ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this video lesson, students explore ways to find vertical and horizontal distances in the coordinate plane. In the first activity, students use repeated reasoning to explore the relationship between points with opposite coordinates. In the second activity, students develop strategies for finding the distance between two points where the coordinates might not be integers. Students can use previous strategies, such as considering the distance of a point from zero or counting squares.

   View Standards     Standard(s): [MA2015] (6) 9 :

9 ) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6-NS6]

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., - (-3) = 3, and that 0 is its own opposite. [6-NS6a]

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. [6-NS6b]

c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. [6-NS6c]

[MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In Module 3, Topic C, students extend their understanding of the ordering of rational numbers in one dimension (on a number line) to the two-dimensional space of the coordinate plane. They construct the plane’s vertical and horizontal axes, discovering the relationship between the four quadrants and the signs of the coordinates of points that lie in each quadrant (6.NS.C.6b, 6.NS.C.6c). Students build upon their foundational understanding from 5th Grade (5.G.1, 5.G.2) of plotting points in the first quadrant and transition to locating points in all four quadrants. Students apply the concept of absolute value to find the distance between points located on vertical or horizontal lines and solve real-world problems related to distance, segments, and shapes (6.NS.C.8).