MATHEMATICS 8
QUARTER 1 | WEEK 4 | M8AL-Ie-1
ONLINE CLASSROOM RULES
Teacher Ace
8TH GRADE
RECTANGULAR
COORDINATE
SYSTEM
Quarter 1 | Lesson 4
WHAT WE HAVE ACHIEVED SO FAR?
FACTORING
POLYNOMIALS
OPERATIONS ON RATIONAL
ALGEBRAIC EXPRESSIONS
Week1
Week 3
Week 2
SIMPLIFYING RATIONAL
ALGEBRAIC EXPRESSION
8th GRADE
Let’s Play!
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C O R N E
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R
8th GRADE
Story
Retelling
8th GRADE
RENÉ
DESCARTES
In the nineteenth century,
algebra and analysis took
precedence over geometry,
the coordinate system of
algebraic geometry came to
be called “Cartesian
coordinates” in honor of his
discovery.
Source: https://plato.stanford.edu/entries/descartes
8th GRADE
RECTANGULAR
COORDINATE
SYSTEM
Source: https://plato.stanford.edu/entries/descartes
What are in
store for us?
What are in
store for us?
1. Illustrate the rectangular
coordinate system;
2. Determine of the coordinates of
given points in the cartesian plane;
3. Plot the given points in the
cartesian plane;
What are in
store for us?
4. Formulate a rule in plotting and
identifying the quadrant of a given
ordered pair;
5. Validate the answers of your
classmates in a given activity; and
6. Construct a rectangular coordinate
plane to solve real-world problem.
LET’S
EXPLORE!
Class Seating
Arrangement
a. In what row does Maria
sit?
First row
b. In what column you
can find Pedro?
Fifth column
c. Who sits at the
intersection of second
row and fifth column?
Matt
T. Rosa
Ace
Maria
Ben
Lora
Pedro
Gina
Carlos
Mica
Rye
Cara
Adonis
Sue
Juan
Ana
Carlos
Karen
Matt
Nina
Greg
Nina
Checkmate!
a. What white piece must
be moved in order to
checkmate all the black
kings?
horse
b. In what position you
should move it?
e5
Where in
the World?
a. What is the
approximate
coordinates of the
Philippines relative
to the world map
presented?
10º North, 120º East
Where in
the World?
b. What body of
water lies at
20º South, 80º
East?
Indian Ocean
Where in
the World?
c. What is the
coordinates of the
intersection of the
prime meridian and
equator?
0º North, 0º East
https://blogs.loc.gov/maps/2016/04/
the-geographical-oddity-of-nullisland/
THINK ABOUT THIS!
What similarities or differences you can identify
among the three situations based on the
rule/system in identifying location/position?
LET’S
STUDY IT
FURTHER!
Get a sheet of
graphing paper.
How many creases
were created after
folding the paper?
1. Fold the paper in
half, from
How
manyright to
left
partitions
were
created in your
2. Unfold the
graphing paper?
previous step to
fold it again at top
edge up to the
bottom edge.
Where does the
intersection of the
horizontal and
vertical creases
located?
10
9
8
7
6
5
4
3
What numbers
must line up on the
right (left) side of
zero?
What numbers
must line up above
(below) of zero?
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0 1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
2
3
4
5
6
7
8
9
10
INHS SATELLITE MAP
B
A
C
D
E
J
G
F
H
I
INHS SATELLITE MAP
Building
A
B
C
H
V
10
9
TLE Laboratory
C
Canteen
Covered Court
E
Coop Building
F
Maliksi Building
G
SSC Building
A
7
6
5
JICA Building
D
B
8
E
4
D
3
2
1
-10 -9
-8 -7 -6
-5
G
-4 -3 -2 -1
J
1
-1
Flag Pole
-3
-4
I
Subj. Department Bldng.
J
Poultry
I
3
4
5
6
7
-2
-5
H
2
-6
-7
-8
-9
-10
F
H
8
9
10
THINK ABOUT THIS!
What position is relative to each of the building
that we have identified?
How did you able to locate the specified
building?
RECTANGULAR COORDINATE PLANE
The x and y axes are
just like the number
line, with positive
distances to the right
and negative to the left
in the x-axis, and
positive distances
measured upwards and
negative down for the
y-axis.
y-axis
x-axis
RECTANGULAR COORDINATE PLANE
Locations on the graph
are measured relative
to a fixed point, called
the origin, and are
measured according to
the distance along the
pair of axes.
y-axis
origin (0,0)
x-axis
THINK ABOUT THIS!
How did we name the location
of the building in the school?
RECTANGULAR COORDINATE SYSTEM
The location of a point is
determined by first giving
its x coordinate (abscissa),
the left or right
displacement from the
origin, and then the
y coordinate (ordinate), the
up or down displacement
from the origin.
RECTANGULAR COORDINATE SYSTEM
Thus, every point on the
plane can be identified by
a pair of numbers (x,y),
called coordinates.
EXAMINE THIS!
Identify the points on
each partition made by
the intersecting x and y
axes.
EXAMINE THIS!
List all the points that
falls into:
Upper Right Region:
Upper Left Region:
Lower Left Region:
Lower Right Region:
RECTANGULAR COORDINATE PLANE
The axes divide the
plane into quarters. We
call these quadrants,
and number them from
one to four.
The numbering begins in
the upper right quadrant
and continues around in
the counter–clockwise
direction.
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
RECTANGULAR COORDINATE PLANE
Analyze the pair of signs
exhibited by each point
based on their quadrants.
