Learn on PengiPengi Math (Grade 6)Chapter 5: Coordinate Plane & Graphs

Lesson 1: Quadrants, Signs, and Plotting in All Four Quadrants

In this Grade 6 Pengi Math lesson, students learn to name and locate Quadrants I through IV on the coordinate plane by connecting each quadrant to its sign pattern — (+/+), (−/+), (−/−), and (+/−). Students practice plotting points with negative coordinates using left/right and up/down direction rules, and determine whether a given point falls within a specific quadrant or on an axis based on coordinate signs and zeros. The lesson also challenges students to generate possible coordinate pairs that satisfy a given quadrant and partial coordinate condition.

Section 1

Quadrants and Points on the Axes

Property

The axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise.

Quadrant IQuadrant IIQuadrant IIIQuadrant IV
(+,+)(+, +)(,+)(-, +)(,)(-, -)(+,)(+, -)

Points on the Axes
Points with a yy-coordinate equal to 0 are on the xx-axis, and have coordinates (a,0)(a, 0).
Points with an xx-coordinate equal to 0 are on the yy-axis, and have coordinates (0,b)(0, b).

Section 2

Plotting Points in the Coordinate Plane

Property

To plot a point (x,y)(x, y) on the coordinate plane:
start at the origin (0,0)(0, 0), move x|x| units horizontally (right if x>0x > 0, left if x<0x < 0), then move y|y| units vertically (up if y>0y > 0, down if y<0y < 0).

Examples

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Chapter 5: Coordinate Plane & Graphs

  1. Lesson 1Current

    Lesson 1: Quadrants, Signs, and Plotting in All Four Quadrants

  2. Lesson 2

    Lesson 2: Horizontal & Vertical Distance on the Plane

  3. Lesson 3

    Lesson 3: Polygons on the Coordinate Plane

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Quadrants and Points on the Axes

Property

The axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise.

Quadrant IQuadrant IIQuadrant IIIQuadrant IV
(+,+)(+, +)(,+)(-, +)(,)(-, -)(+,)(+, -)

Points on the Axes
Points with a yy-coordinate equal to 0 are on the xx-axis, and have coordinates (a,0)(a, 0).
Points with an xx-coordinate equal to 0 are on the yy-axis, and have coordinates (0,b)(0, b).

Section 2

Plotting Points in the Coordinate Plane

Property

To plot a point (x,y)(x, y) on the coordinate plane:
start at the origin (0,0)(0, 0), move x|x| units horizontally (right if x>0x > 0, left if x<0x < 0), then move y|y| units vertically (up if y>0y > 0, down if y<0y < 0).

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Coordinate Plane & Graphs

  1. Lesson 1Current

    Lesson 1: Quadrants, Signs, and Plotting in All Four Quadrants

  2. Lesson 2

    Lesson 2: Horizontal & Vertical Distance on the Plane

  3. Lesson 3

    Lesson 3: Polygons on the Coordinate Plane