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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.LE.B

    Interpret expressions for functions in terms of the situation they model.

    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.

    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.

    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.4

    Model with mathematics

    MP.2

    Reason abstractly and quantitatively

    (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). CCbadge 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.