Phase 1 of 5

Mission Briefing

Welcome aboard, Navigator! Captain Meridian needs your coordinate skills to find lost treasure across the Cartesian Seas.

Navigator Registration

Enter your details to begin the expedition.

Navigator Name

Crew (Class Period)

Expedition Date

Your Mission

Captain Meridian has discovered an ancient treasure map encoded with coordinates. You must use the coordinate plane to decode locations, calculate distances between islands, and reflect hidden routes to uncover the treasure!

Skills You'll Use:

Plotting ordered pairs (x, y)
All four quadrants
Distance between points
Reflections across axes
Midpoints of segments

Treasure Map Legend:

🌎 Home Port = Origin (0, 0)
⚓ Lighthouses = Positive coordinates
💣 Danger Zones = Negative coordinates
💰 Treasure = Reflected points
⏱ Supply Stops = Midpoints

Level 1 Support — Key Vocabulary:

Coordinate plane = a flat surface with two number lines (x and y) crossing at the origin
Ordered pair = two numbers like (3, 5) that show a location; x first, then y
Quadrant = one of the four sections of the coordinate plane
Reflection = a mirror image; flipping a point across a line
Distance = how far apart two points are
Midpoint = the point exactly in the middle between two points

Phase 2 of 5

Map Research

Study the coordinate plane and practice plotting locations for your expedition.

Interactive Coordinate Grid

Click anywhere on the grid to plot a point. Use this tool throughout your expedition!

Click grid to plot • (?, ?)

Quadrant Identification

Captain Meridian's map divides the ocean into four quadrants. Identify which quadrant each island belongs to.

Reminder: Quadrant I = (+, +) upper right • Quadrant II = (-, +) upper left • Quadrant III = (-, -) lower left • Quadrant IV = (+, -) lower right

Lighthouse Island at (5, 3) is in Quadrant:

Shipwreck Bay at (-4, 6) is in Quadrant:

Kraken Cave at (-7, -2) is in Quadrant:

Mermaid Cove at (8, -5) is in Quadrant:

Look at the signs of x and y. Positive x is right, positive y is up. The quadrants go counterclockwise starting from the upper right: I, II, III, IV.

Plot the Treasure Locations

Use the interactive grid above to plot each treasure location, then record the coordinates below.

Gold Chest: Start at the origin, go right 6 units, up 4 units. Coordinates:

Silver Doubloons: Start at origin, go left 3 units, up 7 units. Coordinates:

Ruby Crown: Start at origin, go left 5 units, down 4 units. Coordinates:

Emerald Ring: Start at origin, go right 2 units, down 8 units. Coordinates:

Right = positive x, Left = negative x, Up = positive y, Down = negative y. Write as (x, y).

Map the Island Chain

Captain Meridian discovered 6 islands. Plot them on the grid and describe the shape they form when connected in order.

Islands: A(2,6), B(6,3), C(6,-3), D(2,-6), E(-2,-3), F(-2,3). What shape do they form when connected?

Challenge: What is the area enclosed by this hexagon? Show your work.

Connect the points in order: A→B→C→D→E→F→A. Count the sides. What regular polygon has 6 sides?

Axes & Origin Knowledge

Answer these navigation questions about the coordinate plane.

What are the coordinates of the origin (Home Port)?

A point on the x-axis always has y = ___. Why?

A point on the y-axis always has x = ___. Why?

Which axis does the point (0, -7) lie on? Explain.

The origin is where the two axes cross. Points on the x-axis have no vertical distance from center. Points on the y-axis have no horizontal distance from center.

Phase 3 of 5

Route Planning

Calculate distances, find midpoints, and plan the safest route to the treasure.

Distance Calculator

Enter two points to calculate the distance between them. Use this tool for the tasks below!

📏 Distance Between Two Points

Point 1: ( , )

Point 2: ( , )

Enter two points and click Calculate.

How to find distance: If points share the same x-value, subtract the y-values and use absolute value. If they share the same y-value, subtract the x-values and use absolute value.

Midpoint Calculator

Find the exact halfway point between two locations — perfect for supply stops!

📍 Find the Midpoint

Point A: ( , )

Point B: ( , )

Enter two points and click Find Midpoint.

Midpoint formula: Add the x-values and divide by 2. Add the y-values and divide by 2. Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

Distance Between Islands

Calculate the distance between these island pairs. Show your method!

Distance from Lighthouse (3, 7) to Watchtower (3, -2): (same x-value)

Distance from Dock (-4, 5) to Market (6, 5): (same y-value)

Distance from Fort (-3, -1) to Armory (-3, -9): (same x-value)

Distance from Harbor (0, 6) to Cove (0, -4): (on the y-axis)

Challenge: The pirate's route goes from (1, 2) to (4, 6). Use the Pythagorean theorem: d = √((x₂-x₁)² + (y₂-y₁)²)

When points share the same x or y coordinate, distance = |difference of the other coordinate|. The absolute value makes it always positive!

Supply Stop Midpoints

The crew needs supply stops at the midpoint between islands. Find each midpoint.

