## By Arizona State University, Clayton State University, & Florida State University

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Description: Vector Unknown challenges players to guide a bunny to a basket full of eggs. The player is presented with four different vectors that can be placed into a vector equation and weighted providing a pathway to the basket. As the player progresses through different levels and difficulties they will encounter different combinations of vectors and eventually have to collect keys before finally reaching their ultimate egg-citing prize.

Skills and Ideas Taught: Properties of vectors in two-dimensional space including:

1. Scaling a vector algebraically and connecting it to its geometric representation
2. Adding two vectors algebraically and connecting the sum to its geometric representation.
3. Finding a linear combination of vectors that results in a goal vector.
4. Two vectors that are multiples of each other cannot span a two-dimensional space.

Goal or Challenge: The challenge of the game is to have the bunny reach the basket by choosing up to two vectors (that specify how the bunny is traveling) and weighting the vectors in order to find a linear combination(s) that reaches the goal.

Primary Audience:  College students who are taking or about to take linear algebra. High school students/college students who are studying vector equations.

Assessment Approach: The player’s learning is measured by if they are able to reach the goal, what is the difficulty of the level they are able to complete, and how long it takes to for them to reach the goal.

The first level provides a geometric support for the player in order to aid them in reaching the goal.
The second level removes the geometric support forcing the player to focus on the more algebraic notions of the vector equation or develop a geometric understanding connected to the algebraic notion of the vector equation. The third and fourth levels limit the number of linear combinations the player can try to use to reach the basket. The fifth level adds keys that the player must obtain before reaching the goal and the players have access to the geometric support. The game displays the keys solely geometrically and thus forces the player to look at some geometric aspects of the vector equation and consider starting from a point other than the origin.

The difficulties easy, medium, and hard are meant to represent the difficulty of the vector selections provided. On easy difficulty, the players will always have two vectors that are multiples of the standard basis (vectors with a zero in one coordinate). On medium difficulty, there are no standard basis vectors, but at least two of the vectors have small magnitudes. On hard difficulty, the magnitudes of the vector choices are larger making it more difficult to spot linear combinations with the goal of forcing the player to develop advanced strategies for choosing vectors (such as choosing a pair of linearly independent vectors or using a system of equations to
solve).

Game Engine: Unity

Operating System: Web

Platform: PC

Special Hardware: None