Functions for Character Animation

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Lessons

Standards in this Lesson

Common Core Math Standards

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.
8.F.B: Use functions to model relationships between quantities.
HSF.BF.A: Build a function that models a relationship between two quantities.
HSF.BF.A.1: Write a function that describes a relationship between two quantities.
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.
HSF.IF.B: Interpret functions that arise in applications in terms of the context.

CSTA Standards

1B-AP-10: Create programs that include sequences, events, loops, and conditionals.
2-AP-11: Create clearly named variables that represent different data types and perform operations on their values.
2-AP-17: Systematically test and refine programs using a range of test cases
2-AP-19: Document programs in order to make them easier to follow, test, and debug.
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.
3B-AP-14: Construct solutions to problems using student-created components, such as procedures, modules and/or objects.
3B-AP-21: Develop and use a series of test cases to verify that a program performs according to its design specifications.

K-12CS Standards

6-8.Algorithms and Programming.Control: Programmers select and combine control structures, such as loops, event handlers, and conditionals, to create more complex program behavior.
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.

Alabama Standards

AL.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.
AL.8.F.B: Use functions to model relationships between quantities.
AL.HSF.BF.A: Build a function that models a relationship between two quantities.
AL.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
AL.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.
AL.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Arkansas Standards

AR.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.
AR.8.F.B: Use functions to model relationships between quantities.
AR.HSF.BF.A: Build a function that models a relationship between two quantities.
AR.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
AR.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.
AR.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

California Standards

CA.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.
CA.8.F.B: Use functions to model relationships between quantities.
CA.HSF.BF.A: Build a function that models a relationship between two quantities.
CA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CA.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.
CA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Colorado Standards

CO.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.
CO.8.F.B: Use functions to model relationships between quantities.
CO.HSF.BF.A: Build a function that models a relationship between two quantities.
CO.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CO.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.
CO.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Connecticut Standards

CT.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.
CT.8.F.B: Use functions to model relationships between quantities.
CT.HSF.BF.A: Build a function that models a relationship between two quantities.
CT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CT.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.
CT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Delaware Standards

DE.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.
DE.8.F.B: Use functions to model relationships between quantities.
DE.HSF.BF.A: Build a function that models a relationship between two quantities.
DE.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
DE.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.
DE.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Delaware Standards

GA.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.
GA.8.F.B: Use functions to model relationships between quantities.
GA.HSF.BF.A: Build a function that models a relationship between two quantities.
GA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
GA.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.
GA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Hawaii Standards

HI.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.
HI.8.F.B: Use functions to model relationships between quantities.
HI.HSF.BF.A: Build a function that models a relationship between two quantities.
HI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
HI.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.
HI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Idaho Standards

ID.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.
ID.8.F.B: Use functions to model relationships between quantities.
ID.HSF.BF.A: Build a function that models a relationship between two quantities.
ID.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ID.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.
ID.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Illinois Standards

IL.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.
IL.8.F.B: Use functions to model relationships between quantities.
IL.HSF.BF.A: Build a function that models a relationship between two quantities.
IL.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
IL.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.
IL.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Iowa Standards

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.
IA.8.F.B: Use functions to model relationships between quantities.
IA.HSF.BF.A: Build a function that models a relationship between two quantities.
IA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
IA.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.
IA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Kansas Standards

KS.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.
KS.8.F.B: Use functions to model relationships between quantities.
KS.HSF.BF.A: Build a function that models a relationship between two quantities.
KS.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
KS.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.
KS.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Kentucky Standards

KY.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.
KY.8.F.B: Use functions to model relationships between quantities.
KY.HSF.BF.A: Build a function that models a relationship between two quantities.
KY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
KY.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.
KY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Louisiana Standards

LA.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.
LA.8.F.B: Use functions to model relationships between quantities.
LA.HSF.BF.A: Build a function that models a relationship between two quantities.
LA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
LA.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.
LA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Maine Standards

ME.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.
ME.8.F.B: Use functions to model relationships between quantities.
ME.HSF.BF.A: Build a function that models a relationship between two quantities.
ME.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ME.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.
ME.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Michigan Standards

MI.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.
MI.8.F.B: Use functions to model relationships between quantities.
MI.HSF.BF.A: Build a function that models a relationship between two quantities.
MI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MI.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.
MI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Maryland Standards

MD.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.
MD.8.F.B: Use functions to model relationships between quantities.
MD.HSF.BF.A: Build a function that models a relationship between two quantities.
MD.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MD.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.
MD.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Massachusetts Standards

