Comprehensive Grade 10 Mathematics Lesson on Quadratic Inequalities in One Variable

Mathematics 10 - Quadratic Inequalities in One Variable | Grade 10 - Galilei
Mathematics 10
Topic: Quadratic Inequalities in One Variable
Lesson Details
Lesson Title Solving and Illustrating Quadratic Inequalities in One Variable
Learning Area/s Mathematics
Name of Teacher/s JERSON NATURAL
Grade Level and Section Grade 10 - Galilei
No. of Sessions 5 Sessions
Topic Quadratic Inequalities in One Variable
Learning Competency Illustrate on the number line quadratic inequalities in one variable.
Solve quadratic inequalities in one variable and express solutions in various notations.
References Mathematics 10 Learner's Module; DepEd Budget of Work; teacher-prepared PowerPoint presentation; teacher-
selected instructional videos; GeoGebra/Desmos graphing tools; MATATAG Curriculum guidance.
Teaching Strategy Inquiry-based learning, collaborative activities, multimedia integration, interactive discussion, differentiated
instruction, and formative assessment. These strategies support varied readiness, numeracy, reasoning, and
inclusive participation.
Declaration of AI use AI was used to assist in drafting this lesson plan, organizing activities, generating differentiated tasks, creating
HOTS questions, and aligning the plan with the uploaded DepEd 2026 lesson plan template. The teacher
reviewed, revised, contextualized, and takes full professional responsibility for the final lesson plan. This supports
transparency in accordance with DepEd Order No. 003, s. 2026 on the foundational guidelines for AI in basic
education.

1. Intentions
Meaningful learning experiences are anchored in clear competencies, objectives, and learner context.
Component MONDAY / Session 1 TUESDAY / Session 2 WEDNESDAY / Session 3 THURSDAY / Session 4 FRIDAY / Session 5
Learning
Competency
and
Curriculum
Standards
Learning Competency:
Illustrate on the number
line quadratic
inequalities in one
variable.
Focus: Review of
quadratic equations,
roots/zeros, factors, and
intervals.
Illustrate on the number
line quadratic
inequalities in one
variable.
Focus: Determine critical
numbers and use sign
analysis.
Solve quadratic
inequalities in one
variable and express
solutions in various
notations.
Focus: Solve quadratic
inequalities using
factoring and number
line testing.
Solve quadratic
inequalities in one
variable and express
solutions in various
notations.
Focus: Express solution
sets using inequality
notation, interval
notation, and set-builder
notation.
Illustrate and solve
quadratic inequalities in
one variable and
express solutions in
various notations.
Focus: Real-life
applications,
performance task,
synthesis, and reflection.
Learning
Objectives
Knowledge: Recall the
relationship among
factors, roots, zeros, and
x-intercepts of a
quadratic expression.
Skills: Identify critical
numbers from a
factored quadratic
expression.
Understanding: Explain
why the roots divide the
number line into
intervals.
Knowledge: Define
quadratic inequality
and critical numbers.
Skills: Construct a sign
chart and test intervals.
how signs of a quadratic
expression determine
the solution set.
Knowledge: Identify
whether boundary
points are included or
excluded based on the
inequality symbol.
Skills: Solve quadratic
inequalities by factoring
and testing intervals.
Understanding: Justify
the solution set using
mathematical
reasoning.
Knowledge:
Differentiate inequality
notation, interval
notation, and set-builder
notation.
Skills: Convert solution
sets from number line
form to different
notations.
Understanding:
Communicate
mathematical solutions
clearly and accurately.
Knowledge: Recognize
real-life situations that
may be modeled by
quadratic inequalities.
Skills: Solve and interpret
a quadratic inequality in
context.
how quadratic
inequalities help in
decision-making in real-
life situations.
Learner
Context
Grade 10 - Galilei
learners are expected
to have prior knowledge
of linear inequalities,
factoring trinomials,
Learners may find sign
testing abstract, so
visual support through
number lines, color-
coded intervals, and
Learners are expected
to demonstrate gradual
independence. Some
may still confuse greater
than and less than
Learners may need
literacy support in
reading and writing set-
builder notation.
Teacher will model
Learners will connect the
lesson to Filipino real-life
contexts such as school
fairs, sari-sari store profit,
basketball shooting

