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Bootstrap lessons align with several important teaching standards. Select particular standards from the following menu to see which lessons meet those standards.

Common Core Math Standards

5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [See: Coordinates and Game Design.]

6.EE.B.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [See: Simple Inequalities.]

6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Function Composition; Defining Values; Defining Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly - Applying Inequalities; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly - Applying Inequalities.]

6.G.A.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. [See: Surface Area of a Rectangular Prism.]

6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]

6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]

7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]

7.EE.B

Solve real-life and mathematical problems using numerical and algebraic expressions and equations. [See: Solving Word Problems; Problem Decomposition; Sam the Butterfly - Applying Inequalities; Piecewise Functions; Player Animation; The Distance Formula.]

7.EE.B.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Defining Functions; Solving Word Problems; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

7.G.B.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Surface Area of a Rectangular Prism.]

7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Game Images.]

8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts.]

8.F.B

Use functions to model relationships between quantities. [See: Defining Functions; Solving Word Problems; Restating the Problem; Functions for Character Animation.]

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]

8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]

8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [See: The Distance Formula.]

8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]

8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Defining Functions.]

HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly - Applying Inequalities.]

HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly - Applying Inequalities.]

HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Defining Functions.]

HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions; Player Animation.]

HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions; Player Animation.]

HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]

HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]

HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Composition; Problem Decomposition.]

HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Defining Functions; Restating the Problem; Problem Decomposition; Collision Detection - Distance and Inequality.]

HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly - Applying Inequalities.]

HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly - Applying Inequalities; Collision Detection - Distance and Inequality.]

HSF.IF.A

Understand the concept of a function and use function notation. [See: Defining Functions.]

HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts.]

HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Defining Functions; Solving Word Problems; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Making Flags; Defining Functions.]

HSF.IF.C

Analyze functions using different representations. [See: Defining Functions.]

HSF.LE.B

Interpret expressions for functions in terms of the situation they model. [See: Functions for Character Animation.]

HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]

HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & Non-Solutions.]

Connected Math Standards

CMP.6.1

Prime Time: Factors & Multiples [See: Order of Operations.]

CMP.6.4

Covering and Surrounding: Two Dimensional Measurement [See: Surface Area of a Rectangular Prism.]

CMP.6.6

Variables and Patterns: Focus on Algebra [See: Defining Values.]

CMP.7.2

Accentuate the Negative: Integers and Rational Numbers [See: Order of Operations.]

CMP.7.7

Filling and Wrapping: Three Dimensional Measurement [See: Surface Area of a Rectangular Prism.]

CMP.8.2

Looking for Pythagoras: The Pythagorean Theorem [See: The Distance Formula.]

CMP.Alg-Ext.2

Function Junction: Families of Functions [See: Piecewise Functions.]

CSTA Standards

1B-AP-10

Create programs that include sequences, events, loops, and conditionals. [See: Functions for Character Animation; Player Animation.]

1B-AP-11

Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process. [See: Problem Decomposition.]

1B-AP-12

Modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features. [See: Piecewise Functions.]

1B-AP-14

Observe intellectual property rights and give appropriate attribution when creating or remixing programs. [See: Making Game Images.]

1B-AP-15

Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended. [See: Defining Functions.]

1B-IC-21

Use public domain or creative commons media, and refrain from copying or using material created by others without permission. [See: Making Game Images.]

2-AP-11

Create clearly named variables that represent different data types and perform operations on their values. [See: Function Composition; Defining Values; Defining Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

2-AP-13

Decompose problems and subproblems into parts to facilitate the design, implementation, and review of programs [See: Problem Decomposition.]

2-AP-14

Create procedures with parameters to organize code and make it easier to reuse. [See: Defining Functions.]

2-AP-16

Incorporate existing code, media, and libraries into original programs, and give attribution. [See: Making Game Images.]

2-AP-17

Systematically test and refine programs using a range of test cases [See: Function Composition; Defining Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

2-AP-19

Document programs in order to make them easier to follow, test, and debug. [See: Function Composition; Defining Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

3A-AP-16

Design and iteratively develop computational artifacts for practical intent, personal expression, or to address a societal issue by using events to initiate instructions. [See: Functions for Character Animation; Player Animation.]

3A-AP-17

Decompose problems into smaller components through systematic analysis, using constructs such as procedures, modules, and/or objects. [See: Problem Decomposition.]

3A-AP-18

Create artifacts by using procedures within a program, combinations of data and procedures, or independent but interrelated programs. [See: Making Game Images.]

3A-AP-20

Evaluate licenses that limit or restrict use of computational artifacts when using resources such as libraries [See: Making Game Images.]

