Bootstrap: Algebra 🖼Show image
(Also available in WeScheme)
Lesson Plans
 The Numbers Inside Video Games

Students play a simple video game, identifying which components are constant, which are variables, and how they change. They discuss their favorite games and think about the work involved in making them.
 Coordinates and Game Design

Students learn that characters' positions in videogames can be described using coordinates, then brainstorm the context and characters for the games they will design.
 Order of Operations

Students learn to model arithmetic expressions with a visual tool for Order of Operations, known as "Circles of Evaluation".
 Simple Data Types

Students begin to program, explorings how Numbers, Strings, Booleans and operations on those data types work in this programming language.
 Contracts

Students learn how to apply Functions in the programming environment and interpret the information contained in Contracts: Name, Domain and Range. Imageproducing functions provide an engaging context for this exploration.
 Function Composition

Students learn to combine image transformation functions as well as to describe the order of operations involved in algebraic function compositions such as f(g(h(x))) using Circles of Evaluation.
 Defining Values

Students learn to improve readability, performance and maintanability of code by defining values that repeat in code, just as we would define variables in math.
 Making Flags

Students recreate images of flags of varying complexity by transforming and composing image functions and applying their knowledge of ratios and coordinates to scale and position the shapes precisely.
 Making Game Images

Students choose, import, scale and orient images for their game, practicing reading comments to make sense of and begin to edit a large body of code.
 Defining Functions

Students discover that they can make their own functions, and learn to connect function descriptions across three representations: Contracts (a mapping between Domain and Range), Examples (a list of discrete inputs and outputs), and Definitions (symbolic).
 Solving Word Problems

Students are introduced to the Design Recipe as a scaffold for breaking down word problems into chunks that will support them in writing code.
 Restating the Problem

Students practice using the Design Recipe to write purpose statements for word problems that describe linear relationships, volume & surface area calculations, image functions, etc.
 Functions for Character Animation

Students define functions that control the movement of the target and danger in their games.
 Surface Area of a Rectangular Prism

Students define the shapes used to build a rectangular prism, print them, cut them out, and build the rectangular prism. Then they use their model to calculate the surface area.
 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 identify solutions and nonsolutions of inequalities using an interactive starter file. This lesson also reviews the
Boolean
data type.  Compound Inequalities: Solutions & NonSolutions

Students build upon their understanding of booleans and simple inequalities to compose compound inequalities using the concepts of union and intersection.
 Sam the Butterfly  Applying Inequalities

Students discover that inequalities have an important application in video games: keeping game characters on the screen! Students apply their understanding to edit code so that it will keep Sam the Butterfly safely in view.
 Piecewise Functions

Students learn how to define a function so that it behaves differently depending on the input.
 Player Animation

Students apply their knowledge of piecewise functions to write a function that will move the player in their game in different directions and at different speeds depending on which key is pressed.
 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  Distance and Inequality

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.
Ordering Student Workbooks?
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Teaching Remotely?
If you’re teaching remotely, we’ve assembed an Implementation Notes page that makes specific recommendations for inperson v. remote instruction.
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 National and State Standards, as well as some of the most commonly used math textbooks.

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 paperandpencil practice and activities that don’t require a computer.

TeacherOnly Resources — We also offer several teachersonly materials, including an answer key to the student workbook, keys to all the exercises, and pre and posttests 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.

Online Community (Discourse) — Want to be kept uptodate 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 by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.