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(Also available for Pyret)

Students apply their knowledge of piecewise functions to write a function to move the player in their game.

Prerequisites

Piecewise Functions

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.

7.EE.B

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients.

HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity.

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.

3B-AP-22

Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality).

Oklahoma Standards
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.

Lesson Goals

Students will be able to:

  • Apply previous knowledge of piecewise functions to a new problem situation.

Student-Facing Lesson Goals

  • I can write a function using conditionals to move my player.

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 challenge themselves when creating update-player by completing one of the extension activities.

  • The update-player function is one of the main places where students can set their game apart and make it theirs. Encourage exploration and experimentation!

  • Adding comments to code - if you have to ask a student "What are you trying to do there?", then they probably need more comments!

Language Table

Types

Functions

Values

Number

+, -, *, /, expt, sqr, sqrt

4, -1.2, 2/3, pi

String

string-length, string-repeat, string-contains?

"hello", "91"

Boolean

<, >, <>, <=, >=, string-equal, string<?, string>?, string=?, string<>?, string>=?, and, or

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
contract

a statement of the name, domain, and range of a function

debug

to find and fix errors in one’s code

function

a mathematical object that consumes inputs and produces an output

piecewise function

a function that computes different expressions based on its input

🔗Defining Piecewise Functions 30 minutes

Overview

Students define a piecewise function. This is a challenging task, which is motivated by introducing key events in their video game.

Launch

Students should have their computer, workbook, contracts page, and pencil and be logged in to WeScheme and have their workbooks with a pen or pencil.

You’ve already defined functions to move your DANGER and TARGET. Take a moment to look at your code or workbook, and refresh your memory on how they work.

  • What controlled the speed of your characters?

  • What controlled the direction of your characters?

If we wanted our PLAYER to go up all the time, we would already know how to do that. If we wanted our PLAYER to go down all the time, we would already know how to do that. But we want the player to go up only when the "up" arrow is pressed, and down when the "down" arrow is pressed. Do we know how to make a function behave differently, based on its input?

Investigate

Students open their Game Project file and look for update-player, then figure out what the contract represents.

Strategies for English Language Learners

MLR 6 - Three Reads: Have students read through the problem statement three times, looking for different information. What is the problem asking me? What is the contract for this function? What information do I need to create that function?

  • What is the contract for update-player?

    The Name is update-player, the Domain consists of a Number and String, and Range is a Number.

  • What does each part of the domain and range represent?

    Domain: the Number is the y-coordinate of PLAYER, the String is the key that the user pressed; Range: the Number is the new y-coordinate of `PLAYER`

  • How does the y-coordinate of PLAYER change when the user presses the "up" key?

    It should increase, the program should add something to it

Player Movement Player Movement🖼Show image

Students complete Word Problem: update-player (Page 81) with a partner, then type their code into their Game Project file and test.

Common Misconceptions

  • Students often think of this function as returning a relative distance (e.g. "it adds 20"), instead of an absolute coordinate (e.g. "the new y-coordinate is the old y plus 20")

Synthesize

  • How is this function similar to the piecewise functions you’ve seen before? How is it different?

  • How could we change this function so that the "W" key makes the player go up, instead of the arrow key?

  • How could we change this function so that the "W" key makes the player go up, in addition to the arrow key?

  • Suppose your little brother or sister walks by and hits a random key. What should happen if you hit a random key that doesn’t have a meaning in your function? What happens now?

🔗Cheat Codes and Customizations flexible

Overview

Students choose one or more features to make their game more unique. These features can be quite simple, such as adding another key that does the same thing that "up" or "down" does. But they can also be extremely sophisticated, requiring students to exploit properties of the number line in conjuntion with function composition and compound inequalities!

Launch

Right now, all of your games allow the player to move up and down at a constant speed. But what if we wanted to add a special key that made the player warp to the top of the screen, or move down twice as fast? What if we wanted the player to wrap, so going off one side of the screen would make it re-appear on the other?

Investigate

Now is your time to customize your game! Try implementing some of the following features, or make your own!

  • Warping - program one key to "warp" the player to a set location, such as the center of the screen

  • Boundaries - change update-player such that PLAYER cannot move off the top or bottom of the screen

  • Wrapping - add code to update-player such that when PLAYER moves to the top of the screen, it reappears at the bottom, and vice versa

  • Hiding - add a key that will make PLAYER seem to disappear, and reappear when the same key is pressed again

Reminder: Use ; to add comments to code!

Adding useful comments to code is an important part of programming. It lets us leave messages for other programmers, leave notes for ourselves, or "turn off" pieces of code that we don’t want or need to debug later.

Have students complete at least one of the Challenges for update-player (Page 82) before turning to their computers.

Synthesize

Have students share back what they implemented. Sharing solutions is encouraged!

Question: What would it take to make the player move left and right? Why can’t we do this without changing the contract?

ifproglang{wescheme}{ WeScheme supports the ability to change the Domain of a function, which allows update-player to take both an x- and a y-coordinate! However, the computer won’t know what the new coordinate is if the Range is just a single number. This optional lesson covers the beginnings of data structures, teaching just enough to allow students to move their PLAYER left and right! }

Pedagogy Note

It’s likely that once they hear other students' ideas, they will want more time to try them out. If time allows, give students additional slices of "hacking time", bringing them back to share each other’s ideas and solutions before sending them off to program some more. This dramatically ramps up the creativity and engagement in the classroom, giving better results than having one long stretch of programming time.

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.