Deep Six Salvage
A cargo plane went down over the Mariana Trench, and Deep Six Salvage Co. has hired you as the sub's sonar navigator. You'll ride the depth gauge down through positive and negative water, then sweep a four-quadrant sonar grid to map every piece of wreckage. Plot the debris, reflect the recovery beacon, and measure the distances your robot arm must travel — before the oxygen runs low.
Welcome Aboard the Nereus
Below the surface there is no "zero feet." Sea level is just the starting line, and everything important happens above and below it. Depth, temperature, and pressure all swing between positive and negative — so a navigator who can read integers, judge how far a number sits from zero, and pinpoint a target on a grid is the most valuable person on the sub.
The Driving Question
How do negative numbers, absolute value, and the coordinate plane let us describe and measure positions in a world that goes both up and down?
The Mission
By the end of this WebQuest you will hand the captain a completed Salvage Log. A mission-ready log must:
- Order the dive checkpoints from shallowest to deepest using the depth gauge.
- Use absolute value to report how deep each checkpoint is (its distance from sea level).
- Plot four wreck pieces on the sonar grid — including a coordinate with a fraction.
- Reflect the recovery beacon across an axis and name its new coordinates.
- Find the distance between two pieces that share a row or column.
- Pass the Check Your Understanding self-check at the bottom.
The Process
Run the dive in order. Each step fills one section of your Salvage Log.
Step 1 — Read the navigator's toolbox
Four ideas power this whole mission. Keep this reference open while you work.
Step 2 — Order the dive checkpoints
The sub passes these checkpoints on the way down. The reading is the elevation relative to sea level (0 ft). Order them from shallowest (closest to the surface) to deepest.
| Checkpoint | Elevation reading | What's there |
|---|---|---|
| Buoy | +12 ft | Surface marker |
| Thermocline | −85 ft | Cold-water layer |
| Reef shelf | −140 ft | Coral wall |
| Wreck field | −310 ft | Cargo debris |
| Trench lip | −455 ft | Drop-off edge |
Worked example — ordering negatives:
On the gauge, the lower a number sits, the smaller it is. So −455 < −310 < −140 < −85 < +12. Shallowest → deepest: Buoy, Thermocline, Reef shelf, Wreck field, Trench lip.
Step 3 — Report depth with absolute value
The captain doesn't want the sign — she wants the depth: how far each checkpoint is from sea level. That is the absolute value of the elevation.
Worked example:
Wreck field elevation = −310 ft → depth = |−310| = 310 ft below sea level.
Step 4 — Sweep the sonar grid (plot the wreckage)
Switch from the gauge (a vertical line) to the full coordinate plane. The sub sits at the origin (0, 0). Each ping returns an ordered pair (x, y): x is east(+)/west(−), y is north(+)/south(−). Plot these four pieces and name each quadrant.
- Piece A — engine block: (3, 2)
- Piece B — wing section: (−2, 3)
- Piece C — tail fin: (−3, −2)
- Piece D — cargo crate: (2, −3½)
Step 5 — Reflect the recovery beacon
You drop a recovery beacon at (3, 2), right on top of the engine block. The current sweeps it across the y-axis to the opposite side. Reflecting across the y-axis flips the sign of x only; the y stays the same.
Worked example — reflect (3, 2) across the y-axis:
x changes sign, y stays: (3, 2) → (−3, 2). The beacon and its reflection are the same distance from the y-axis, like a mirror.
Step 6 — Measure the robot arm's reach (distance)
When two points share a row (same y) or a column (same x), the distance between them is the distance on a number line — you can find it with absolute value, no diagonal needed.
Worked example:
Pieces at (−4, 1) and (5, 1) share the row y = 1. Distance = |−4 − 5| = |−9| = 9 units. (Opposite sides of zero? Add the absolute values. Same side? Subtract.)
Resources
Use these Neft Teacher tools as you dive. They open in the same window — use your back button to return to the sub.
Key vocabulary · Vocabulario clave
- Integer / Entero — a whole number that can be positive, negative, or zero (…−2, −1, 0, 1, 2…).
- Absolute value / Valor absoluto — a number's distance from zero, always positive: |−7| = 7.
- Ordered pair / Par ordenado — (x, y), the address of a point on the grid.
- Quadrant / Cuadrante — one of the four regions of the coordinate plane.
- Reflection / Reflexión — a mirror flip across the x-axis or y-axis.
Evaluation
Your Salvage Log will be scored on this rubric.
| Criteria | 4 · Captain | 3 · Navigator | 2 · Trainee | 1 · Stowaway |
|---|---|---|---|---|
| Compare & order | All checkpoints ordered correctly with reasoning. | One ordering slip. | Several ordering errors. | Order not shown or incorrect. |
| Absolute value | All depths reported as positive distances. | Mostly correct depths. | Confuses sign with distance. | No depths given. |
| Plotting & quadrants | All 4 pieces plotted; quadrants named (incl. fraction). | 3 pieces plotted correctly. | Some points or quadrants wrong. | Points not plotted. |
| Reflection & distance | Reflection and distance both correct and justified. | One of the two correct. | Attempts with errors. | Not attempted. |
| Labels & reasoning | Units (ft, units) labeled; clear explanation. | Most answers labeled. | Some labels missing. | No units or reasoning. |
Teacher Notes & Answer Key (not printed)
Deep Six Salvage · Salvage Log — pairs with the Evaluation rubric above.
Sample Answers — Salvage Log
- Order checkpoints: −455 < −310 < −140 < −85 < +12, so shallowest → deepest is +12, −85, −140, −310, −455.
- Absolute value (depth): |−310| = 310 ft deep — distance from sea level regardless of sign.
- Plot pieces: A (3, 2) Quadrant I; D (2, −3½) Quadrant IV — plot the fractional coordinate halfway between −3 and −4.
- Reflect beacon: (3, 2) across the y-axis → (−3, 2) (x changes sign, y stays).
- Distance: for points on the same line, subtract coordinates (or add absolute values across an axis).
Facilitation
- On the gauge, lower = smaller: −455 is deeper (and smaller) than −85.
- Reflection across the y-axis flips only the sign of x; across the x-axis flips only y.
Standard
CCSS 6.NS.C.5–8.
Check Your Understanding
Answer all six. Click Check My Answers when you are done. These match the steps in your Salvage Log.
Conclusion
You navigated a world that goes both up and down. You ordered depths, turned negatives into distances with absolute value, mapped wreckage across all four quadrants, mirrored a beacon, and measured a robot arm's reach — every piece of 6.NS.5–8 working together. The Nereus surfaces with a complete Salvage Log. Mission accomplished, navigator.
Take it further · Level 2
The robot arm must travel from Piece C (−3, −2) to a new ping at (2, −2). They share row y = −2. Find that distance, then plan the shortest path that visits all four pieces.
Reflect · Reflexiona
Two checkpoints, −85 ft and +12 ft, are different elevations. Could two different elevations ever have the same absolute value? Explain. ¿Pueden dos elevaciones diferentes tener el mismo valor absoluto?
Real careers · Carreras reales
Submarine pilots, marine biologists, and video-game level designers all use signed coordinates and distance every day — the exact skills you just used.