Comprehensive Grade 10 Mathematics: Cartesian Plane and Geometric Transformations

Mathematics 10 – Galilei | Measurement and Geometry | Cartesian Plane and Transformations | 5 Sessions
LESSON DETAILS
Lesson Title Exploring the Cartesian Plane and Transformations Using Coordinates
Learning Area/s Mathematics
Name of Teacher/s JERSON NATURAL
Grade Level and Section Grade 10 – Galilei
No. of Sessions 5 Sessions
Topic Measurement and Geometry
Learning Competency 1. Describe the position of points in the Cartesian plane.
2. Describe translations, reflections, and rotations in the Cartesian plane using coordinates.
References Mathematics 10 learner’s module; DepEd BOW; teacher-made PPT; videos on the Cartesian plane and
geometric transformations; graphing paper; ruler; activity sheets; coordinate grid posters; online/offline graphing
tools such as GeoGebra or Desmos, when available.
Teaching Strategy Inquiry-based learning, collaborative activities, multimedia integration, interactive discussion, differentiated
instruction, and contextualized problem solving are suggested by AI based on learners’ needs and level.
Declaration of AI use AI was used as a support tool to draft, organize, contextualize, and refine the lesson plan, including objectives,
learner-centered activities, HOTS questions, differentiated tasks, formative assessments, accommodations, and
reflection prompts. The teacher remains responsible for validating, localizing, and implementing the plan in
accordance with DepEd Order No. 003, s. 2026 on responsible and ethical AI use in basic education.
1. INTENTIONS
Section MONDAY / Session 1 TUESDAY / Session
2
WEDNESDAY /
Session 3
THURSDAY /
Session 4
FRIDAY / Session 5
Learning
Competency and
Curriculum
Standards
Target Competency:
Describe the position
of points in the
Cartesian plane.
Content Standard:
Learners demonstrate
understanding of
coordinate systems,
ordered pairs, axes,
origin, and quadrants.
Performance
Target Competency:
Describe translations
in the Cartesian plane
using coordinates.
Learners explain how
a point or figure
moves left, right, up,
or down while keeping
the same size and
shape.
Target Competency:
Describe reflections in
the Cartesian plane
using coordinates.
Learners identify
images reflected
across the x-axis, y-
axis, and origin using
coordinate rules.
Target Competency:
Describe rotations in
the Cartesian plane
using coordinates.
Learners describe and
perform 90°, 180°,
and 270° rotations
about the origin.
Target Competency:
Describe positions of
points and
transformations in the
Cartesian plane using
coordinates.
Learners apply
translations,
reflections, and
rotations in a real-life
performance task.

Standard: Learners
accurately locate,
label, and describe
points using
coordinates and relate
them to real-life
location systems.
Learning Objectives Knowledge: Identify x-
axis, y-axis, origin,
quadrants, ordered
pair, x-coordinate, and
y-coordinate.
Skills: Plot and
describe points in the
four quadrants.
Understanding:
Explain how
coordinates help
locate places or
objects accurately.
Knowledge: Define
translation as a slide
of a point or figure.
Skills: Translate
points/figures using
rules such as (x, y) →
(x+a, y+b).
Understanding:
Explain that
translation changes
location but not size,
shape, or orientation.
Knowledge: Define
reflection as a flip
across a line of
reflection.
Skills: Reflect
points/figures across
the x-axis, y-axis, and
origin.
Understanding:
Explain how reflected
images are
symmetrical to the
original figure.
Knowledge: Define
rotation as a turn
around a fixed point.
Skills: Rotate
points/figures about
the origin by 90°,
180°, and 270°.
Understanding:
Explain how rotation
changes position and
orientation while
preserving size and
shape.
Knowledge: Compare
translation, reflection,
and rotation.
Skills: Complete a
collaborative
coordinate
transformation map or
design.
Understanding:
Explain how
coordinate geometry
is useful in maps,
games, design,
navigation, and
community planning.
Learner Context Grade 10 – Galilei
learners are expected
to have prior
knowledge of number
lines, integers, graph
reading, and simple
geometric figures.
Strengths may include
visual learning,
interest in mobile
maps/games, and
Learners may
understand translation
better through
movement, classroom
seating, barangay
street directions, and
game-grid examples.
Pair work and graph
paper will provide
concrete scaffolds.
Learners may struggle
with sign changes
during reflections.
Color-coded axes,
mirrors, folded paper,
sign charts, and step-
by-step rules will
support
understanding.
Learners may need
kinesthetic and visual
support for rotations.
Tracing paper, cut-out
shapes, body turns,
PPT animations, or
GeoGebra/Desmos
tools will be used
when available.
Learners will show
varied mastery.
Differentiated tasks,
enlarged grids, oral
explanation, visual
outputs, peer
coaching, guided
worksheets, and
flexible grouping will
ensure inclusive
participation.