3B-AP-14

Construct solutions to problems using student-created components, such as procedures, modules and/or objects. [See: Defining Functions; Solving Word Problems; Functions for Character Animation; Problem Decomposition; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

3B-AP-21

Develop and use a series of test cases to verify that a program performs according to its design specifications. [See: Function Composition; Defining Functions; Solving Word Problems; Functions for Character Animation; Problem Decomposition; Piecewise Functions; Player Animation; The Distance Formula; Collision Detection - Distance and Inequality.]

3B-AP-22

Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality). [See: Player Animation.]

Iowa Standards

IA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [See: Coordinates and Game Design.]

IA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Defining Values.]

IA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]

IA.HSF.BF.A.1.C

Compose functions. [See: Function Composition.]

IA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts.]

K-12CS Standards

6-8.Algorithms and Programming.Modularity

Programs use procedures to organize code, hide implementation details, and make code easier to reuse. Procedures can be repurposed in new programs. Defining parameters for procedures can generalize behavior and increase reusability. [See: Defining Functions.]

6-8.Algorithms and Programming.Variables

Programmers create variables to store data values of selected types. A meaningful identifier is assigned to each variable to access and perform operations on the value by name. Variables enable the flexibility to represent different situations, process different sets of data, and produce varying outputs. [See: Defining Values; Defining Functions.]

9-12.Algorithms and Programming.Modularity

Complex programs are designed as systems of interacting modules, each with a specific role, coordinating for a common overall purpose. These modules can be procedures within a program; combinations of data and procedures; or independent, but interrelated, programs. Modules allow for better management of complex tasks. [See: Defining Functions.]

P4

Developing and Using Abstractions [See: Defining Functions.]

Next-Gen Science Standards

HS-SEP5-3

Apply techniques of algebra and functions to represent and solve scientific and engineering problems. [See: Defining Functions.]

Oklahoma Standards

OK.3.A.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]

OK.3.AP.A.01

Compare multiple algorithms for the same task. [See: Making Flags.]

OK.3.AP.M.01

Decompose the steps needed to solve a problem into a precise sequence of instructions. [See: Making Flags.]

OK.3.AP.PD.03

Analyze and debug a program that includes sequencing, repetition and variables in a programming language. [See: Making Flags.]

OK.4.AP.C.01

Create programs using a programming language that utilize sequencing, repetition, conditionals and variables using math operations manipulate values to solve a problem or express ideas both independently and collaboratively. [See: Making Flags.]

OK.4.AP.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]

OK.5.AP.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]

OK.6.AP.M.01

Decompose problems into parts to facilitate the design, implementation, and review of programs. [See: Making Flags.]

OK.8.AP.PD.02

Incorporate existing code, media, and libraries into original programs of increasing complexity and give attribution. [See: Defining Functions.]

OK.A1.A.1.1

Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context. [See: Defining Functions.]

OK.A1.A.2

Represent and solve real-world and mathematical problems using linear inequalities, compound inequalities and systems of linear inequalities; interpret solutions in the original context. [See: Sam the Butterfly - Applying Inequalities.]

OK.A1.A.3

Generate equivalent algebraic expressions and use algebraic properties to evaluate expressions and arithmetic and geometric sequences. [See: Order of Operations.]

OK.A1.A.3.1

Solve equations involving several variables for one variable in terms of the others. [See: Problem Decomposition.]

OK.A1.F.1.2

Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in real-world contexts. [See: Contracts.]

OK.A1.F.1.3

Write linear functions, using function notation, to model real-world and mathematical situations. [See: Defining Functions.]

OK.MAP.1

Develop a deep and flexible conceptual understanding. [See: Making Flags.]

OK.MAP.4

Develop mathematical reasoning. [See: Making Flags.]

OK.PA.A.1.1

Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. [See: Contracts; Defining Functions; Piecewise Functions; Player Animation.]

OK.PA.A.1.2

Use linear functions to represent and explain real-world and mathematical situations. [See: Defining Functions; Restating the Problem; Functions for Character Animation.]

OK.PA.A.1.3

Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line. [See: Solving Word Problems.]

OK.PA.A.2.1

Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. [See: Solving Word Problems.]

OK.PA.A.3

Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions. [See: Order of Operations.]

OK.PA.A.3.1

Use substitution to simplify and evaluate algebraic expressions. [See: Function Composition; Defining Values.]

OK.PA.A.4

Represent real-world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context. [See: Making Flags.]

OK.PA.A.4.3

Represent real-world situations using equations and inequalities involving one variable. [See: Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

OK.PA.GM.1.2

Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane. [See: The Distance Formula.]

OK.PA.GM.2.1

Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units of measure, such as square centimeters. [See: Surface Area of a Rectangular Prism.]