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Integers & the Coordinate Plane

Standards: 6.NS.C.5 (Positive/Negative) · 6.NS.C.6 (Number Line/Plane) · 6.NS.C.7 (Absolute Value) · 6.NS.C.8 (Graphing)

Directions: Study the vocabulary box and worked examples first. Then answer each problem in the space provided. Use the hints if you need them. Show your work.

Vocabulary Helper

➕➖ Integer
A whole number that can be positive, negative, or zero (…−2, −1, 0, 1, 2…).
🪞 Opposite
The same number with the other sign. The opposite of 7 is −7.
📏 Absolute Value
Distance from zero on a number line. Always positive. |−9| = 9.
➕ Coordinate Plane
A grid made by an x-axis and y-axis crossing at the origin (0, 0).
📍 Ordered Pair
(x, y): go right/left for x first, then up/down for y.
🧭 Quadrant
One of four sections of the plane, labeled I, II, III, IV.

Worked Examples

EXAMPLE A — Plot a Point

Plot (−3, 4):

  1. Start at the origin (0, 0).
  2. x = −3: move 3 units left.
  3. y = 4: move 4 units up.
  4. This point is in Quadrant II.
EXAMPLE B — Distance on a Number Line

Distance between −3 and 5:

  1. They are on opposite sides of 0.
  2. Add the absolute values: |−3| + |5| = 3 + 5.
  3. The distance is 8 units.

Sentence Frames

The opposite of −12 is because it has the same number but a different .
The point (4, −5) is in Quadrant because x is and y is .
|−9| equals because absolute value is the from zero.

Guided Practice

1. What is the opposite of 7?

Hint: Same number, different sign.

2. What is |−9|?

Hint: Distance from 0 is always positive.

3. Which is greater: −3 or −8?

Hint: On a number line, the number farther right is greater.

4. In which quadrant is the point (4, −5)?

Hint: x positive (right), y negative (down) = bottom-right.

5. What is the opposite of −12?

Hint: Negative becomes positive.

6. Order from least to greatest: 3, −5, 0, −1, 4

Hint: More negative = smaller.

7. What is the distance between −3 and 5 on a number line?

Hint: Add |−3| + |5|.

8. In which quadrant is (−2, −6)?

Hint: Both negative = bottom-left.

9. Give the coordinates of a point 3 units left and 4 units up from the origin.

Hint: Left = negative x. Up = positive y.

10. Find the distance between (2, 5) and (2, −3).

Hint: Same x, so use the y-values: |5| + |−3|.

Answer Key

  1. −7
  2. 9 — −9 is 9 units from zero
  3. −3 > −8 — −3 is closer to zero
  4. Quadrant IV
  5. 12
  6. −5, −1, 0, 3, 4
  7. 8 units — 3 + 5 = 8
  8. Quadrant III
  9. (−3, 4)
  10. 8 units — |5| + |−3| = 5 + 3 = 8