#### Math - 2017-18

# 6.11 and *6.8 - Coordinate Plane

**6.11 ** The student
will

a) **identify **the
coordinates of a point in a coordinate plane; and

b) **graph **ordered
pairs in a coordinate plane.

6.8The student willa)

identifythe components of the coordinate plane; andb)

identifythe coordinates of a point andgraphordered pairs in a coordinate plane.

**Bloom's Level:** Understand, Apply

*Adopted: 2009*

### BIG IDEAS

- I can find specific locations on a grid or map.

- I will understand
that an ordered pair represents a unique location in space.

### UNDERSTANDING THE STANDARD

- In a coordinate plane, the coordinates of a
point are typically represented by the ordered pair (x, y), where x is the first coordinate and y is the second coordinate. However, any
letters may be used to label the axes and the corresponding ordered pairs.
- The quadrants of a coordinate plane are the four
regions created by the two intersecting perpendicular number lines. Quadrants are
named in counterclockwise order. The signs on the ordered pairs for quadrant I
are (+,+); for quadrant II, (–,+); for quadrant III, (–, –); and for quadrant
IV, (+,–).
- In a coordinate plane, the origin is the point
at the intersection of the x-axis and y-axis; the coordinates of this point are
(0,0).
- For all points on the x-axis, the y-coordinate
is 0. For all points on the y-axis, the
x-coordinate is 0.
- The coordinates may be used to name the point. (e.g., the point (2,7)).
It is not necessary to say “the point whose coordinates are(2,7)”.

2016 VDOE Curriculum Framework - 6.8 Understanding

·
In a
coordinate plane, the coordinates of a point are typically represented by the
ordered pair (*x*, *y*), where *x* is the first
coordinate and *y* is the second
coordinate.

· Any given point is defined by only one ordered pair in the coordinate plane.

· The grid lines on a coordinate plane are perpendicular.

·
The axes of
the coordinate plane are the two intersecting perpendicular lines that divide
it into its four quadrants. The *x*-axis
is the horizontal axis and the *y*-axis
is the vertical axis.

·
The
quadrants of a coordinate plane are the four regions created by the two
intersecting perpendicular lines (*x-*
and *y*-axes). Quadrants are named in
counterclockwise order. The signs on the ordered pairs for quadrant I are
(+,+); for quadrant II, (–,+); for quadrant III, (–, –); and for quadrant IV,
(+,–).

·
In a
coordinate plane, the origin is the point at the intersection of the *x*-axis and *y*-axis; the coordinates of this point are (0, 0).

·
For all
points on the *x*-axis, the *y*-coordinate is 0. For all points on the *y*-axis, the *x*-coordinate
is 0.

·
The
coordinates may be used to name the point. (e.g., the point (2, 7)). It is not
necessary to say

“the point whose coordinates are(2, 7).” The first coordinate
tells the location or distance of the point to the left or right of the *y*-axis and the second coordinate tells
the location or distance of the point above or below the* x*-axis. For example, (2, 7) is two units to the right of the *y*-axis and seven units above the *x*-axis.

·
Coordinates
of points having the same *x*-coordinate
are located on the same vertical line. For example, (2, 4) and (2, -3) are both
two units to the right of the *y*-axis
and are vertically seven units from each other.

·
Coordinates
of points having the same *y*-coordinate
are located on the same horizontal line. For example, (-4, -2) and (2, -2) are
both two units below the *x*-axis and
are horizontally six units from each other.

### ESSENTIALS

- Can any given point be represented by more than
one ordered pair?

The coordinates of a point define its unique location in a coordinate plane. Any given point is defined by only one ordered pair. - In naming a point in the plane, does the order
of the two coordinates matter?

Yes. The first coordinate tells the location of the point to the left or right of the y-axis and the second point tells the location of the point above or below the x-axis. Point (0, 0) is at the origin.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

6.11a_{1} **Identify**
and **label** the axes of a coordinate
plane.

6.11a_{2} **Identify**
and **label** the quadrants of a
coordinate plane.

·
6.8a_{1} **Identify**
and **label** the axes, origin, and
quadrants of a coordinate plane.

6.11a_{3} **Identify**
the quadrant or the axis on which a point is positioned by examining the
coordinates (ordered pair) of the point.

·
6.8a_{2} **Identify**
the quadrant or the axis on which a point is positioned by examining the
coordinates (ordered pair) of the point. Ordered pairs will be limited to
coordinates expressed as integers.

6.11a_{4} **Identify**
ordered pairs represented by points in the 4 quadrants and on the axes of the
coordinate plane

·
6.8b_{2} **Identify**
ordered pairs represented by points in the four quadrants and on the axes of
the coordinate plane. Ordered pairs will be limited to coordinates expressed as
integers.

6.11a_{5} **Relate**
the coordinates of a point to the distance from each axis and **relate** the coordinates of a single
point to another point on the same horizontal or vertical line.

·
6.8b_{3} **Relate**
the coordinates of a point to the distance from each axis and **relate** the coordinates of a single
point to another point on the same horizontal or vertical line. Ordered pairs
will be limited to coordinates expressed as integers.

6.11b_{1} **Graph**
ordered pairs in the 4 quadrants and on the axes of a coordinate plane.

·
6.8b_{1} **Graph**
ordered pairs in the four quadrants and on the axes of a coordinate plane.
Ordered pairs will be limited to coordinates expressed as integers.

·
6.8b_{4} **Draw**
polygons in the coordinate plane given coordinates for the vertices; **use** coordinates to determine the length
of a side joining points with the same first coordinate or the same second
coordinate. Ordered pairs will be limited to coordinates expressed as integers.
**Apply** these techniques in the
context of solving practical and mathematical problems.

### KEY VOCABULARY

coordinate plane, ordered pair, quadrant, perpendicular,
counterclockwise, origin, x-axis, y-axis, location, intersection, intersecting
lines, horizontal, vertical, graph

*Updated: Oct 27, 2017*