solving quadratic
equations, and
graphing on a number
line. Some learners may
be confident in
factoring but may need
support in interpreting
inequality symbols and
interval notation.
Learners may enjoy
interactive board work,
group problem-solving,
and digital graphing
tools.
ICT-based graphing will
be provided.
Collaborative peer
support will help learners
who need scaffolding.
Learners with difficulty in
computation may use
guided worksheets with
step-by-step prompts.
regions on the number
line. Differentiated tasks
will be given: basic,
guided, and challenge
levels. Learners may
respond orally, visually,
or in writing.
mathematical
language in simple
terms. Pair activities will
allow learners to explain
solutions using Filipino-
English mathematical
language where
appropriate.
height, garden fencing,
and barangay project
budgeting. The session
will support confidence,
communication,
collaboration, and
reflection.
2. Learning Experience
A thoughtfully designed learning journey uses interaction, collaboration, inquiry, and reflection to build understanding.
A. Pre-Lesson Prayer and Routine:
Begin with a short
prayer or moment of
silence. Check
attendance, classroom
cleanliness, and
readiness of materials.
Classroom
Management: Math kit
check: notebook, pen,
calculator if allowed,
and worksheet.
Review: Ask: How do we
solve x^2 - 5x + 6 = 0?
Expected: Factor as (x -
2)(x - 3) = 0; x = 2 or x =
Prayer and Routine:
Begin with prayer or
mindfulness breathing.
Check attendance and
seating groups.
Review: Mini drill:
Identify roots of x^2 - 7x
+ 10 = 0. Expected: x = 2
and x = 5.
Motivation: Show a
number line with roots 2
and 5. Ask what
happens before 2,
between 2 and 5, and
after 5.
Lesson Introduction:
Prayer and Routine: Start
with prayer and class
norms: Listen, Try, Ask,
Help.
Review: If the inequality
is >= or <=, boundary
points are included.
Motivation: A barangay
basketball league wants
the ball height above a
safety marker. How can
inequality help?
Learners solve complete
quadratic inequalities
step by step.
Prayer and Routine:
Begin with prayer,
attendance, and quick
readiness check.
Review: Learners identify
the correct number line
for x < -1 or x > 4.
Motivation: Display x < -1
or x > 4, (-infinity, -1)
union (4, infinity), and {x |
x < -1 or x > 4}. Ask why
mathematicians use
different notations.
Learners practice
communicating solutions
Prayer and Routine:
Begin with prayer or
reflection. Check
attendance and group
arrangement.
Review: Ask the steps in
solving a quadratic
inequality. Expected:
Move all terms to one
side, factor, find roots,
test intervals, select
solution, write notation.
Motivation: Present a
school fundraising
booth or sari-sari store
profit problem.