peer collaboration.
Possible barriers
include switching x
and y, difficulty with
negative integers,
weak spatial
visualization, limited
device access, and
math anxiety.
2. LEARNING EXPERIENCE
Section MONDAY / Session
1
TUESDAY / Session 2 WEDNESDAY /
Session 3
THURSDAY / Session
4
FRIDAY / Session 5
Pre-Lesson Prayer and greetings.
Check attendance,
seating, graphing
paper, pencil, ruler,
and readiness.
Review number line
and integers.
Motivation: show a
school/barangay
map. Ask: “How can
we tell the exact
location of the
canteen, clinic, or
barangay hall?”
Prayer and routine
check. Review: plot
three points and name
their quadrants.
Motivation: ask learners
to imagine moving a
chair 3 steps right and 2
steps forward. Ask: “Did
its shape change or
only its position?”
Expected: Only its
position changed.
Prayer and readiness
check. Review
translation rules.
Motivation: show
mirror reflection,
butterfly wings, water
reflection, or parol
symmetry. Ask: “What
do you notice about
the object and its
image?” Expected:
Same figure but
flipped/opposite.
Prayer and routine.
Review translation vs
reflection. Motivation:
show a fan, bicycle
wheel, jeepney wheel,
clock hand, or mobile
game object turning.
Ask: “What stays the
same when an object
turns?” Expected: Size
and shape stay the
same.
Prayer and routine.
Review game:
“Transformation
Charades” for slide,
flip, and turn.
Motivation: learners
become “community
map/game designers”
who will use
coordinates and
transformations.
Flow 1. State objective:
locate and describe
points in the
Cartesian plane.
2. Connect past
lesson: Cartesian
plane is like two
1. State objective:
describe and perform
translations.
2. Guided discovery:
move triangle A(1,1),
B(3,1), C(2,4) four units
right and two units up.
1. State objective:
describe reflections
using coordinates.
2. Guided exploration:
plot P(3,4), then
reflect across x-axis
and y-axis.
1. State objective:
describe rotations using
coordinates.
2. Kinesthetic activity:
learners turn 90°, 180°,
and 270° to model
rotation.
1. State objective:
apply coordinates and
transformations.
2. Review
comparison chart:
translation, reflection,
rotation.

number lines
crossing.
3. Discuss x-axis, y-
axis, origin,
quadrants, ordered
pairs.
4. Guided plotting:
(3,2), (-4,1), (-2,-3),
(5,-2).
5. Questions: Which
coordinate tells
left/right? Expected:
x-coordinate. Which
tells up/down?
Expected: y-
coordinate.
6. Pair activity:
“Coordinate Hunt”
plotting points to form
a simple shape.
7. Real-life examples:
classroom seating,
barangay map,
mobile map pin.
8. Check
understanding using
mini-whiteboards/card
s.
9. Processing: Why is
accuracy important
when giving a
location?
3. Questions: What
happened to all x-
coordinates? Expected:
They increased by 4.
What happened to y-
coordinates? Expected:
They increased by 2.
4. Input: (x,y) →
(x+a,y+b).
5. Group activity:
“Barangay Route Slide”
translating points for
house, school, market,
and barangay hall.
6. Differentiated tasks:
A-single points with
arrows; B-polygons; C-
create a real-life
translation problem.
7. Quick drill: “Rule or
Result.”
8. Processing: What
changes during
translation? What does
not change?
3. Questions: Across
x-axis, what happens
to y? Expected: y
changes sign. Across
y-axis, what happens
to x? Expected: x
changes sign.
4. Rules: x-axis
(x,y)→(x,-y); y-axis
(x,y)→(-x,y); origin
(x,y)→(-x,-y).
5. Activity: “Mirror,
Mirror on the Grid.”
Learners reflect
shapes using graph
paper or digital tool.
6. Filipino examples:
puddles after rain,
parol, banig, butterfly
wings, house/church
tile patterns.
7. Group challenge:
explain the rule used.
8. Processing: How
does reflection help
artists/designers
create balanced
patterns?
3. Guided practice: plot
A(2,3), then rotate about
the origin.
4. Rules,
counterclockwise: 90°
(x,y)→(-y,x); 180°→(-x,-
y); 270°→(y,-x).
5. Question: What
happens to the distance
of the point from the
origin? Expected: It
stays the same.
6. Group activity:
“Rotate the Landmark”
using a polygon for
park, basketball court,
or school garden.
7. ICT: GeoGebra,
Desmos, or PPT
animation.
8. Support: tracing
paper, cut-outs, color-
coded formula guide.
9. HOTS: Why is
rotation important in
design, animation, and
engineering?
3. Performance task:
“Design a Community
Map or Game Grid.”
Groups plot at least
four locations, apply
one translation, one
reflection, and one
rotation, and explain
coordinate rules
used.
4. Questions: How did
you know which rule
to use? Which
transformation
changed orientation?
Which only slid the
figure? Expected:
translation slides;
reflection flips;
rotation turns.
5. Gallery walk with
“Glow and Grow”
feedback.
6. Individual quiz:
plotting, identifying
quadrants, applying
transformation rules,
interpreting a
map/grid.
7. Reflection: “How
can coordinate
geometry help us in
real life?”

