Bootstrap:Algebra Pathway

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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.

Teaching Remotely?

If you’re teaching remotely, we’ve assembled an Implementation Notes page that makes specific recommendations for in-person v. remote instruction.

Ordering Student Workbooks?

While we give our workbooks away as a PDF (see below), we understand that printing them yourself an be expensive! You can purchase beautifully-bound copies of the student workbook from Lulu.com.

Click here to order.

We provide all of our materials free of charge, to anyone who is interested in using our lesson plans or student workbooks.

Lesson Plans

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.

Other Resources

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.

Glossary — A list of vocabulary words used in this pathway.
Standards Alignment — Find out how our materials align with Common Core Content and Practice Standards, as well as the TEK and CSTA Standards.
Student Workbook — Sometimes, the best way for students to get real thinking done is to step away from the keyboard! Our lesson plans are tightly integrated with the Student Workbook, allowing for paper-and-pencil practice and activities that don’t require a computer.
Teacher-Only Resources — We also offer several teachers-only materials, including an answer key to the student workbook, a quick-start guide to making the final project, and pre- and post-tests for teachers who are participating in our research study. For access to these materials, please fill out the password request form. We’ll get back to you soon with the necessary login information.
Bootstrap Discussion Forum — Want to be kept up-to-date about Bootstrap events, workshops, and curricular changes? Want to ask a question or pose a lesson idea for other Bootstrap teachers? These forums are the place to do it.

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.