3.
Motivation: A school
booth earns profit
depending on tickets
sold. When is the profit
positive?
Lesson Introduction: This
week, learners solve
when expressions are
greater than, less than,
at least, or at most zero.
Introduce sign analysis
as a method for solving
in different mathematical
forms.
Learners apply
quadratic inequalities to
real-life situations and
present solutions.
B. Flow 1. Clarify Objectives:
Teacher says, Today,
you will identify roots
and explain why they
divide the number line
into intervals.
2. Guided Review: Solve
x^2 - 5x + 6 = 0 as a
class. Connect roots 2
and 3 to number line
points.
Teacher Question: Why
are x = 2 and x = 3
important? Expected:
They make the
expression zero.
3. Inquiry Activity - Zero
Points Matter: In pairs,
learners substitute x-
values before,
between, and after 2
and 3 into x^2 - 5x + 6.
They observe whether
1. Clarify Objectives:
Today, you will create a
sign chart and use it to
identify solution
intervals.
2. Teacher Modeling:
Use (x - 2)(x - 5). Identify
critical numbers 2 and
5. Create intervals x < 2,
2 < x < 5, and x > 5.
Teacher Question: What
test value can we use in
each interval?
Expected: Any number
in that interval, like 0, 3,
and 6.
3. Interactive Activity -
Human Number Line:
Learners hold cards -1,
0, 2, 3, 5, 6 and stand
along a number line.
The class decides which
intervals are positive or
Today, you will solve
quadratic inequalities
and justify your answer.
2. Step-by-Step Method:
Write inequality with zero
on one side; factor; find
critical numbers; test
intervals; choose
intervals; write and
illustrate the solution.
3. Guided Example:
Solve x^2 - 5x + 6 > 0.
Factor: (x - 2)(x - 3) > 0.
Critical numbers: 2 and
3. Test intervals. Solution:
x < 2 or x > 3.
Teacher Question: Why
are 2 and 3 not
included? Expected:
Because the symbol is >,
not >=.
Today, you will express
solutions in inequality,
interval, set-builder, and
number line forms.
2. Mini-Lesson on
Notations: x < 2 or x > 3; (-
infinity, 2) union (3,
infinity); {x | x < 2 or x >
3}.
does the open circle
mean? Expected: The
endpoint is not included.
3. Matching Activity:
Learners match number
lines, inequality notation,
interval notation, and
set-builder notation
cards.
4. ICT Integration: Use
Desmos or GeoGebra to
Today, you will apply
quadratic inequalities to
real-life situations and
present your reasoning.
2. Real-Life Filipino
Context Problem: A
Grade 10 class plans a
mini food booth. Profit in
pesos can be modeled
by P(x) = -x^2 + 50x -
400, where x is food
packs sold. For what
values of x will the class
earn at least PHP 200?
3. Guided
Interpretation: Form -
x^2 + 50x - 400 >= 200,
then solve -x^2 + 50x -
600 >= 0.
does the solution mean
in real life? Expected: It

the result is positive,
zero, or negative.
4. Group Processing:
What pattern do you
notice? Expected: The
sign changes across the
roots.
5. HOTS Question: If a
quadratic has two roots,
will the signs always
alternate across
intervals? Why or why
not?
6. Inclusivity Support:
Use color-coded
number lines: green
positive, red negative,
blue zero. Allow oral
explanation for learners
who struggle with
written responses.
negative.
4. Collaborative Work:
Groups solve sign charts
for (x - 1)(x - 4), (x + 2)(x -
3), and x^2 - x - 6.
5. Processing Questions:
How did you choose
test values? Why are
the roots called
boundary points?
6. HOTS Question: Can
two different test values
in the same interval give
different signs? Explain.
7. Differentiation: Basic
group: factored
expressions. Guided
group: partially
completed sign charts.
Challenge group:
unfactored quadratic
expressions.
4. Group Work - Solve
and Defend: Group 1:
x^2 - 4x + 3 < 0; Group 2:
x^2 + x - 6 >= 0; Group 3:
x^2 - 9 <= 0; Group 4:
x^2 - 2x - 8 > 0.
5. Gallery Walk: Groups
post solutions. Learners
leave sticky-note
feedback: I agree
because... or Please
clarify...
6. HOTS Question: How
would the solution
change if > became
>=? What mathematical
idea changes?
show where y = x^2 - 5x +
6 is above or below the x-
axis. Compare graph
results with number line
solutions.
5. Collaborative Task -
Notation Relay: Groups
rotate through stations:
solve inequality, draw
number line, write
interval notation, write
set-builder notation.
6. HOTS Question: Which
notation is most useful for
explaining the answer to
a non-math person?
Why?
7. Inclusivity Support:
Provide notation guide
cards. Allow Filipino or
mixed Filipino-English
explanations before
formal mathematical
notation.
tells the number of
packs that must be sold
to reach at least PHP
200 profit.
4. Performance Task -
Math in Real Life:
Groups choose one
context: sari-sari store
income, basketball ball
height, garden area,
school fair booth, or
barangay clean-up
budget. They solve the
quadratic inequality
and present three
notations.
5. Processing Questions:
How did mathematics
help you make a
decision? What
mistakes should we
avoid when interpreting
answers?
6. HOTS Question: Why
might some
mathematical solutions
not be reasonable in
real life?
7. Reflection: One thing
I understand now is...
One thing I still need
help with is...
C. Learning
Resources
PowerPoint slides;
Mathematics 10
PowerPoint; printed sign
chart templates;
PowerPoint; activity
worksheets; sticky notes;
Desmos or GeoGebra;
projector/TV; notation
Performance task
sheets; rubric; real-life

