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

Prerequisites

Restating the Problem

Relevant Standards

Select one or more standards from the menu on the left (⌘-click on Mac, Ctrl-click elsewhere).

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.

MP.2

Reason abstractly and quantitatively

MP.4

Model with mathematics

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.PA.A.1.2

Use linear functions to represent and explain real-world and mathematical situations.

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

Preparation

  • Make sure all materials have been gathered

  • Decide how students will be grouped in pairs

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 press the Run button!

Language Table

Types

Functions

Values

Number

num-expt, num-sqr, num-sqrt

4, -1.2, 2/3, pi

String

string-length, string-repeat, string-contains

"hello", "91"

Boolean

<, <>, <=, >=, <, >, ==, <>, >=

true, false

Image

star, triangle, circle, square, rectangle, rhombus, ellipse, regular-polygon, radial-star, text, overlay, above, beside, rotate, scale, flip-horizontal, flip-vertical

🔵🔺🔶

Click here to see the prior unit-based version

Glossary
coordinate

a number or set of numbers describing an object’s location

design recipe

a sequence of steps that helps people document, test, and write functions

function

a mathematical object that consumes inputs and produces an output

🔗Animation 45 minutes

Overview

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

Launch

Students should have their computer, contracts page, and pencil. Students should have their own game file open in a separate window or tab.

  • 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-coordinate for the TARGET, and have the volunteer move to that position on the number line or coordinate plane.

  • The TARGET character moves by 50 (pixels) on each frame of the game.

  • When they hear "update target" followed by their current location, the TARGET takes a step in the negative direction, moving down the x-axis by 50 (pixels).

  • We make TARGET move by calling out update-target(300), update-target(250), etc.

How quickly could I get TARGET to move across the classroom?

After practicing with TARGET, add DANGER in.

  • DANGER takes a step in the positive direction when they hear "update danger" followed by their current x-coordinate.

  • We make DANGER move by calling out update-danger(40), update-danger(39), etc.

  • On a standard number line, if the DANGER is moving to the right, is its x-coordinate increasing or decreasing?

Practice this a few times with your volunteer, asking the class what their new x-coordinate is each time. Then have the other students call the update-danger function.

  • 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

  • Have students examine the update-danger function in their Game Starter File, identify the contract, and interpret what the function is currently doing.

  • Guide students as they complete the first word problem on Danger and Target Movement (Page 63), and transfer the code to their Game Starter File.

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

Have students complete the second word problem on Danger and Target Movement (Page 63), with their partner and transfer the code to their Game Starter File. Press 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.

Want 2-D movement? A supplemental lesson linked here provides information on how to modify these functions to allow movement in the x and y directions!

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Algebra 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.