Midpoint between Port (2, 8) and Cove (10, 8):

Midpoint between Reef (-6, 4) and Lagoon (4, -2):

Midpoint between Volcano (-8, -3) and Bay (2, 7):

Midpoint between Shipwreck (-5, -9) and Lighthouse (5, 3):

Midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2). Add the two x-values and divide by 2. Do the same for y-values.

Plan the Expedition Route

Visit these 4 islands in order. Calculate the total distance traveled (count grid squares).

Distance A(4,4) to B(8,0):

Distance B(8,0) to C(4,-4):

Distance C(4,-4) to D(-4,0):

Total distance for the full route (A→B→C→D→back to A):

For each leg, count the horizontal and vertical distance on the grid. From A(4,4) to B(8,0): horizontal = |8-4| = 4 and vertical = |0-4| = 4.

Phase 4 of 5

Expedition Build

Use reflections, design treasure maps, and complete advanced navigation challenges.

Reflection Tool

Enter a point and see its reflection across the x-axis, y-axis, or both!

🔄 Flip Across Axes

Original Point: ( , )

ACROSS X-AXIS

—

ACROSS Y-AXIS

—

ACROSS BOTH

—

How reflections work:

Across x-axis: Keep x the same, flip the sign of y. (3, 5) → (3, -5)
Across y-axis: Flip the sign of x, keep y the same. (3, 5) → (-3, 5)
Across both: Flip both signs. (3, 5) → (-3, -5)

Mirror Island Reflections

The treasure map has mirror clues! Find the reflected coordinates for each island.

Reflect Skull Rock (5, 3) across the x-axis:

Reflect Parrot Bay (-4, 7) across the y-axis:

Reflect Cannon Point (6, -2) across the x-axis:

Reflect Anchor Atoll (-3, -8) across the y-axis:

Across x-axis: change the sign of y only. Across y-axis: change the sign of x only. Think of it as folding the paper along that axis.

Reflection Pattern Discovery

Reflect the entire treasure triangle across both axes and describe the pattern.

Triangle vertices: A(2,2), B(4,4), C(6,2). Write all 3 reflected vertices across the x-axis:

Write all 3 reflected vertices across the y-axis:

Write all 3 reflected vertices across BOTH axes:

Describe the pattern you notice about reflections:

For x-axis: flip all y-signs. For y-axis: flip all x-signs. For both: flip both signs. The shape stays the same size!

Design Your Own Treasure Map

Create a treasure map with at least 5 locations. Use at least 3 different quadrants!

Location 1 — Name & Coordinates:

Location 2 — Name & Coordinates:

Location 3 — Name & Coordinates:

Location 4 — Name & Coordinates:

Location 5 — Name & Coordinates:

Which quadrants did you use? (List them)

Challenge: Calculate the total perimeter of your treasure route (sum of all distances between consecutive locations).

Treasure Path Tracer

Follow the coded directions to find the treasure! Start at the origin (0, 0).

            Coded Route:

            Step 1: Move right 3, up 4 → Record position

            Step 2: Move right 5, stay same height → Record position

            Step 3: Stay same spot left-right, move down 6 → Record
            position

            Step 4: Move left 8, stay same height → Record position

            Step 5: Stay same spot left-right, move up 2 → TREASURE!

After Step 1, your position is:

After Step 2, your position is:

After Step 3, your position is:

After Step 4, your position is:

TREASURE location (after Step 5):

What shape did your path trace? Describe it.

Start at (0,0). "Right 3" means add 3 to x. "Up 4" means add 4 to y. Keep a running total of your (x, y) position after each step.

Symmetry & Reflection Challenge

Captain Meridian hid treasure at points that are symmetric across axes. Find the missing info!

Point A is at (7, 3). Its x-axis reflection is at (7, -3). What is the distance between them?

Point B is at (-5, 4). Its y-axis reflection is at (5, 4). What is the distance between them?

Pattern: When you reflect a point across the x-axis, the distance between the original and reflection equals ___.

Challenge: If a point and its x-axis reflection are 12 units apart, what could the original point be? Give 3 examples.

The distance between (x, y) and (x, -y) is |y - (-y)| = |2y|. So the distance is always 2 times the absolute value of the y-coordinate.

Coordinate Riddles

Solve each riddle by finding the mystery coordinates!

I am 5 units right of the origin and 3 units above the x-axis. Who am I?

I am the reflection of (4, -6) across the y-axis. Who am I?

I am the midpoint between (-8, 2) and (4, 2). Who am I?

I am on the x-axis, 6 units left of the origin. Who am I?

Challenge Riddle: My x-coordinate is double my y-coordinate, I am in Quadrant III, and the sum of my coordinates is -9. Who am I?

Read each clue carefully. "Right of origin" means positive x. "Above x-axis" means positive y. For the challenge: if x = 2y and x + y = -9, substitute to get 2y + y = -9.

Captain's Map Design Challenge

Create a coordinate art design! Plot at least 8 points that form a recognizable picture when connected.

List your ordered pairs in the order they should be connected:

What picture/shape do your points create?

How many quadrants does your design span?