Bootstrap:Algebra 🖼Show image
The Bootstrap:Algebra Pathway applies mathematical concepts and rigorous programming principles to creating a simple video game, and is aligned to National and State Standards for Mathematics, as well as the CSTA standards and K12CS frameworks. The module can be taught as a separate, standalone tech or CS class, or can be integrated into a mainstream math class, delivered by a math teacher with no prior CS experience.
In this series of lessons, students create a simple, 3-character game involving a player, a target and a danger. They design what each character looks like, and use mathematical concepts such as coordinate planes, order of operations, ratio and proportion, domain and range, function composition, word problems and the distance formula to detect collisions, handle keystrokes, and determine how they move and interact.
If you’re teaching remotely, we’ve assembled an Implementation Notes page that makes specific recommendations for in-person v. remote instruction.
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- The Numbers Inside Video Games
Students reverse engineer a video game and research what takes to create a video game.
- Coordinates and Game Design
Students review the importance and need for coordinates in the context of a video game and brainstorm a game of their own.
- Order of Operations
Students learn to model arithmetic expressions with a visual tool for order of operations, known as "Circles of Evaluation".
- Domain and Range
Students encounter String and Image datatypes and use "contracts" to make sense of the domain and range of functions.
- Function Composition
Students encounter new image transformation functions and strengthen their understanding of Circles of Evaluation by using functions within other functions.
- Defining Values
Students learn how to define lines of code as a set value that can be used repeatedly in different situations, similar to a variable in math.
- Making Game Images
Students practice using a new function alongside previously-learned functions to choose images for their game.
- Defining Functions
Students discover functions as an abstraction over a programming pattern, and are introduced to a structured approach to building them called the Design Recipe.
- Solving Word Problems
Students discover functions as an abstraction over an arithmetic pattern, applying the Design Recipe to traditional word problems.
- Restating the Problem
Students apply their skills in using the Design Recipe and writing purpose statements to a variety of word problems.
- Character Animation
Students define functions that control the movement of the target and danger in their games
- Problem Decomposition
Students take a closer look at how functions can work together by investigating the relationship between revenue, cost, and profit.
- Simple Inequalities
Students discover the Boolean data type, and apply knowledge of inequalities to simple programming problems.
- Compound Inequalities
Students learn to compose inequalities using the concepts of union and intersection, and solve problems using compound inequalities. Finally, they apply what they’ve learned to set screen boundaries in their game.
- Piecewise Functions
Students will learn how one function can have different behaviors based on the input.
- Player Animation
Students apply their knowledge of piecewise functions to write a function to move the player in their game.
- The Distance Formula
Students apply their knowledge of the Pythagorean Theorem and Circles of Evaluation to develop a function for the distance formula.
- Collision Detection
Students use function composition and the distance formula to detect when characters in their games collide.
- All the lessons
This is a single page that contains all the lessons listed above.
Of course, there’s more to a curriculum than software and lesson plans! We also provide a number of resources to educators, including standards alignment, a complete student workbook, an answer key for the programming exercises and a forum where they can ask questions and share ideas.
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). Bootstrap:Algebra by Emmanuel Schanzer, Jen Poole, Ed Campos Jr, Flannery Denny, and Dorai Sitaram is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.