What students learn
An ordered pair is a set of directions from the origin: the first number (x) says how far to go left or right, and the second number (y) says how far to go up or down. Every turn of the game practices that rule twice: once when the student fires, and once when they find the computer's shot on their own board.
- 1-Star General (First Quadrant): x and y from 0 to 4, with the origin in the bottom-left corner. No negative numbers.
- 2-Star General (Full Coordinate Plane): x and y from −2 to 2, with the origin in the center. Positive and negative coordinates, points on both axes, and all four quadrants.
- 3-Star General (Coordinate Commander): the same −2 to 2 plane with a 30-second timer, fully typed ordered pairs, enemy shots described in words, and short Radar Check questions about quadrants and coordinates.
How the game works
- Placing the fleet: Boat Buddy covers 3 points and Giant Galley covers 4. Ships sit on the grid points (not in squares), horizontally or vertically, and can lie on an axis or across the origin. Students drag them on, click to rotate, or press Randomize Ships. The game refuses ships that would go off the board or overlap, and says why.
- Firing: students type x, then y (1-Star and 2-Star General have two boxes; 3-Star General needs the whole pair, parentheses and comma included). Only whole numbers on the board are accepted.
- The plane: after every shot, a small plane starts at the origin, flies left or right for x, turns in place, then flies up or down for y. After the first three shots the plane flies 50% faster; right after a wrong answer (finding the enemy's shot, a Radar Check, or a turn prediction) it slows to normal speed for one flight, then speeds up again. Each leg is labeled ("2 right", "3 down"). Then the shot lands: an X for a miss, a flame for a hit.
- Repeated shots are allowed on purpose. A student who types (1, 2) when they meant (2, 1) sees the plane land in the wrong place, and the miss stays on the board. The shot log lists every shot, so reversed pairs are easy to spot.
- The computer's turn: the computer names a coordinate and the student must click (or arrow-key to) that point on their own board. A wrong pick says what went wrong ("Your y-coordinate is correct, but your x-coordinate should move RIGHT, not LEFT", "Check the order!") and adds a stronger hint each time: x comes first; start at the origin and move left or right first; the exact moves; and on the fourth try the path is drawn on the board.
- The computer plays fair, and gets sharper with each rank: its ships are placed at random every game and it never fires at the same point twice, except at 1-Star (see below). At 1-Star and 2-Star General it tries the points around a hit (a 1-Star general also sometimes forgets and wastes a shot on a point it already tried); at 3-Star it also works out which way the ship runs and follows it.
- 3-Star General mode wording: the computer's shots come in many forms, often with y first: "The y-coordinate is −2 and the x-coordinate is 1", "Move 2 units down and 1 unit right", "1 unit to the right of the y-axis and 2 units below the x-axis". The answer is always (1, −2).
- Radar Checks (3-Star General): between turns students answer one question before their next shot: which quadrant a point is in (or whether it's on an axis), the coordinates of a highlighted point, which number is x or y, which way to move first, positive or negative x or y, which point is farther right or higher, which point is in a given quadrant, or which pair has a negative x-coordinate.
- Turn Checks: clockwise or counterclockwise (3-Star General): some turns start with a Turn Check, a question of its own: a scout plane flies to a point, and students predict which way it will turn when it reaches the x-axis. Each turn asks at most one question before the shot (a Radar Check, a Turn Check, or Orders from HQ). For points in Quadrants I and III the turn is always counterclockwise; for points in Quadrants II and IV it is always clockwise. The plane then shows the turn, with a ↺ or ↻ arrow at the turning point.
- The timer (3-Star General): if time runs out on a shot, that shot is lost; on the computer's shot, the game shows where it lands; on a Radar Check, the answer is shown and explained, then play continues.
- Orders from HQ (3-Star General): before some shots, HQ describes a target in words (for example "the y-coordinate is 0 and the x-coordinate is −2") and students must type it as an ordered pair to fire. The first wrong try names the mistake; the second shows the answer.
- Points on the axes come up regularly: at least one of every three targets (the computer's shots and HQ orders) is on an axis, like (0, 2) or (−1, 0), since that is where students most often mix up x and y.
- Battle report: the end screen shows how many of each kind of question the student got right on the first try, their most common mistake (like switching x and y, or a wrong sign), and a tip for that mistake. Nothing is saved.
