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6th grade · Math · Unit 15 of 17

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.

Minnesota K-12 Academic Standards benchmark: 6.3.5.2; 6.2.4.3 · graphing points in all four quadrants and finding lengths on the coordinate plane

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 Minnesota

In the Minnesota K-12 Academic Standards, this is unit 15 of 17 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: Minnesota Department of Education (MDE)

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

    How far apart are (2, −8) and (2, 1)?

    • 11
    • 12
    • 7
    • 9

  2. Question 2

    What are the coordinates of point P?

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

  3. Question 3

    Which quadrant is the point (−1, 9) in?

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

  4. Question 4

    A rectangle has corners (−3, −6), (4, −6), (4, 2) and (−3, 2). What is its area?

    • 57 square units
    • 59 square units
    • 63 square units
    • 56 square units
    • 30 square units

  5. Question 5

    The point (−3, 7) is reflected across the x-axis. Where does it land?

    • (3, 7)
    • (−3, −7)
    • (3, −7)
    • (7, −3)

  6. Question 6

    What are the coordinates of point P?

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

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