MA.6-8.CT.a.2: Define a simple function that represents a more complex task/problem and can be reused to solve similar tasks/problems.
MA.6-8.CT.b.2: Use logical reasoning to predict outputs given varying inputs.
MA.6-8.CT.d.2: Use functions to hide the detail in a program.
MA.6-8.CT.d.5: Trace programs step-by-step in order to predict their behavior.
MA.6-8.DTC.a.4: Individually and collaboratively use advanced tools to design and create online content (e.g., digital portfolio, multimedia, blog, webpage).
MA.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.
MA.8.F.B: Use functions to model relationships between quantities.
MA.9-12.CT.b.2: Represent algorithms using structured language, such as pseudocode.
MA.HSF.BF.A: Build a function that models a relationship between two quantities.
MA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MA.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.
MA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Mississippi Standards

MS.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.
MS.8.F.B: Use functions to model relationships between quantities.
MS.HSF.BF.A: Build a function that models a relationship between two quantities.
MS.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MS.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.
MS.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Missouri Standards

MO.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.
MO.8.F.B: Use functions to model relationships between quantities.
MO.HSF.BF.A: Build a function that models a relationship between two quantities.
MO.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MO.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.
MO.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Montana Standards

MT.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.
MT.8.F.B: Use functions to model relationships between quantities.
MT.HSF.BF.A: Build a function that models a relationship between two quantities.
MT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MT.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.
MT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Hampshire Standards

NH.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.
NH.8.F.B: Use functions to model relationships between quantities.
NH.HSF.BF.A: Build a function that models a relationship between two quantities.
NH.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NH.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.
NH.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Nevada Standards

NV.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.
NV.8.F.B: Use functions to model relationships between quantities.
NV.HSF.BF.A: Build a function that models a relationship between two quantities.
NV.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NV.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.
NV.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Jersey Standards

NJ.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.
NJ.8.F.B: Use functions to model relationships between quantities.
NJ.HSF.BF.A: Build a function that models a relationship between two quantities.
NJ.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NJ.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.
NJ.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Mexico Standards

NM.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.
NM.8.F.B: Use functions to model relationships between quantities.
NM.HSF.BF.A: Build a function that models a relationship between two quantities.
NM.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NM.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.
NM.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

North Carolina Standards

NC.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.
NC.8.F.B: Use functions to model relationships between quantities.
NC.HSF.BF.A: Build a function that models a relationship between two quantities.
NC.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NC.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.
NC.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

North Dakota Standards

ND.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.
ND.8.F.B: Use functions to model relationships between quantities.
ND.HSF.BF.A: Build a function that models a relationship between two quantities.
ND.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ND.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.
ND.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New York Standards

NY.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.
NY.8.F.B: Use functions to model relationships between quantities.
NY.HSF.BF.A: Build a function that models a relationship between two quantities.
NY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NY.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.
NY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Oklahoma Standards

OK.3.AP.M.02: With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features.
OK.4.AP.M.02: With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features.
OK.5.AP.M.02: With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features.
OK.6.AP.PD.01: Seek and incorporate feedback from team members to refine a solution to a problem.
OK.7.AP.PD.01: Seek and incorporate feedback from team members and users to refine a solution to a problem.
OK.8.AP.A.01: Design algorithms in natural language, flow and control diagrams, comments within code, and/or pseudocode to solve complex problems.
OK.MAP.3: Develop strategies for problem solving.
OK.PA.A.1.2: Use linear functions to represent and explain real-world and mathematical situations.
OK.PA.A.2: Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context.
OK.PA.A.2.1: Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.

Ohio Standards

OH.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.
OH.8.F.B: Use functions to model relationships between quantities.
OH.HSF.BF.A: Build a function that models a relationship between two quantities.
OH.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
OH.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.
OH.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Oregon Standards

OR.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.
OR.8.F.B: Use functions to model relationships between quantities.
OR.HSF.BF.A: Build a function that models a relationship between two quantities.
OR.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
OR.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.
OR.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Pennsylvania Standards

PA.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.
PA.8.F.B: Use functions to model relationships between quantities.
PA.HSF.BF.A: Build a function that models a relationship between two quantities.
PA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
PA.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.
PA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Rhode Island Standards

RI.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.
RI.8.F.B: Use functions to model relationships between quantities.
RI.HSF.BF.A: Build a function that models a relationship between two quantities.
RI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
RI.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.
RI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

South Dakota Standards

SD.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.
SD.8.F.B: Use functions to model relationships between quantities.
SD.HSF.BF.A: Build a function that models a relationship between two quantities.
SD.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
SD.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.
SD.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Tennessee Standards

TN.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.
TN.8.F.B: Use functions to model relationships between quantities.
TN.HSF.BF.A: Build a function that models a relationship between two quantities.
TN.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
TN.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.
TN.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Utah Standards

UT.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.
UT.8.F.B: Use functions to model relationships between quantities.
UT.HSF.BF.A: Build a function that models a relationship between two quantities.
UT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
UT.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.
UT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Vermont Standards

