Coordinate plane

What is this skill?

The coordinate plane is a flat grid with two number lines that cross at a point called the origin. The horizontal line is the x-axis and the vertical line is the y-axis. Every point has an address, written as an ordered pair (x, y). The first number tells how far to go across from the origin, and the second tells how far to go up. The point (3, 4) is three steps right and four steps up.

In fifth grade, children work only in the first quadrant, where both numbers are zero or positive. Negative numbers and the other three quadrants come in sixth grade. The practice here asks children to read a point off a grid, either by picking its coordinates from several choices or by giving one coordinate, either x or y, when a point is shown.

Why it matters

The coordinate plane connects numbers to pictures. It is the way graphs of every kind are built, from a line graph of temperature across a week to the graph of an equation in later years. Maps, video-game screens and spreadsheets use the same idea of finding a position with two numbers.

In fifth grade it is also used to explore patterns: points from two number sequences can be plotted and compared. Learning to read and place points accurately now makes graphing in middle school straightforward.

Common mistakes

• Swapping the order, so (3, 4) is read as four across and three up. A rule of thumb is to walk across the floor first and then climb up the stairs.
• Counting the grid lines, not the steps, and starting at 1 instead of 0. The count starts from the origin.
• Mixing up which axis is x and which is y. The x-axis lies flat, the y-axis stands up.
• Forgetting that a coordinate can be 0. A point on an axis, like (0, 5), has a zero in it.
• Reading a label that happens to sit near the point, instead of following the grid line straight down or across to the axis.

How to help at home

• Play a hidden-treasure game on graph paper. One person hides a treasure at a point and the other guesses ordered pairs. The answer is “warmer” or “colder.”
• Make a map of your home or street on a grid and give each place coordinates.
• Say the movement out loud: “across 3, then up 4.” Pairing words with the numbers makes the order stick.
• Draw simple shapes by plotting points and joining them. A rectangle needs just four ordered pairs.
• Use a chessboard or a spreadsheet to show that other places in life use the same idea of a grid with two addresses.

Worked examples

These are real questions from the Tutorsaurus coordinate plane practice, with the answers worked out.

1. Example 1

   What are the coordinates of the point?

   Choices: (3, 0), (0, 4), (0, 3), (0, 2)

   Answer: (0, 3). Go right 0, then up 3: (0, 3). The x-coordinate always comes first.

2. Example 2

   What is the y-coordinate of the point?

   Answer: 10. The point is 7 across and 10 up, so it is (7, 10). The y-coordinate is 10.

3. Example 3

   What are the coordinates of the point?

   Choices: (3, 3), (2, 4), (2, 2), (2, 3)

   Answer: (2, 3). Go right 2, then up 3: (2, 3). The x-coordinate always comes first.