- Less motion: the Esc menu has a LESS MOTION switch that stills the storm, rain, lightning and board shaking for students who find them distracting. It is on automatically for devices set to reduce motion.
Worked examples
Plotting (−2, 1): Start at the origin.
x = −2: move 2 units LEFT y = 1: then move 1 unit UP
Reading the words: "The y-coordinate is −2 and the x-coordinate is 1."
x always goes first, so the point is (1, −2), not (−2, 1)
Quadrants: Which quadrant is (2, −1) in?
x positive (right), y negative (down) Quadrant IV
On an axis: Where is (0, −2)?
x = 0, so the point is ON the y-axis. It is not in any quadrant.
Common mistakes
- Reversing x and y. Students plot (1, 2) for (2, 1). The plane always flies sideways first, and repeated shots are allowed so the reversed miss stays visible.
- Wrong direction for a negative. Going right for x = −2, or up for y = −3. The feedback names which coordinate went the wrong way.
- Calling an axis point part of a quadrant. (0, 2) and (−2, 0) are on an axis, not in a quadrant. Radar Checks include these on purpose.
- Reading in the order given. In 3-Star General mode, "the y-coordinate is 1 and the x-coordinate is −2" is still (−2, 1).
Key vocabulary
Words and phrases to use when you talk through the game with students. Each one appears in the game, its questions or its feedback.
- coordinate plane: a flat grid formed by two number lines that cross at right angles
- x-axis: the horizontal number line
- y-axis: the vertical number line
- origin: the point (0, 0), where the axes cross
- ordered pair: two numbers (x, y) that name one point; the order matters
- x-coordinate: the first number: how far to move left (negative) or right (positive) from the origin
- y-coordinate: the second number: how far to move down (negative) or up (positive)
- quadrant: one of the four regions made by the axes, numbered I to IV counterclockwise from the upper right
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- Build up the modes. Start with 1-Star General when the coordinate plane is new, move to 2-Star General once negative numbers are introduced, and use 3-Star General as a challenge or review.
- Pairs. One student fires while the partner predicts out loud which way the plane will turn before it flies.
- Unplugged follow-up. After a few games, students play a paper version in pairs on graph paper: each draws a −2 to 2 plane, hides two ships on points, and calls out ordered pairs.
Discussion questions
- Why does the plane always fly left or right before it flies up or down?
- (2, 1) and (1, 2) use the same numbers. Why are they different points?
- How can you tell which quadrant a point is in just from the signs of its coordinates?
- Why isn't (0, 2) in any quadrant?
Standards
CCSS.MATH.CONTENT.5.G.A.1Use a pair of perpendicular number lines (axes) to define a coordinate system; the first number tells how far to travel along the x-axis and the second along the y-axis. Every shot and the plane's x-then-y flight path.
CCSS.MATH.CONTENT.5.G.A.2Graph points in the first quadrant and interpret coordinate values. 1-Star General mode.
CCSS.MATH.CONTENT.6.NS.C.6Extend coordinate axes to negative numbers; signs of coordinates show the quadrant (6.NS.C.6b); find and position pairs of integers on a coordinate plane (6.NS.C.6c). 2-Star and 3-Star General modes, quadrant Radar Checks.
CCSS.MATH.CONTENT.6.NS.C.8Graph points in all four quadrants of the coordinate plane. 2-Star and 3-Star General modes.
Access and privacy
En español: the 🌐 Español button in the game's top bar switches everything students see into Spanish. No accounts, no scores, no student data: nothing is saved, and every game starts fresh. Plays fully with the keyboard (Tab between controls, arrow keys to move ships and to move around a board, R to rotate a ship, Enter to choose, Esc for the menu), with a mouse (drag and click; an on-screen keypad can enter coordinates), or with touch. Hits use a flame and the word HIT; misses use an X and the word MISS, so nothing depends on color alone. Sound effects only, with a Sound on/off button; no music. 2-Star General and 3-Star General are set in a storm at sea (rain, lightning, crashing waves and water plumes on the horizon) to make the battle feel real; 1-Star General stays bright and calm. The storm stays behind the boards, which keep their light, high-contrast grids. Turning on the device's "reduce motion" setting stops the lightning and other moving effects.