5.G.1: The Coordinate Plane and Ordered Pairs
Also written as 5.G.A.1 and CCSS.MATH.CONTENT.5.G.A.1 · Cluster: Graph points on the coordinate plane to solve real-world and mathematical problems.
The Official Wording
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. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
Common Core State Standards, Grade 5, Geometry · Read it at the source · Checked October 14, 2026
What 5.G.1 Means in Plain English
Fifth graders build the grid themselves: two number lines crossing at 0, one across and one up. The pair (4, 2) means start at the origin, travel 4 along the x-axis, then 2 up. Swap the numbers to (2, 4) and the point lands somewhere else entirely.
The axes are the number lines students have used since 2nd grade (2.MD.6), crossed at a right angle. In 5.G.2 the points start to mean hours, miles or dollars, and in 6th grade both axes run past 0 into negative numbers and all four quadrants (6.NS.6).
5.G.1 I Can Statements
- I can draw x- and y-axes that cross at the origin.
- I can plot a point from an ordered pair, across first and then up.
- I can read the coordinates of a point already on the grid.
5.G.1 Worked Example
A grid drawn from scratch, two points that use the same numbers in a different order, a point on an axis, and one point read back.
Draw a coordinate grid numbered 0 to 6 on each axis. Plot A (4, 2), B (2, 4) and C (0, 3). Then name the coordinates of point D, which sits 5 squares right of the y-axis and 1 square above the x-axis.
- Draw two perpendicular number lines that meet at the 0 of each. The horizontal one is the x-axis, the vertical one the y-axis.Origin (0, 0) where the axes cross
- Plot A: from the origin, travel 4 along the x-axis, then 2 up.A (4, 2)
- Plot B the same way: 2 across, then 4 up. Same numbers, different point.B (2, 4), up and to the left of A
- C has 0 as its first number, so there is no travel across. It climbs 3 up the y-axis itself.C (0, 3), on the y-axis
- D is 5 squares from the y-axis, so its x-coordinate is 5. It is 1 square above the x-axis, so its y-coordinate is 1.D (5, 1)
Check it: From each point, drop straight down to the x-axis and slide straight across to the y-axis. The two numbers you land on are the pair, in that order.
Common Mistakes with 5.G.1
Up first, then across
(4, 2) plotted 4 up and 2 across, landing on (2, 4)
Try this: Say “across, then up” while tracing with a finger, and label the axes x and y to match the order of the pair.
Counting the origin as 1
The first grid line counted as 1, so (3, 2) lands one square short in each direction
Try this: Number the axes before plotting, starting with 0 at the origin, and write the numbers on the lines, never in the spaces.
Putting a zero on the wrong axis
(0, 3) plotted on the x-axis at 3
Try this: Read a zero as “stay put”: no travel across means the point stays on the y-axis and climbs 3.
Where 5.G.1 Fits
Practice 5.G.1
Quick Check
- Where is the point (0, 0)?
- Start at the origin, go 6 across and 3 up. What ordered pair names the point?
- Is (2, 5) the same point as (5, 2)?