Learner's Module;
whiteboard; number
line strips; colored
markers; activity cards;
worksheets; projector or
TV.
Emergency Alternatives:
Manila paper,
chalkboard number
line, printed sheets, peer
tutoring cards.
number cards; masking
tape for human number
line; calculators if
permitted; teacher-
made worksheet.
Chalkboard sign chart;
improvised paper
number cards; oral
group reporting.
Manila paper; colored
pens; Mathematics 10
Learner's Module;
optional video clip on
Board work, seatwork,
peer checker system.
matching cards;
PowerPoint; printed
notation guide; graph
paper.
Teacher-drawn graphs;
printed screenshots;
number line templates.
problem cards; Manila
paper; markers;
calculator if allowed;
mobile phone or laptop
for graph checking if
available.
Printed contextual
problems; oral
presentation; paper-
based number line.
D.
Opportunities
for
Integration
Numeracy: Factoring,
roots, intervals, sign
reasoning.
Literacy: Learners
explain mathematical
observations in
complete sentences.
Values: Patience and
accuracy in problem-
solving.
ICT: Optional use of
presentation slides and
digital number line.
Collaboration: Human
number line promotes
peer learning.
Inclusivity: Supports
visual, kinesthetic, and
auditory learners.
Communication:
Learners defend
solutions using
mathematical
reasoning.
PPST Link: Supports
content knowledge,
HOTS, learner-centered
strategies, differentiated
learning, and formative
assessment.
Technology:
Desmos/GeoGebra
graphing.
Literacy: Translating
solutions across
mathematical
representations.
Inclusivity: Multiple
response formats: oral,
written, visual.
Real-Life Filipino
Contexts: Sari-sari store,
school booth,
basketball, garden
planning, barangay
projects.
Values and Financial
Literacy: Decision-
making, budgeting,
and responsible
planning.
3. Assessment
Assessments reveal what learners have gained and what support they still need.
A.
Formative
Assessment
Exit Ticket: 1. Find the
roots of x^2 - 4x + 3 = 0.
2. Plot the roots on a
number line. 3. Explain
why these roots are
important.
Accommodation:
Quick Check: Complete
a sign chart for (x - 1)(x -
4).
Peer Assessment: Pair-
check using answer key
projected on screen.
Accommodation:
5-Item Mini Quiz: 1. Solve
x^2 - 4x + 3 < 0. 2. Solve
x^2 + x - 6 >= 0. 3.
Identify critical numbers
of x^2 - 9 <= 0. 4. Explain
whether endpoints are
included in <=. 5. Draw
Notation Check:
Learners convert one
solution set into three
forms: number line,
interval notation, and
set-builder notation.
Collaborative
Performance-Based
Assessment: Group
solves a contextual
quadratic inequality and
presents: mathematical
model, solution process,
number line, interval