Learning
Resources
Mathematics 10
Learner’s Module;
DepEd BOW; PPT;
graphing paper; ruler;
pencil; Cartesian
plane poster;
projector/TV; short
video. Emergency:
printed grids,
chalkboard grid, floor
tiles as coordinate
plane, manila paper
grid.
Mathematics 10
Learner’s Module; PPT;
graphing paper; ruler;
translation cards;
projector;
GeoGebra/Desmos if
available. Emergency:
chalkboard grid, printed
worksheets, classroom
floor grid.
Mathematics 10
Learner’s Module;
PPT; graphing paper;
mirror or folded
paper; ruler; reflection
cards;
videos/simulations.
Emergency: paper
folding, manual
graphing, chalkboard
demonstration.
Mathematics 10
Learner’s Module; PPT;
graphing paper; tracing
paper; cut-out shapes;
ruler;
GeoGebra/Desmos/PPT
animation. Emergency:
rotating paper cut-outs,
board demonstration,
partner coaching.
Mathematics 10
Learner’s Module;
activity sheets;
rubrics; quiz sheets;
graphing paper;
manila paper;
markers; projector if
available.
Emergency: paper-
based outputs, oral
presentations, board-
based performance
task.
Opportunities for
Integration
ICT: PPT/video/digital
graphing. Literacy:
coordinate, origin,
quadrant, ordered
pair. Numeracy:
integers, direction,
ordered pairs. Real-
life: maps, seating
plan, mobile location
pins.
ICT:
GeoGebra/Desmos/PP
T animation. Araling
Panlipunan: map
directions. Numeracy:
integer
addition/subtraction.
Values: accuracy and
cooperation.
Arts and Culture:
parol, banig, textile,
and tile patterns. ICT:
reflection simulation.
Literacy: explain rules
in complete
sentences. Inclusivity:
visual, tactile, and
oral response
options.
ICT: rotation animation
or graphing app.
Science/Technology:
wheels, fans, machines,
digital animation. Arts:
rotational symmetry.
Numeracy: coordinate
rules and integer signs.
DRRM/Community
Planning: evacuation
centers and safe
routes. ICT: optional
digital map/game-grid
design.
Communication:
group presentation
and peer feedback.
Values: teamwork
and evidence-based
explanation.
3. ASSESSMENT
2
WEDNESDAY /
Session 3
THURSDAY /
Session 4
FRIDAY / Session 5
Formative
Assessment
Exit ticket: label x-
axis, y-axis, origin,
quadrants; plot two
points; identify
quadrants. HOTS:
Pair worksheet:
translate points and a
simple triangle.
HOTS: If all points
move by the same
Reflection challenge:
reflect a figure across
x-axis, y-axis, and
origin. HOTS: How
can you predict a
Rotation drill and
small-group output:
rotate points/figures
by 90°, 180°, and
270°. HOTS: Why
Performance task,
individual quiz, and
reflection slip. Criteria:
accurate plotting,
correct transformation

