Grade: Grade 5 Subject: Mathematics Unit: Coordinate Plane SAT: Algebra ACT: Math

Word Problems: Coordinate Plane

Apply your coordinate plane skills to solve real-world problems involving maps, treasure hunts, and everyday locations!

Why Word Problems Matter

Coordinates in the Real World

The coordinate plane is not just for math class! It is used everywhere:

  • Maps and GPS: Every location has latitude and longitude coordinates
  • Video games: Characters move on coordinate grids
  • City planning: Streets often form a grid pattern
  • Battleship: The game uses coordinates to find ships
Problem-Solving Strategy:
  1. Read carefully and identify what the question asks
  2. Draw or visualize the coordinate grid
  3. Plot the given points
  4. Use coordinates to find distances or new locations
  5. Check that your answer makes sense

Worked Examples

Example 1: The Treasure Map

🗺️ Scenario: A treasure map shows the following locations:
  • Start at the old oak tree at (1, 1)
  • The treasure chest is at (4, 5)
Question: How many units east (right) and how many units north (up) must you travel from the tree to reach the treasure?
Tree (1,1)
Treasure (4,5)
Step 1 Find the horizontal distance: 4 - 1 = 3 units east
Step 2 Find the vertical distance: 5 - 1 = 4 units north
Answer Travel 3 units east and 4 units north

Example 2: The School Map

🏫 Scenario: On the school grounds map:
  • The main entrance is at (0, 0)
  • The library is 3 units east and 2 units north of the entrance
  • The cafeteria is 5 units east and 1 unit north of the entrance
Question: What are the coordinates of the library and the cafeteria?
Library Start at (0, 0). Add 3 to x and 2 to y: (3, 2)
Cafeteria Start at (0, 0). Add 5 to x and 1 to y: (5, 1)

Example 3: The Garden Plot

🌱 Scenario: Maria is planning a rectangular garden. The corners are at:
  • (1, 2), (5, 2), (5, 4), and (1, 4)
Question: What is the length and width of Maria's garden?
Length Bottom side: from (1, 2) to (5, 2). Length = 5 - 1 = 4 units
Width Left side: from (1, 2) to (1, 4). Width = 4 - 2 = 2 units

Practice Problems

Problem 1: The Campsite

A hiker starts at the base camp at (2, 1). She hikes 3 units east and 4 units north to reach a scenic overlook. What are the coordinates of the overlook?

Problem 2: The Pizza Delivery

The pizza shop is at (1, 1) and a customer's house is at (4, 5). How many blocks east and how many blocks north does the delivery driver travel?

Problem 3: The Zoo Map

At the zoo, the entrance is at (0, 0), the elephant exhibit is at (3, 2), and the lion exhibit is at (3, 5). How far apart are the two exhibits?

Problem 4: The Video Game Character

In a video game, your character is at (2, 3). You move the character 2 units left. What are the new coordinates?

Problem 5: The City Park

A rectangular park has corners at (0, 0), (6, 0), (6, 4), and (0, 4). What is the area of the park in square units?

Problem 6: The Scavenger Hunt

Clue 1 says: "Start at (1, 2). Move 4 units east." Clue 2 says: "Now move 3 units north." Where do you end up?

Problem 7: The Meeting Point

Alex is at (1, 4) and Bailey is at (5, 4). They agree to meet exactly halfway between them. What are the coordinates of the meeting point?

Problem 8: The Fence

A farmer wants to build a fence around a square chicken coop. If one corner is at (2, 2) and the opposite corner is at (5, 5), what is the perimeter of the fence?

Problem 9: The Robot

A robot starts at (3, 3). It receives these commands: "Move down 2 units, then move right 1 unit." Where does the robot end up?

Problem 10: The Triangle

A triangle has vertices at (0, 0), (4, 0), and (2, 3). Which point is at the top of the triangle (highest y-value)?

Check Your Understanding

Challenge 1

When finding the horizontal distance between two points, which coordinates do you subtract?

Challenge 2

When finding the vertical distance between two points, which coordinates do you subtract?

What You Learned

🗺️

Real-World Coordinates

Coordinates describe locations on maps, in games, and in everyday life.

📏

Finding Distances

Subtract coordinates to find horizontal or vertical distances.

🚶

Movement Problems

Add or subtract from coordinates when moving on the grid.

📐

Shape Problems

Use coordinates to find perimeter, area, and dimensions.

Test-Taking Tip: When solving word problems on the SAT or ACT, always sketch a quick coordinate grid to visualize the problem. This helps prevent mistakes with direction and distance!

Next Steps

  • Review the Common Mistakes lesson to avoid typical errors
  • Create your own word problems using locations in your neighborhood
  • Take the Unit Quiz when you feel ready