Distances in the Coordinate Plane
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to review plotting and determining the coordinates of points in the coordinate plane. Students use repeated reasoning to generalize patterns in the coordinates of points in each quadrant (MP8).
Launch
Arrange students in groups of 4. Assign each person in the a group a different quadrant. Give students 3 minutes of quiet work time to plot and label at least three points, and up to six if they have time, in their assigned quadrant. Follow with a whole-class discussion.
Student Task
Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
Sample Response
Sample responses:
- Quadrant I: (4,7), (2,3), and (6,1)
- Quadrant II: (-5,5), (-3,6), and (-2,4)
- Quadrant III: (-1,-3), (-5,-4), and (-2,-6)
- Quadrant IV: (3,-6), (7,-2), and (1,-1)
Activity Synthesis (Teacher Notes)
The focus of this discussion is for students to recognize that the following patterns emerge:
- In Quadrants I and IV, the x-coordinate of a point (or the first number in an ordered pair) is positive.
- In Quadrants II and III, the x-coordinate of a point is negative.
- In Quadrants I and II, the y-coordinate of a point (or the second number in an ordered pair) is positive.
- In Quadrants III and IV, the y-coordinate of a point is negative.
Invite students to share any patterns they noticed. After each student shares, ask the rest of the class if they noticed the same pattern within their small group. Record and display these patterns for all to see. If possible, plot and label a few example points in each quadrant based on students’ observations.
Standards
- 6.NS.6·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.NS.6.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.NS.C.6·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.NS.C.6.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.
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Distances in the Coordinate Plane
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to review plotting and determining the coordinates of points in the coordinate plane. Students use repeated reasoning to generalize patterns in the coordinates of points in each quadrant (MP8).
Launch
Arrange students in groups of 4. Assign each person in the a group a different quadrant. Give students 3 minutes of quiet work time to plot and label at least three points, and up to six if they have time, in their assigned quadrant. Follow with a whole-class discussion.
Student Task
Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
Sample Response
Sample responses:
- Quadrant I: (4,7), (2,3), and (6,1)
- Quadrant II: (-5,5), (-3,6), and (-2,4)
- Quadrant III: (-1,-3), (-5,-4), and (-2,-6)
- Quadrant IV: (3,-6), (7,-2), and (1,-1)
Activity Synthesis (Teacher Notes)
The focus of this discussion is for students to recognize that the following patterns emerge:
- In Quadrants I and IV, the x-coordinate of a point (or the first number in an ordered pair) is positive.
- In Quadrants II and III, the x-coordinate of a point is negative.
- In Quadrants I and II, the y-coordinate of a point (or the second number in an ordered pair) is positive.
- In Quadrants III and IV, the y-coordinate of a point is negative.
Invite students to share any patterns they noticed. After each student shares, ask the rest of the class if they noticed the same pattern within their small group. Record and display these patterns for all to see. If possible, plot and label a few example points in each quadrant based on students’ observations.
Standards
- 6.NS.6·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.NS.6.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.NS.C.6·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.NS.C.6.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.