Background
Introduction
Negative numbers are central to mathematics and used in a multitude of applications from basic everyday problem solving all the way to the advanced applications in fields like physics, economics, or engineering, to list just few. Simply stated, a negative value describes quantities that exist "to the left " of zero.
The mathematical world evolved over centuries and the introduction of negative number is an example of that development . Initially, the concept of a number smaller than 0 appeared unnatural, since how can you have less of something than nothing, but the need of describing various phenomena and solving different types of mathematical or everyday life problems brought the negative value to life
Understanding how negative numbers behave is an important step towards understanding more complex equations, expressions and problem formulating. While they largely operate in the same manner to their "normal" counterparts , getting a grip on the nuances and details requires quite some practice. This project is aiming towards providing that much needed practical experience while also keeping it playful and engaging
Context and Importance
Negative numbers are far from being an abstract mathematical playground concept, rather they have a multitude of important and tangible applications in real life . For example they are being used in finances to denote debt, in the temperature scales for degrees below 0 and in measuring the depth below a certain surface level.
Getting comfortable with understanding and manipulating negative numbers is not only important from an economical perspective but also for understanding weather forecasts predicting low temperatures or correctly analyzing graphs and data sets from various disciplines.
Activity
Activity Title: Battleship with Negative Numbers
Objectives
To practice and improve negative numbers handling skill by introducing a collaborative and competitive game, which encourages the usage of negative values. Learning to detect the location, identify and work with different numerical values on the numeric scale.
In depth project description
The activity asks teams to play and create a variation of a popular board game , Battleship, which introduces a twist in the form negative numerical values . Instead the classic 10x10 grid, the playing field for this version will be one dimensional number scale, with the range of - 10 to +10. Players will secretly place their ships in different locations along that number scale and then take turns guessing the location of their opponent's ships using negative and non-negative number guesses.
## Required Material
-
Graphing paper or regular piece of notebook paper.
-
Markers or color pencils
-
ruler
## Detailed step-by-step description
-
Form into Teams: The students will form into teams of three to five people . Each team is going to compete against all of the other team.
-
Set up of the game: On a piece of graphing paper each group will design two parallel numeric scales from -10 to 10. The first number scale will be used to secretly plot their "ships," the second one will serve as an opponents battlefield where each number value represents an attempt to "hit" one of the opponents " ships."
-
Place Ships: The "ships" are line segments varying in length from 1 to 5. The student will decide on the length and location for each "ship" they own. Ships can be placed freely anywhere on the number scale, thus occupying both negative and positive number value spaces. The exact location of every "ship" must be recorded on a separate sheet.
-
Gameplay: Teams will take turn "firing" a number value at an opposing team's number scale, attempting to "hit." An opponent "ship" is hit if the number value matches the value where some part of an opponents "Ship" occupy. For example, a team may call out to "Fire" at "-7." If an opponent has part of its " ship" located at - 7 on their plotted scale, a successful " hit " has been made
5. Score: Each " ship" is worth a number of points based on its length, For every successfully " Hit" on an opponents " ship" , the team firing earns the amount of the points corresponding to the length of the segment representing the sunk ship.
- Winning: The activity continues until each team had an equal number of turns " shooting" at their opponents "ships" and defended their own fleet . The group that has the most total points at the conclusion of the game, will be the victor and has successfully navigated the high sea of negative number arithmetic
## Deliverables
Once the activity has been concluded every team should compile a project document covering the following topics
1. An introduction: Here every team will explain the purpose and objectives, provide a basic explanation on what negative numbers and why their understanding is essential, as well as describe how your team's game variation of the Battleship is promoting the practice and understanding with negative values on the numeric number scale .
2. Development In this section your team needs describe step-by-step how your specific game play evolved. This should cover the creation of game rules your team came up with, include a detailing on how the "ships were placed, how decisions within the group were made and include examples of negative value calculations used . Discuss which of these strategic approaches worked well or maybe not so much, providing reasons and offering suggestion for possible improvements.
3 Results and Conclusion: Here you are asked to discuss and analyze your gameplay results and observations. How was the overall game experience like, how did it feel to practice using negative values in such an active and interactive manner ? Summarized what your main takeaways are regarding the understanding of negative values as well as their general behavior on the real numbers scale
4 References: Please include any resource used during the project's development and execution. This includes books, websites , apps or videos that influenced or supported your team in this activity.
