Rearranging Equations Game

SCOPE AND BREAKDOWN OF WORK

TIMELINE

High-level plan

Plan

Feb 10 - Feb 28:

• Math rules and conceptual scope
• Game objective
• List down problem types
• Game mechanic ideas

Feb 21 - Mar 21:

• Gameplay and mechanics to be discussed and shortlisted
• Translation of Math rules to Game rules
• 🚧 Game design - Decide Freedoms vs Constraints
  (in progress)

Apr 4 - May 2:

• Make and share prototype for internal reviews
  (in progress)
  • Data structures
  • Visual hierarchy
  • Data flow logic
  • 🚧 Input handling
  • Portal logic
  • Equation transformations
• 🚧 Narrative and Visual Design: Ideas, Discussion, Finalize
  (in progress)
• Deploy prototype to URL for internal testing

May 2 - Jun 6:

• 🚧 Create levels (equations)
• Prototype testing. Questions to answer: is it engaging? does it make learning happen?
• Server metrics setup

May 9 - Jun 6:

• Integrate visual design and narrative elements
• Review & iteration of levels

Jun 6 - Jul:

• User testing with students and teachers
• Review & iteration of game as a whole

IDEAS FOR INTRODUCING THE MATHS THROUGH NON-MATHS

We have already thought about having the first few levels having the mathematics hidden, but with identical mechanics. So for instance, we can disregard consolidation of sums (e.g., we don't worry about

$4-3=1$) and we keep each item as it is. So suppose underneath, we have

$$4x+2=-3.$$
We have characters for the numbers, and something significant for

$x$ itself. I don't know what yet, but let's try a shark for 4, a car for 2, and a horse for 3. The direction that each of these characters determines their parity. So

$-3$ is a horse facing to the right. Then we use concatenation for multiplication and Egyptian walking legs for addition and subtraction. Multiplication by right-facing walk-legs changes the direction of the character (the parity).

𓂻 |

(but the racehorse faces to the right).

TECHNICAL APPROACH

Technical Approach notes.

Annotated source code

GAMEPLAY

How Portals work

How location indicators work

(blue circles on the rightmost section show Portal locations)

On the right, trying out what specifying location indicators only for the variable to isolate would look like:

Mechanics

Every move from one side of the equals sign to other is through a portal.

A portal window will be on both sides of equal sign, drag and drop it to the number you intend to move to other side, and then click.

Portal window has the rules of movement embedded in it. For instance, in 3x+1/4 = 4x-2, here, 3 cannot move from left to right side without being detangled, and this will be ensured by the portal.

MATH RULES

Core math goal in every problem statement:

• Simplify the terms on both side, by combining what can be, by removing brackets where possible, etc
• Isolate the variable terms on one side of the equation

Math rules

• In fractions, denominator flips position and goes with a multiplication operand to numerator, and vice versa
• In sums, operands go to the other side a sign opposite to the one they currently hold

LEVELS

Levels breakdown

WORLD

Ideas:

• x wants to go to the left side to climb and board a spaceship, while numbers and other variables are trying to stop it (by keeping it stuck in the equation under operations and brackets (bubbles)).
• x and numbers have a halo or horns depending on whether they are currently where they belong, ie, on the left side x has halo and numbers have horns, and on the right side x (if any) has horns and numbers have halo. and bringing number to right gives it halo, and bringing x to left gives it halo. player wants to make everything have halos, and remove all horns.

ROUGH NOTES

Rough notes and ideas

tags: Equations Game Plan