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
RECTANGULAR COORDINATE PLANE
Analyze the pair of signs
exhibited by each point
based on their quadrants.
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
MORE EXAMPLES
Plot the following points
and identify the
quadrants.
1.
2.
3.
(5, -4)
9
8
7
6
5
4
Quadrant II3
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
Quadrant I
(-5/2,
-6) Quadrant III
Quadrant I
2
Quadrant IV
(9, 5)
9TH GRADE
10
0 1
-1
(-3, 5)
Quadrant II
3
4
5
6
7
8
9
-2
-3
-4
-5
-6
4. Three units to the left of yaxis and 5 units above x-axis.
2
Quadrant III -7
-8
-9
-10
Quadrant IV
10
ONLINE GROUP
ACTIVITY
Each team will be assigned
to a breakout room and will
be given 10 minutes to
complete the objective of an
online game related to
rectangular coordinate
system.
ONLINE GROUP
ACTIVITY
After completing the game, you
must do the following:
1. Screen shot the game result;
2. Note all the coordinates used
and identify their quadrants; and
3. Present you results and
answers in class.
ONLINE GROUP
ACTIVITY
The other groups will validate
or correct the answers of the
presenting group.
ONLINE GROUP
ACTIVITY
Team 1: Boat Coordinates
https://www.mathnook.com/math/boatcoordinates.html
Team 2: Rocket Down
https://www.mathnook.com/math/rocket-down-2.html
Team 3: Graphing Puzzle
https://www.mathnook.com/math2/graphing-puzzle.html
BREAKOUT
SESSIONS
PRESENTATION OF
RESULTS &
ANSWERS
KEY TAKEAWAYS
In the rectangular
coordinate system what
do you call the two real
number lines that
intersect at a right angle?
All positions in the
rectangular coordinate
system is relative to what
point?
What do you call a
pair of numbers that
identifies a position
on the rectangular
plane?
x-axis
&
y-axis
(0,0)
origin
coordinates
KEY TAKEAWAYS
What do you call the
regions made by the
intersecting axes?
What are the signs of the
coordinates in the
following quadrants?
How do you plot points in
rectangular coordinate
system?
(open response)
quadrants
QI
QII
QIII
QIV
(+,+)
(-,+)
(-,-)
(+,+)
Did we hit
the marks?
Did we hit
the marks?
1. Illustrate the rectangular
coordinate system;
2. Determine of the coordinates of
given points in the cartesian plane;
3. Plot the given points in the
cartesian plane;
Did we hit
the marks?
4. Formulate a rule in plotting and
identifying the quadrant of a given
ordered pair;
5. Validate the answers of your
classmates in a given activity; and
6. Construct a rectangular coordinate
plane to solve real-world problem.
PERFORMANCE
TASKS
Goal
Situation
Construct a rectangular
coordinate plane to solve
real-world problems.
Distribution of modules for learners
under modular modality. The school is
expecting 30 parents per grade level
every two hours to receive the modules
Role
Teacher/ School Floor
Manager
Audience
Parents, learners, and school
administrators
Product
Seating plan for parents during the
module distribution of INHS.
STANDARDS
Deadline: Nov. 22
Categories
Excellent
Learners are
able to clearly
draw the
rectangular
coordinate
Content
system and
Integration,
represent the
Representation, positions in the
& Accuracy
seating
arrangement
with appropriate
symbols.
Good
Learners are able
to appropriately
draw the
rectangular
coordinate system
and represent the
positions in the
seating
arrangement with
minor (1 – 2)
flaw/s in using
symbols.
Satisfactory
Learners are able
to adequately
draw the
rectangular
coordinate system
and represent the
positions in the
seating
arrangement with
numerous (3 and
above) flaws in
using symbols.
Unsatisfactory
Learners did not
illustrate
appropriately the
rectangular
coordinate system
and unclearly
represent the
positions in the
seating arrangement
with confusing
symbols.
10-9
The seating plan
is extremely
neat, organized,
and easy to
understand by
the audience.
8-6
The seating plan
is, neat, organized,
and could be
understand by the
audience.
5-3
The seating plan is
organized with
minor mess and
may be hard to
understand by the
audience
2-1
The seating plan
appears sloppy,
unorganized, and
hard to understand.
6-5
The illustration is
exceptionally
appealing in
terms of layout
and design.
4
4-3
The illustration is
acceptable in
terms of layout
and design.
2
The illustration is
acceptable though
it may be a bit
unappealing.
1
The illustration is
distractingly messy
and very poorly
designed.
Neatness and
Organization
Overall
illustration
Comments:
3
2
1
Score
Total: ____/20
Let’s ponder about this.
Some systems might be relative in terms of
their usability and purpose.
Can you think of any system that might not
applicable to all people or groups of
people?
References:
Larson, R., & Hostetler, R. P. (2012). The Rectangular Coordinate
System and Graphs. In Algebra and Trigonometry (pp. 55–65). Cengage
Learning Asia Pte Ltd.
Oronce, O. A., Mendoza, M. O., & author. (2019). Rectangular
Coordinate System. In E-math: Worktext in Mathematics 8 (pp. 112–119).
Rex Book Store.
Rectangular Coordinate System. TSI assessment preparation. (n.d.).
Retrieved November 3, 2021, from https://sites.austincc.edu/tsiprep/mathreview/graphing/the-rectangular-coordinate-system-and-point-plotting/.
Thank you!
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Teacher Ace