Learners may answer
using a drawing, verbal
explanation, or guided
sentence starter.
Feedback Strategy:
Teacher marks responses
with: Correct, Needs
explanation, Good
reasoning.
Provide pre-drawn
number lines and test-
value choices for
learners needing
support.
Feedback Strategy:
Teacher conducts quick
conferencing with
groups showing
confusion.
the number line solution
for x < -2 or x > 3.
Accommodation:
Learners may use a sign-
chart template.
Feedback Strategy: Use
correct-and-explain
feedback rather than
simply marking wrong.
Assessment: Group
notation relay output.
Accommodation:
Provide notation guide
and allow oral
explanation before
written output.
Feedback Strategy:
Teacher gives
immediate corrective
prompts: Check your
endpoint; Use
parenthesis or bracket
correctly; What does the
symbol mean?
notation, real-life
interpretation.
Rubric Criteria:
Accuracy 40%;
Explanation 25%;
Representation 20%;
Collaboration 15%.
Accommodation:
Learners may present
through oral
explanation, poster,
written solution, or digital
slide.
Feedback Strategy:
Teacher uses Glow and
Grow: one strength and
one area for
improvement.
4. Ways Forward / Wrap-Up
Meaningful learning can happen beyond classroom hours and through teacher reflection.
A. Extended
Learning
Opportunities
Home Task: Find the
roots of three quadratic
expressions and plot
them on number lines.
Enrichment: Observe
where a parabola
crosses the x-axis using a
graphing app if
available.
Home Task: Create a
sign chart for two
factored quadratic
expressions.
Support Task: Watch
teacher-approved
video on sign charts or
review printed guide.
Home Task: Solve three
quadratic inequalities:
one using <, one using >,
and one using >= or <=.
Enrichment: Create a
short explanation video
or written guide titled
How to Solve Quadratic
Inequalities.
Home Task: Convert five
solution sets into interval
and set-builder notation.
Real-Life Link: Identify
one situation at home or
in the community where
a range of values
matters.
Home Task / Enrichment:
Create one original real-
life problem involving a
quadratic inequality.
Include solution and
interpretation.
Support Task: Learners
who need remediation
may complete a guided
worksheet with step-by-
step hints.

B. Reflections Learner Engagement:
Did learners actively
participate in identifying
roots and intervals?
Lesson Effectiveness:
Were learners able to
connect quadratic
equations to quadratic
inequalities?
Positive Improvements:
Use more visual number
lines if learners struggled.
Learner Interest: Note if
learners responded well
to profit or school booth
examples.
Support Needed: Ask
math co-teacher for
additional remediation
materials on factoring if
needed.
Learner Engagement:
Did the human number
line help learners
understand intervals?
correctly select test
values?
Provide more guided
sign-chart practice for
learners needing
support.
Learner Interest:
Observe which learners
enjoyed movement-
based activities.
Support Needed:
Consult ICT coordinator
if digital tools are
needed for the next
lesson.
Learner Engagement:
Did group work
encourage participation
from quiet learners?
Lesson Effectiveness: Did
learners justify why
endpoints are included
or excluded?
Strengthen explanation
of inequality symbols if
errors persist.
real-life basketball or
barangay examples
increased attention.
Support Needed:
Coordinate with adviser
for learners needing
extra support.
Learner Engagement:
match notations
accurately?
Lesson Effectiveness: Did
learners understand the
meaning of
parentheses, brackets,
and union symbol?
Prepare more notation
drills.
graphing technology
improved
understanding.
Support Needed: Ask
instructional coach for
strategies in teaching
mathematical
language.
Learner Engagement:
Did learners participate
meaningfully in the
performance task?
interpret mathematical
solutions in context?
Use more localized
problems in future
lessons.
Learner Interest: Identify
which real-life contexts
learners found most
meaningful.
Support Needed: Share
outputs with co-
teachers for possible
integration with TLE,
Economics, or Science.
Prepared by:
JERSON A. NATURAL
Mathematics Teacher Checked by:
EFREN B. ALCOVENDAS JR.
Principal II

Comprehensive Grade 10 Mathematics Lesson on Quadratic Inequalities in One Variable

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