You are the lead planner for Gridport, a new smart city. Every street, park, and station is mapped on a four-quadrant coordinate grid centered on City Hall at (0, 0). Use coordinates, integers, absolute value, distance, and reflections to lay out the city, log elevations, route the subway, and mirror a matching district — then sign off your master plan.
The city engineering office handed you the official Gridport site map. Read every coordinate the same way:
MAP RULE (x, y) = (blocks right/left, blocks up/down) from City Hall (0, 0) · 1 grid square = 1 city block
A coordinate (x, y) tells you two moves from the center. The x tells you right (+) or left (−). The y tells you up (+) or down (−). Always do the x-move first, then the y-move.
Español: Una coordenada (x, y) da dos movimientos desde el centro. La x va a la derecha (+) o izquierda (−). La y va arriba (+) o abajo (−). Muévete primero en x, luego en y.Four key landmarks are already marked on the city map. Read each point's coordinates straight off the grid and record them. Watch the signs in each quadrant.
Q1.1 — Coordinates of Green Park
Q1.2 — Coordinates of Gold Stadium
Q1.3 — Pink Market is at (−3, −6). Which quadrant is it in? (Type the number: 1, 2, 3, or 4.)
Find each point by counting from the center. Right is +x, left is −x. Up is +y, down is −y. Quadrants are numbered counter-clockwise starting from the top-right: I (+,+), II (−,+), III (−,−), IV (+,−).
Español: Cuenta desde el centro. Derecha = +x, izquierda = −x, arriba = +y, abajo = −y. Cuadrantes: I (+,+), II (−,+), III (−,−), IV (+,−).Your survey crew logged the elevation of four sites in meters, where 0 = sea level. Positive means above sea level; negative means below. Read the number line, then order them and use absolute value.
| Site | Elevation (m) |
|---|---|
| Riverside Docks | −6 |
| Old Harbor | −2 |
| City Hall Plaza | +1 |
| Hilltop Reservoir | +5 |
On a number line, left is less and right is more. So −6 < −2 < 1 < 5. Absolute value |n| is the distance from 0 — it is never negative. |−6| = 6 because the Docks are 6 meters from sea level.
Español: En la recta numérica, izquierda = menor, derecha = mayor. El valor absoluto |n| es la distancia desde 0 y nunca es negativo. |−6| = 6.Q2.1 — Which site has the lowest elevation? Type its elevation number (with sign).
Q2.2 — The Docks sit at −6 m. How far is that from sea level? Find |−6|.
Q2.3 — A diver says "the Docks are deeper below sea level than the Harbor." Compare distances: |−6| ___ |−2|. Type the symbol >, <, or =.
Careful: −6 is less than −2 (it is colder / lower), but |−6| is greater than |−2| (it is farther from sea level). In one sentence, explain how a number can be smaller yet have a larger absolute value.
The new subway runs in straight blocks. Find how many blocks long each straight segment is by using the coordinates — when two stops share an x- or a y-value, the distance is the absolute value of the difference of the other coordinates.
Q3.1 — North (−4, 6) → East (5, 6). Same y, so distance = |5 − (−4)|. How many blocks?
Q3.2 — East (5, 6) → South (5, −3). Same x, so distance = |6 − (−3)|. How many blocks?
Q3.3 — Total subway length = segment 1 + segment 2. How many blocks of track in all?
Same row (same y)? Subtract the x-values and take the absolute value. Same column (same x)? Subtract the y-values and take the absolute value. Subtracting a negative is the same as adding: 5 − (−4) = 5 + 4 = 9.
Español: Misma fila (misma y): resta las x y toma el valor absoluto. Misma columna (misma x): resta las y. Restar un negativo es sumar: 5 − (−4) = 9.A rider wants to go straight from North (−4, 6) to South (5, −3), but no diagonal track exists. Why must the train ride both segments (9 + 9 = 18 blocks) instead of a shorter diagonal?
The Riverside district sits at R = (3, 5). The plan calls for a twin district that is its mirror image. Reflect the point, then check the picture. Pick the axis on the pad, see the reflection update, and answer the coordinate questions.
Q4.1 — Reflect R = (3, 5) across the y-axis. What are the coordinates of R′? (Format: x, y)
Q4.2 — Now reflect R = (3, 5) across the x-axis instead. What are the coordinates of R′? (Format: x, y)
A reflection flips a point to the opposite side of the mirror line. Across the y-axis: keep y, change the sign of x. Across the x-axis: keep x, change the sign of y. Only one number changes sign.
Español: Reflejar sobre el eje y: conserva la y, cambia el signo de la x. Sobre el eje x: conserva la x, cambia el signo de la y. Solo un número cambia de signo.Reflect R across the y-axis, then reflect that image across the x-axis. Where does R end up, and what single move from (3, 5) would get there in one step?
Fill in the official summary line so the city council can read your plan at a glance. Use your earlier answers.
Check your work in Tasks 2–4, then press Update summary to fill this board before you submit.
When every plan check is approved, file your master plan with the city. 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 | 10–11 / 11 | Names coordinates in all four quadrants, orders signed elevations and applies absolute value correctly, computes same-line distances, and reflects across both axes. Can explain the difference between order and absolute value and generalize the reflection rule. |
| 3 — Meets | 8–9 / 11 | Correctly handles most plan checks with at most two sign or arithmetic slips. Completes the route and at least one reflection accurately. |
| 2 — Approaching | 5–7 / 11 | Plots and names simple points but mixes up quadrant signs, or confuses "less than" with absolute value, or changes both signs in a reflection. Partial distance work. |
| 1 — Beginning | 0–4 / 11 | Few correct coordinates. Misreads signs or the grid. Needs reteaching on plotting, integers, and absolute value. |