Dive below zero, read the sonar, and chart all four quadrants of the treasure map.
REMEMBER: Zero is a chosen reference point — sea
level, freezing, an empty account. Greater means higher up (or
further right), so −3 beats −7. Absolute value is pure DISTANCE
from zero — it is never negative, and −30 can be LESS than −10 while sitting
FARTHER from zero. On the grid, coordinates run (x, y): across
first, then up or down.
Part 1 · Submarine Explorer
Pilot the submarine along a vertical number line. Pick a mission, then dive and
surface — watch the readouts: the value (with its sign), its
opposite (the ghost sub, mirrored across zero), and the
sonar, which reports |value| — the pure distance from zero.
Part 2 · Sonar Duel — Greater vs. Farther
Two submarines report their positions. Read the question carefully — sometimes
it asks which value is GREATER (higher on the line), sometimes
which is FARTHER from zero (bigger absolute value). They are
NOT the same question! Commit before the reveal.
Correct calls: 0
Part 3 · Treasure Grid Machines
The treasure map runs on three machines. Each prints its steps — starting at
the origin, every time.
Enter a treasure's coordinates — the machine walks there from the origin and names the quadrant.
Reflect a treasure across an axis — and discover which SIGN flips.
Two treasures share a coordinate — how far is the swim between them? (Same x OR same y required.)
Part 4 · Fleet Command Quiz
Question 1 of 10Score: 0
📗 Word Box
Negative number
A number less than zero — a position below or left of the reference point, like −30 m (30 m below sea level).
Opposites
Two numbers the same distance from zero on opposite sides, like 4 and −4. Zero is its own opposite.
Rational number
Any number that can be written as a fraction — including negative fractions and decimals like −2.5 and −1/2. Each one is a POINT on the number line.
Absolute value
The distance between a number and zero, written |−30| = 30. Distance is never negative.
Ordered pair
A point's address (x, y): the x tells how far across, the y how far up or down. Order matters — (−3, 5) and (5, −3) are different treasures!
Origin
The point (0, 0) where the axes cross — the grid's reference point, where every plot begins.
Quadrant
One of the four regions of the plane: I (+,+), II (−,+), III (−,−), IV (+,−), counted counterclockwise from top right.
Reflection
A mirror flip across an axis. Across the x-axis, the y-sign flips; across the y-axis, the x-sign flips.