VT.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.
VT.8.F.B: Use functions to model relationships between quantities.
VT.HSF.BF.A: Build a function that models a relationship between two quantities.
VT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
VT.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.
VT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Washington Standards

WA.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.
WA.8.F.B: Use functions to model relationships between quantities.
WA.HSF.BF.A: Build a function that models a relationship between two quantities.
WA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WA.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.
WA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

West Virginia Standards

WV.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.
WV.8.F.B: Use functions to model relationships between quantities.
WV.HSF.BF.A: Build a function that models a relationship between two quantities.
WV.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WV.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.
WV.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Wisconsin Standards

WI.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.
WI.8.F.B: Use functions to model relationships between quantities.
WI.HSF.BF.A: Build a function that models a relationship between two quantities.
WI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WI.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.
WI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Wyoming Standards

WY.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.
WY.8.F.B: Use functions to model relationships between quantities.
WY.HSF.BF.A: Build a function that models a relationship between two quantities.
WY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WY.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.
WY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Textbook Alignment

IM Algebra 1

IM.Alg1.4.10: Domain and Range (Part 1)
IM.Alg1.4.6: Features of Graphs

IM 8 Math™

IM.8.3.11: Equations of All Kinds of Lines

IM 6 Math™

IM.6.6.6: Write Expressions Where Letters Stand for Numbers
IM.6.3.8: More about Constant Speed

Practices in this Lesson

Math

MP.2: Reason abstractly and quantitatively
MP.4: Model with mathematics

(Also available in Pyret)

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

Lesson Goals

Students will be able to:

Apply the Design Recipe to create a function given the constraints of a word problem.
Explain the basics of animation.

Student-Facing Lesson Goals

I can use the Design Recipe to make a function.
I can describe how animation works.

Materials

Key Points for the Facilitator

Encourage students to take their time in understanding why we want to fix update-danger and update-target.
Students might be confused as to how the animation is working. The make-game function at the bottom of the file has many inputs - including update-danger and update-target. make-game takes in all those inputs, including the functions we’ll write, and creates the interactive window that we see when we click the "Run" button!

Glossary

coordinate: a number describing an object’s location
design recipe: a sequence of steps that helps people document, test, and write functions
domain: the type or set of inputs that a function expects
function: a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output
range: the type or set of outputs that a function produces

🔗Animation 45 minutes

Overview

Students connect the behavior of functions with changing coordinate values, ultimately leading to animation.

Launch

How does a flip-book animation work?
- Each page of the book is slightly different, and the pages go so fast that the motion looks smooth.
Why do we see movement from still images?
- Our eyes fill in the gaps between rapidly changing images.
How might this apply to our game?
- If we change image coordinates a little bit at a time, they will appear to move.

Draw a number line on the board, running from 0 to 1000 (you can also lay tape on the floor, or use a tile floor as a coordinate plane!). Select 2 student volunteers - one to be TARGET, one to be DANGER. Start with just TARGET. Have the class select a starting x- and y-coordinate for the TARGET.

The TARGET starts at a particular position, and then moves by 50 (pixels) to the left on each frame of the game.

When the TARGET hears "update target" followed by their current location, they take a step in the negative direction, moving left across the x-axis by 50 (pixels).

Make TARGET move by calling out (update-target 300), (update-target 250), etc.

Ask students: what if we wanted the update-target function to move the TARGET across the classroom more quickly? How would the function have to change?

Repeat with DANGER, this time moving right across the x-axis. Then ask: what if we wanted update-danger to move the DANGER in the opposite direction?

What did you notice about the movement of TARGET and DANGER? What was changing about them?
- Answers will vary: they were moving horizontally, their x-coordinates were changing, they were not moving smoothly, etc.
What jobs could we hand over to the computer to make it possible for us to play the game?
- The computer could handle automatically moving TARGET and DANGER, then we could control the movement of PLAYER.

Investigate

Sign in to WeScheme and open your saved Game Starter Files, or make a new copy.
Examine the update-danger function. Identify the contract, and interpret what the function is currently doing.
Complete the first word problem on Danger and Target Movement.
Transfer the code to your Game Starter File.

When students click the "Run" button, the working update-danger function should automatically move the DANGER image across the screen!

Complete the second word problem on Danger and Target Movement.
With your partner, transfer the code to your Game Starter File.
Click "Run" to see DANGER and TARGET move across the screen independently!

Extension Activities

Once students have successfully gotten update-target and update-danger working, they can change the functions to make the characters move in whichever direction and whatever speed they want! They should be sure to modify their purpose statements and examples if they change their functions.

Synthesize

Connecting the code to the underlying math is important - especially if you want to customize your game!

What part of the function controls the character’s speed?
What part of the function controls the character’s direction?
If you wanted the characters to move in 2 dimensions (diagonally, for example), would anything have to change about the Domain? What about the Range?

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.