Subscribe

6th grade · Math · Unit 15 of 21

Four Quadrants

Points with negative coordinates

What your child practices

Plotting and naming points in all four quadrants, reflecting points across an axis, and finding distances and areas on the coordinate plane.

New York State Learning Standards learning standard: NY-6.NS.8; NY-6.G.3; NY-6.NS.6 · graphing points in all four quadrants and finding the distance between points with a shared coordinate

How we explain it

Children can open this short lesson before they practice.

  1. Left of 0 is negative x. Below 0 is negative y.
  2. Quadrant I is (+, +), II is (−, +), III is (−, −), IV is (+, −).
  3. Across an axis, one coordinate changes sign.

Example: How far apart are (−3, 2) and (5, 2)? Same y, so count across. 3 to get to 0, then 5 more: 3 + 5. Answer: 8 units

Four Quadrants in New York

In the New York State Learning Standards, this is unit 15 of 21 in 6th grade Math, after Dividing Fractions and before Unit Rates.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    The point (−1, 4) is reflected across the y-axis. Where does it land?

    • (1, 4)
    • (−1, −4)
    • (4, −1)
    • (1, −4)

  2. Question 2

    What are the coordinates of point P?

    -6-6-5-5-4-4-3-3-2-2-1-100112233445566P
    • (2, −6)
    • (−2, 6)
    • (−6, −2)
    • (−2, −6)

  3. Question 3

    A rectangle has corners (−7, −4), (5, −4), (5, 1) and (−7, 1). What is its area?

    • 6 square units
    • 62 square units
    • 72 square units
    • 34 square units
    • 60 square units

  4. Question 4

    Which quadrant is the point (−5, −3) in?

    • Quadrant I
    • Quadrant IV
    • Quadrant III
    • Quadrant II

  5. Question 5

    How far apart are (2, −4) and (2, 6)?

    • 10
    • 2
    • 13
    • 12

  6. Question 6

    A rectangle has corners (−7, −1), (1, −1), (1, 5) and (−7, 5). What is its area?

    • 48 square units
    • 46 square units
    • 49 square units
    • 56 square units
    • 28 square units

More 6th grade