# Ordered Pairs & Coordinate Plane (Grade 6)

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Examples, solutions, videos, and lessons to help Grade 6 students 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.

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.

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.

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.

Common Core: 6.NS.6b and 6.NS.6c

### Suggested Learning Targets

• I can recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located.
• I can reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y axis, e.g., (x,y) and (x,-y).
• I can recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x axis, e.g., (x,y) and (x,-y).
• I can reason that when two ordered pairs differ only by signs, the locations of the points are related by reflections across both axes, e.g., (-x,-y) and (x,y).
Understanding ordered pairs, signs and the coordinate plane (Common Core 6.NS.6b)
Reflections on the Coordinate Plane
You can use what you know about number lines and opposites to compare locations on the coordinate plane.
Reflection across y-axis, X's are opposites.
Reflection across x-axis, Y's are opposites.
Examples:
1. Name the ordered pair that is reflected of (-3,2) across the x-axis.
2. Name the ordered pair that is a reflection of each point across the x-axis.
a. (1,-4)
b. (-2,5)
c. (-3,-1)
3. Kendall is building a square fence. She places fence posts at the locations indicated on the grid. What is the location of the post that reflects (-4,4) across the y-axis?
Kendall also places a fence post at (-4,-4). What is the location of the post that reflects (-4,-4) across the y-axis?

6.NS.6b - Opposite numbers on the coordinate plane
Axis - a number line on the coordinate plane.
Quadrant - one of the 4 regions created by the x and y-axis.
Coordinates - a set of numbers that shows a location on the coordinate plane.
How to plot points with negative numbers:
1. The first number tells how far across you go (from the origin) - positive is to the right and negative is to the left.
2. The second number tells how far up or down to go - positive is up, negative is down.
3. If you change the sign of a coordinate, the point reflects on an axis.
Plotting Points in a Coordinate Plane (Common Core 6.NS.6b)
In this video, students will learn to plot points in all 4 quadrants of a coordinate plane. Rational Numbers on Coordinate Plane (Common Core 6.NS.6c)

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