Bootstrap: Algebra

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.

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

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

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

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

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.

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.

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.

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.

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).

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

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

Students define functions that control the movement of the target and danger in their games.

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.

Students take a closer look at how functions can work together by investigating the relationship between revenue, cost, and profit.

Students identify solutions and non-solutions of inequalities using an interactive starter file. This lesson also reviews the Boolean data type.

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

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.

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

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.

Students apply their knowledge of the Pythagorean Theorem and Circles of Evaluation to develop a function for the distance formula.

Students use function composition and the distance formula to detect when characters in their games collide.

This is a single page that contains all the lessons listed above.