# Coordinate System Word Problems (Grade 5)

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Videos, solutions, examples, and lessons to help Grade 5 students learn how to represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Common Core: 5.G.2

### Suggested Learning Targets

• I can determine when a mathematical problem has a set of ordered pairs.
• I can graph points in the first quadrant of a coordinate plane.

 5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.

### Coordinate plane word problems in the first quadrant

Example:
Naomi lives at Second Avenue and Third Street represented by (2,3) on the graph below. Her school is a Fourth Avenue and 10th Street represented by (4, 10) on the graph. She walks over to Fourth Avenue and up to 10 Street. Plot her home and school on the map. How many blocks did Naomi walk to school?

Interpreting Graphs on Real-World Situations (5.G.2)
Example:
The graph shows how much snow fell during a blizzard. How much snow had fallen after 2 hours? What does the ordered pair (4,8) represent? What ordered pair represents how much snow had fallen after 6 hours? How much snow had fallen after 5 hours? True or false: 3 more inches of snow had fallen after 6 hours than after 4 hours.

How to graph points on the coordinate plane to solve real-world and mathematical problems
Examples:

1. Write the ordered pair for Point S.
2. The locations of Danielle’s favorite rides at the amusement park are shown in the graph below. What order should she ride them if she wants to start at the back of the park and work her way to the front?
3. If a movie theatre is built at (2,4), which of the other locations is closest to the movie theatre?
4. The graph of Haley and Jaden’s run this morning is represented below. According to the graph, how much longer did it take Haley than Jaden after 3 miles?

Examples of word problems that uses the coordinate plane

1. The ice cream store wants to locate their new shop halfway between Riverside and Fairview. Riverside is located at (2,4) on the grid shown below. Greenville is located at (12,4).
Where should the shop be located?
2. Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The starting point is at (3,1) and the ending point is at (3,9). At (3,7), there’s a water station to make sure the walkers stay hydrated.
Plot the starting point, ending point, and the water station.
How far along will Aidan be in the walk when he reaches the water station?
3. Maya is putting up one of her paintings in her living room. Suppose there were a grid on the wall where each unit measured a foot. The painting is represented by the inner square and the frame is represented by the outer square. Maya places a nail so that it lies halfway across the top of the frame.
On the graph, plot the point where Maya places the nail.
Name the point by filling in the blanks.
4. A map of the local disc golf course shows the holes on a grid similar to the coordinate plane. The tee on the first hole is at the point (1,2), and the hole is at the point (8,2).
Plot the two points representing the tee and the hole.
Find the distance between them.
5. Ying is putting up one of her paintings in her living room. Suppose there were a grid on the wall where each unit measured a foot. The upper-left corner of the frame is at the point (1,8) and the upper-right corner at (7,8). The bottom-left corner is at (1,2) and the bottom-right corner at (7,2).
Plot the four corners of the frame.
What is the width of the painting plus frame?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 