You are the flight engineer for the Halcyon rover on Mars. Mission control needs exact numbers and safe limits. Use one-step equations to compute unknowns and inequalities to define the rover's safe operating envelope — then run the final go/no-go launch check.
The Halcyon rover has landed in Jezero Crater. Before it drives, mission control must lock in exact values and safe operating ranges. Two math tools do the job:
Tool A · Equation
An equation uses =. It
finds one exact answer — like the exact distance
remaining. Solve by doing the inverse (opposite)
operation to both sides.
Example: x + 6 = 20 → subtract 6 from
both sides → x = 14
Tool B · Inequality
An inequality uses >, <, ≥, or ≤. It describes a whole range of safe values — like "battery must stay at or above 40 units." Its solutions fill a region on the number line.
Symbol legend:
> greater than ·
< less than ·
≥ at least (includes the boundary) ·
≤ at most (includes the boundary).
Number line: closed circle ● for ≥ or ≤ (boundary
counts) · open circle ○ for > or < (boundary
does not count).
Golden rule. Whatever you do to one side of the equals sign, do to the other — like keeping a balance scale level. To undo an operation, use its inverse: + ↔ − and × ↔ ÷.
Halcyon must reach the river-delta rocks. Build a one-step equation from each readout on the navigation console, then solve it.
Q1.1 — Build the equation for the remaining distance x (driven + remaining = total).
Q1.2 — Solve it: how many km remain?
Q1.3 — Build the equation for drive time m (speed × time = distance).
Q1.4 — Solve it: how many hours is the drive?
To solve, do the inverse to both sides. Plus 6 is undone by minus 6. Times 8 is undone by divide by 8. Always check: put your answer back in and see if both sides match.
Español: Para resolver, usa la operación inversa en ambos lados. Suma ↔ resta, multiplicación ↔ división. Comprueba tu respuesta.Halcyon's robotic arm can lift rock samples, but the deck has a maximum payload. The arm already carries fixed gear. Write the inequality, then find the heaviest sample mass it can add.
Q2.1 — The total load (18 + w) must be at most 45 kg. Pick the symbol:
Q2.2 — Solve 18 + w ≤ 45. The sample mass w can be at most how many kg?
Is w = 27 allowed? Yes — "at most" means the boundary is included, so we use ≤ (a closed circle on the number line). If the rule said "less than 45" (strictly), would 27 + 18 = 45 still be allowed? Explain the difference between ≤ and <.
"At most" = the largest allowed, including that number → use ≤. Solve the inequality the same way you solve an equation: subtract 18 from both sides.
Español: "Como máximo" incluye ese número → usa ≤. Resuelve igual que una ecuación: resta 18 en ambos lados.Halcyon's battery needs the internal heater to reach a minimum level before the rover can drive. The safe operating rule is t ≥ 35 (heater level must be at least 35 units). Use the interactive grapher below to plot the safe zone on the number line.
Q3.1 — "Heater level must be at least 35." Which inequality is correct?
"At least 35" means 35 is OK and anything bigger. That is ≥ (closed circle ●), and you shade to the right (toward bigger numbers).
Español: "Al menos 35" incluye 35 y más → ≥ (círculo lleno ●), sombrea a la derecha.Your graph defines the rover's safe operating envelope. Name one temperature value that is on the boundary, and one that is unsafe. Why does the engineer choose a closed circle here instead of open?
Q3.2 — Set the boundary to 35, a closed circle, shaded right to match t ≥ 35. Then check.
Final check before Halcyon moves out. The solar panels will double the rover's stored charge, then the instruments burn 14 units. The flight rule says the charge remaining after that must be at least 40 units. Enter a starting battery, run the model, and see if it is a GO.
Charge model: final = 2b − 14, where b = starting battery. Flight rule: 2b − 14 ≥ 40.
| Starting battery b (units) | |
| Final charge = 2b − 14 | — |
| Flight rule: final ≥ 40 | — |
Q4 — Solve the flight rule 2b − 14 ≥ 40 for the minimum starting battery b that still launches.
Use the simulator — type a number for b and press "Run go / no-go poll." Try b = 27: final = 2(27) − 14 = 40, and 40 ≥ 40 → GO. Try b = 26: final = 38, and 38 ≥ 40 → NO-GO. The rule 2b − 14 ≥ 40 is solved by adding 14 first, then dividing by 2.
Español: Prueba números en el simulador. b = 27 → final = 40 → SÍ va. b = 26 → final = 38 → NO va. Suma 14, luego divide entre 2.This is a two-step inequality (add 14, then divide by 2) — a preview of Grade 7. Notice 27 is the boundary: b = 27 gives exactly 40, which passes because of ≥ (closed circle). What is the largest whole-number battery that is a no-go? Explain using the number line.
When every system checks out, submit your flight plan to mission control. Enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.
| Level | Score | Descriptor |
|---|---|---|
| 4 — Exceeds | 7 / 7 | Models every situation as a correct one-step equation or inequality, solves with inverse operations, and graphs the safe zone accurately. Explains ≤ vs. <, open vs. closed circles, and solves the two-step launch rule. |
| 3 — Meets | 5–6 / 7 | Writes and solves the equations and inequality correctly with at most one slip. Graphs the inequality and reaches a valid launch decision. |
| 2 — Approaching | 3–4 / 7 | Solves simple equations but confuses inequality symbols (≥ vs. ≤) or open vs. closed circles, or mis-shades the number line. Partial launch check. |
| 1 — Beginning | 0–2 / 7 | Few correct models. Confuses inverse operations or cannot read a constraint as an inequality. Needs reteaching on solving and graphing. |