justified, and examples of challenges given with their solution

3. Conclusion: Reflections should be included here about the game creation experience and what they have learnt from the process, not just about using negative numbers, but regarding team work and time management

4. Bibliography: Any sources used in the learning about negative number operations and the game creation process must be cited

The games that are created will be kept for use by other students going forward, for use as revision tools and general entertainment.

This project should be carried out over a month-long period, and is estimated to require between 5-10 hours from each participant