EQ of Attack Directions

Object:
To get as many points as possible by hitting as many boats as possible

Set-Up:
The game board shows the first quadrant of a coordinate grid, where each player’s boat travels along the y-axis. On the grid, there are three types of boats: boats, bonus boats, and bombs. There will always be a set number of each boat available on the game board for every new turn. The following are displayed under each player’s name: the number of cannonballs (or turns) remaining, the unused bonus lines, the history of linear equations played, and the total points earned.

Play:
Students will spin to generate a fixed value for the slope or y-intercept. Students will have a total of 1 minute 30 seconds to complete the equation if they are playing against a partner. (There is no timer if you play against the computer.) A timer will appear for the last 30 seconds. Once the equation has been defined, press the Fire button. If a free spin token is available for use, simply click on the icon, and the equation will change. One of five total cannonballs will then be shot from your boat’s defined position to collect the boats located on the line of fire.

When you hit a bonus boat, you earn bonus points and a bonus line! There are five types of bonus lines—parallel, perpendicular, translation, reflection, and rotation—that can be generated, depending on the type of bonus boat you hit. Use the information button on the game board to identify these boats and their respective values.

Once a bonus boat is activated, a pop-up window will appear. Use the information button to read definitions and hints. Use the up and down arrow keys to complete the equation. Although values can be typed in, invalid entries will either be rounded or be replaced with a max/min value. The bonus line you create must be in relation to the line that is currently highlighted on the screen.

Your turn ends when you run out of bonus lines to define and press “End Turn”.

Winning the Game:
The player who has the most points at the end of five turns wins.

Math Concepts: Linear functions and transformations

What You Can Do: This game is ideal for use in the classroom or at home. You can use graph paper with a 1-centimeter grid to create a paper-pencil version of it. (Look under Related Resources for instructions on how to do this.) Fun extensions, such as limiting the distance a cannonball can travel, are fantastic ways to diversify the game for high achievers.
As players collect bonus points, questions such as, “Where am I rotating around?” “How does slope affect the direction?” and “Is translating up the same as translating to the left?” will naturally arise. Help students discover the connection between algebra and geometry as they become more proficient with both.
You can also help students become aware of various real-world contexts where slope and y-intercept exist. For example, how does the y-intercept affect when a plane can begin to land? How does the slope of a hill change the speed limit when driving? Being able to see such connections between values and concepts will allow students to build conceptual understanding before procedural understanding.
Many features are built into the game to encourage different strategies for winning. With restrictions on values (for example, the denominator of the slope cannot be more than 4), students can’t simply define any line any way they wish. Due to the time restrictions, students need to discover efficient ways to maximize points without having to consider all the possibilities. And last but not least, the end-of-game Battle Stats allow students to see that more target hits do not always correlate to higher scores. Giving students opportunities to see alternatives and show diversity in their thinking is crucial in building strategic thinking skills.

Math in the Game: This game’s main learning objective is for students to become proficient in understanding linear equations in slope-intercept form and how to transform them. Students can work flexibly with either their linear function or the game board. For example, being able quickly identify high-value boats will allow students to quickly modify their equation (if possible). On the other hand, if a student is given a slope of 1/3, observing the boats located on the lines x = 3, x = 6, and x = 9 will allow students to find an optimal y-intercept.
Many students will quickly find out that bonus boats are favorable over regular boats, because they have high values and allow for multiple lines. Using bonus boats compels students to grapple with transformation concepts such as transformations, rotations, and reflections.

Related Resources:
Equations of Attack
Relate linear equations and graphs in a game of ships and attacks.