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Integers & Coordinate Plane

Interactive study guide — Reveal Math Unit 7 · Standard 6.NS

7.1–7.2 — Integers & Rational Numbers

Understand positive and negative numbers, opposites, and how to place them on a number line.

Key Ideas

Integers are whole numbers and their opposites: …−3, −2, −1, 0, 1, 2, 3…

Rational numbers include fractions and decimals too: −2.5, ¾, −⅓

Every positive number has an opposite (its negative), and vice versa. The opposite of 5 is −5.

←──−4──−3──−2──−1──0──1──2──3──4──→
Comparing: −3 < 1 because −3 is farther left on the number line.
Any negative number is less than any positive number.

Practice

What is the opposite of −8?

−8
8
0

Which is greater: −5 or −2?

−2
−5
They are equal

Put in order from least to greatest: 3, −1, 0, −4

−1, −4, 0, 3
3, 0, −1, −4
−4, −1, 0, 3
Score
0/3

7.3 — Absolute Value

Absolute value is the distance from zero on the number line — always positive or zero.

Key Idea

The absolute value of a number is written with vertical bars: |−5| = 5 and |5| = 5

Think of it as: "How far from zero?" Direction doesn't matter.

←──−5──−4──−3──−2──−1──0──1──2──3──4──5──→
|−5| = 5 units from 0     |3| = 3 units from 0
Comparing with absolute value:
|−7| = 7 and |4| = 4, so |−7| > |4| even though −7 < 4

Practice

What is |−12|?

−12
0
12

Which has a greater absolute value: −6 or 4?

4, because it's positive
−6, because |−6| = 6 > 4
They are equal

|0| = ?

0
1
Undefined
Score
0/3

7.4 — Add & Subtract Integers

Use number lines and rules to add and subtract positive and negative numbers.

Rules for Adding Integers

Same signs: Add the absolute values, keep the sign.
Different signs: Subtract the smaller absolute value from the larger, take the sign of the larger.

Same signs: −3 + (−5) = −8 (both negative, add, keep negative)
Different signs: −7 + 4 = −3 (|7| − |4| = 3, keep the negative)

Subtracting Integers

Add the opposite! Change subtraction to addition and flip the sign of the second number.

Example: 5 − (−3) = 5 + 3 = 8
Example: −2 − 4 = −2 + (−4) = −6

Practice

−6 + (−4) = ?

−2
−10
10

8 + (−3) = ?

5
11
−5

3 − (−7) = ?

−4
4
10
Score
0/3

7.5 — The Coordinate Plane

Plot ordered pairs in all four quadrants. The x-axis goes left-right, the y-axis goes up-down.

Key Ideas

An ordered pair (x, y) tells you where to plot a point. Start at the origin (0, 0).

Move right for positive x, left for negative x. Move up for positive y, down for negative y.

Quadrants:
Quadrant I: (+, +) — top right
Quadrant II: (−, +) — top left
Quadrant III: (−, −) — bottom left
Quadrant IV: (+, −) — bottom right
Example: Plot (−3, 2)
Start at origin → go left 3 → go up 2 → Quadrant II

Practice

Which quadrant contains the point (−4, −2)?

Quadrant II
Quadrant III
Quadrant IV

The point (5, −1) is in which quadrant?

Quadrant IV
Quadrant I
Quadrant III

A point is on the y-axis. What must be true?

The y-coordinate is 0
Both coordinates are 0
The x-coordinate is 0
Score
0/3

7.6–7.7 — Distance & Polygons on the Coordinate Plane

Find distances between points and draw polygons using coordinates.

Distance Between Points

For points on the same horizontal or vertical line, use absolute value to find distance.

Same y-axis (horizontal distance):
(−3, 2) to (5, 2): |−3 − 5| = |−8| = 8 units
Same x-axis (vertical distance):
(4, −1) to (4, 6): |−1 − 6| = |−7| = 7 units

Polygons

Plot vertices as ordered pairs, connect them, then find perimeter by adding side lengths and area using formulas.

Example: Rectangle with vertices (1,1), (1,4), (5,4), (5,1)
Width = |5−1| = 4, Height = |4−1| = 3
Perimeter = 2(4+3) = 14, Area = 4 × 3 = 12 sq units

Practice

Distance from (2, 3) to (2, −4)?

7 units
1 unit
−1 units

Distance from (−3, 5) to (4, 5)?

1 unit
9 units
7 units

A rectangle has vertices at (0,0), (6,0), (6,3), (0,3). What is its area?

9 sq units
18 sq units
24 sq units
Score
0/3

Vocabulary

Tap a card to reveal the definition.

Integer
Whole numbers and their opposites: …−3, −2, −1, 0, 1, 2, 3…
Rational Number
Any number that can be written as a fraction, including integers, decimals, and fractions.
Absolute Value
The distance of a number from zero on the number line. Always positive or zero. Written |x|.
Opposite
Two numbers that are the same distance from zero but on different sides. Example: 5 and −5.
Coordinate Plane
A grid formed by a horizontal x-axis and vertical y-axis, divided into four quadrants.
Ordered Pair
A pair of numbers (x, y) that identifies a point on the coordinate plane.
Origin
The point (0, 0) where the x-axis and y-axis cross.
Quadrant
One of four sections of the coordinate plane. Numbered I–IV counterclockwise from top-right.
x-axis
The horizontal number line on the coordinate plane.
y-axis
The vertical number line on the coordinate plane.