MA.5.GR.4 Geometric Reasoning
Plot points and represent problems on the coordinate plane.
Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.
Clarification 1: Instruction includes the connection between two-column tables and coordinates on a coordinate plane.
Clarification 2: Instruction focuses on the connection of the number line to the 𝑥- and 𝑦-axis.
Clarification 3: Coordinate planes include axes scaled by whole numbers. Ordered pairs contain only whole numbers.
Purpose and Instructional Strategies
The purpose of this benchmark is for students to extend their thinking from Grade 4 (MA.4.NSO.1.3) about horizontal and vertical number lines to plot and label whole number ordered pairs on a coordinate plane. In addition, students will make a connection between a twocolumn table and the ordered pairs represented on the coordinate plane. In Grade 6 (MA.6.GR.1.1), students plot rational number pairs in all four quadrants of the coordinate plane.
During instruction, teachers should relate the coordinate plane as the intersection of two axes – a horizontal number line called the 𝑥 −axis and a vertical number line called the 𝑦 −axis. The number lines that form the axes are perpendicular and meet at the origin, labeled by the ordered pair (0, 0) (K12.MTR.5.1).
When students learn to plot ordered pairs represented in a two-column table, they should understand that the ordered pair (𝑥, 𝑦) represents how far to travel from the origin along the 𝑥 − and 𝑦 −axes. For example, students should understand that in the ordered pair (2,4), the point travels along the 𝑥 −axis 2 whole units to the right, and then vertically (parallel to the 𝑦 −axis) 4 units up (K12.MTR.5.1).
Common Misconceptions or Errors
Students can confuse the 𝑥 − and 𝑦 − values in an ordered pair and move vertically along the 𝑦 −axis before moving horizontally along the 𝑥 −axis. For example, they may mean to plot and label the ordered pair (2, 4), but plot and label (4, 2) instead. To assist students with this misconception, have students practice with creating directions for their student peers to follow to allow them to gain a better understanding of the direction and distance on the coordinate plane.
Some students may not understand what an 𝑥 − or 𝑦 − coordinate value of 0 represents. During instruction, students should justify why ordered pairs with a 0 will plot on the 𝑥 −axis or 𝑦 −axis.
Instructional Task 1
Part A. A point has coordinates (3, 5). If you were to graph this point on a coordinate plane, what does the 3 tell you to do?
Part B. Consider the same point with coordinates (3, 5). What does the 5 tell you to do?
Part C. The point above has coordinates (3, 5). Which of these is the 𝑥 − coordinate? Which of these is the 𝑦 −coordinate?
Instructional Item 1
What ordered pair represents the origin of a coordinate plane?
a. (0, 0)
b. (1, 0)
c. (0, 1)
d. (1, 1)
Instructional Item 2
A point has coordinates (1, 6). If you were to plot this point on a coordinate plane, what does the 1 tell you to do?
a. From the origin, move along the 𝑥 −axis 1 unit up.
b. From the origin, move along the 𝑦 −axis 1 unit up.
c. From the origin, move along the 𝑥 − axis 1 unit right.
d. From the origin, move along the 𝑦 −axis 1 unit right.