Why must coordinates
be written in the
correct order?
Accommodation: large
grid, oral response,
pointing, or peer-
assisted labeling.
Feedback: quick
correction for x/y
switching.
rule, why does the
shape remain
congruent?
Accommodation:
arrows, color-coded
coordinate rules,
guided worksheet.
Feedback: peer check
followed by teacher
clarification.
reflected point without
graphing?
Accommodation:
folded paper, mirror,
sign chart, oral
explanation.
Feedback: immediate
“Check the Sign”
prompts.
does rotation preserve
distance from the
origin?
Accommodation:
tracing paper, cut-
outs, partner
coaching. Feedback:
guided questioning
and error correction.
rules, neatness,
explanation, real-life
connection,
teamwork.
Accommodation:
extended time,
simplified grid,
enlarged print, oral
explanation, peer
support, alternative
task if needed.
Feedback codes: P-
plotting, R-rule, S-
sign, E-explanation.
4. WAYS FORWARD / WRAP-UP
2
WEDNESDAY /
Session 3
THURSDAY /
Session 4
FRIDAY / Session 5
Extended Learning
Opportunities
Learners create a
simple coordinate
map of their
classroom, home
area, or barangay
street and identify at
least five locations
using ordered pairs.
Learners write
directions using
translations, such as
moving from the
classroom to the
canteen on a grid
map. Enrichment:
create a translation
puzzle for a
classmate.
Learners find
examples of reflection
at home or in the
community, such as
tiles, windows,
puddles, logos, parol,
or decorations. They
sketch or describe the
line of reflection.
Learners observe
rotating objects such
as wheels, fans,
clocks, or playground
equipment and
describe the turn
using degrees.
Enrichment: create a
simple rotation art
pattern.
Learners revise their
community map or
game grid based on
feedback.
Remediation: guided
transformation
worksheet.
Enrichment: create a
digital transformation
design using a
graphing tool, if
available.
Reflections Learner engagement:
Did learners actively
plot points? Lesson
effectiveness: Did
Learner engagement:
Did movement and
pair work increase
participation? Lesson
Learner engagement:
Did mirrors/folding
improve
understanding?
Learner engagement:
Did movement/tracing
paper help rotations?
Lesson effectiveness:
Learner engagement:
Which groups
collaborated
creatively? Lesson

they distinguish x from
y? Positive
improvements: note
progress with
negative integers.
Learner interest: Did
map examples
motivate learners?
Support: ask co-
teachers for localized
map examples.
effectiveness: Did
learners apply
translation rules
accurately? Positive
improvements:
identify peer
explainers. Learner
interest: Did barangay
route examples help?
Support: coordinate
with ICT teacher for
offline graphing tools.
Lesson effectiveness:
Were sign changes
clear? Positive
improvements: note
learners who predict
reflected points
mentally. Learner
interest: Did cultural
pattern examples
help? Support:
prepare more visual
aids.
Did learners use
rotation rules
correctly? Positive
improvements:
identify learners who
generalize rotation
patterns. Learner
interest: Did
wheels/fans/animation
examples help?
Support: ask
instructional coach for
spatial reasoning
strategies.
effectiveness: Did
learners combine
directions,
coordinates, and
transformations
correctly? Positive
improvements:
identify learners ready
for enrichment.
Learner interest:
Which real-life
applications did
learners enjoy?
Support: remediate
plotting, signs, and
rules.
HOTS QUESTIONS BANK FOR THE WEEK
Purpose HOTS Question
Analysis How can you determine the quadrant of a point without plotting it first?
Application How can coordinates help locate an evacuation center on a community
map?
Comparison How are translation, reflection, and rotation alike and different?
Evaluation Which transformation would best model a mirror image? Why?
Reasoning Why does a translated or rotated figure keep the same size and shape?
Prediction How can you predict reflected or rotated coordinates without drawing
the figure?
Real-Life Connection How are transformations used in parol designs, floor tiles, mobile
games, maps, and animation?
SAMPLE PERFORMANCE TASK RUBRIC
Criteria 4 – Advanced 3 – Proficient 2 – Developing 1 – Beginning
Accuracy of Coordinates All points are plotted and
labeled correctly.
Most points are plotted
correctly with minor errors.
Some points are correct
but several errors are
present.
Points are mostly incorrect
or incomplete.

Use of Transformation
Rules
Translation, reflection, and
rotation rules are all
correctly applied.
Most transformation rules
are correctly applied.
Some rules are applied
with sign or direction
errors.
Transformation rules are
unclear or incorrect.
Explanation and
Reasoning
Explanation is clear,
logical, and uses correct
mathematical vocabulary.
Explanation is
understandable with minor
gaps.
Explanation is incomplete
or needs prompting.
Explanation is missing or
unclear.
Real-Life Connection Output shows meaningful
and accurate Filipino
community application.
Output includes a relevant
real-life connection.
Real-life connection is
present but weak or
unclear.
No real-life connection is
shown.
Collaboration and
Participation
All members contribute
actively and respectfully.
Most members contribute. Some members contribute;
group needs support.
Minimal collaboration is
observed.
Prepared by:
JERSON A. NATURAL
Mathematics 10 Teacher
Checked by:
EFREN B. ALCOVENDAS JR.
Principal II

Comprehensive Grade 10 Mathematics: Cartesian Plane and Geometric Transformations

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