Detailed Lesson Plan
In
Mathematics 7
I.
Objectives:
At the end of the lesson, the students should be able to:
a. Define point, line, and plane
b. Differentiate collinear from non-collinear points; coplanar from non-coplanar
points; and
c. Represent point, line, and plane using concrete and pictorial models (M7GEIIIa-1)
II.
Subject Matter:
A. Topic: Points, Lines and Planes
B. Reference: Tarepe, D.A and Evelyn Zara, Practical Mathematics. Lipa
City:United Eferza Academic Publications Co, 2012. pp. 277- 282
Orines, F.B et al. Next century mathematics.
Quezon City: Phoenix Publishing House Inc. 2012. pp. 378-380
Evelyn Zara, Practical mathematics teacher’s manual.
Lipa City: United Eferza Academic Publications Co, 2012. pp. 89- 91
C. Materials: PowerPoint Presentation, Charts, Cut-outs
D. Value: Cooperation
III.
Procedure:
Teachers Activity
Students Activity
A. Preliminary
Good morning, Class!
Good morning, Ma’am!
Before anything else let us put ourselves
in the presence of the Lord. May I request
Merly to please lead us with a prayer.
(Merly leads the class with the
prayer)
Before we formally begin our discussion
for today, let’s have a short activity.
Are you ready, class?
Yes ma’am.
B. Motivation
I will be showing you pictures of
the two magnificent buildings
found around the world and
observe. These are Egypt’s Great
Pyramid and India’s Taj Mahal.
Let us try to depict or understand
how or what is the concept of this
buildings.
Base on your observation, what do
you think did the architect used in
designing the building? And what
do you think he consider in
creating such attractive patterns
(The students will give their
observation/ideas about the picture)
Your ideas are amazing, class. You
have shown how well you can
observe even the tiniest details
C. Presentation
The activity has something to do
with our lesson for today. What
you have cited are applications of
Geometry. Let us now then define
what is Geometry.
D. Discussion
Geometry is a branch of
mathematics that studies the sizes,
shapes, position, angles, dimension
of things and the knowledge
dealing with spatial relationship. It
came from the Ancient Greek
words, “geo” meaning “earth”
and “-metrein” mean to measure.
Geometry, just like any other
mathematical system is based on
undefined terms, unproven
statements (postulates and
assumptions) and theorems. In any
mathematical system, definitions
are important. All elements and
objects must be defined precisely.
However, there are some terms or
objects that are the primitive
building blocks of the system and
hence cannot be defined
independently of other objects.
The undefined terms in geometry
are point, line, and plane. Even
though this term are left undefined,
they used together with ordinary
words to define other geometric
terms. Space, for example, is
defined as set of all points.
Try to close your eyes and imagine
that you are star gazing. Then open
your eyes. How do the stars in the
sky look like?
(The students will close their eyes and
imagine the given situation)
Yes, Jocel?
They look like dots, ma’am
Very Good! They look like dots
sparkling in the sky, right? Those
dots represent points.
Now, what is a point?
A point has no size and no dimension
Yes, Jecris?
Yes, you are correct. A point is a
location that has no size and no
dimension- no length, no width, no
height, and no thickness. It could
be represented by a dot (period), a
speck or even a grain of sand.
A point is named by using a capital
letter. With the dice I gave you,
can you name all the points you
can see there? I’ll give you a
minute to do that.
Example 1:
Yes, ma’am
Yes, ma’am
A constellation
Were you able to understand,
class?
A line, ma’am
Now, let us close our eyes and
imagine again the night sky. The
stars represent the points, right?
How about If we try to connect it?
What would it look like?
Okay, correct! Now, what did we
use to connect the points?
Very good! A line is a set of points
arranged in a row. It is a onedimensional figure that extends
endlessly in both directions.
For example:
Line m
m
Students will give examples of a line.
Answers may vary
Line IG
I
G
The second figure is called line IG since it
has two points in it therefore we name it
line IG,
Can you give real life examples of
a line?
Yes, ma’am
Students will describe the bond paper.
Answers may vary
Very good class, do you
understand what line is?
We then proceed. I have here a
bond paper. Can you describe this?
Very good, class. Now a bond
paper is an example of a plane.
Plane extends without end. You
can name a plane by either a
single capital letter or by at
least three of its non-collinear
points (points which are not on the
same line)
For example,
Yes, ma’am.
This is an example of a plane, it is
called plane PQR. Since it consists
of 3 points that are not on the same
line. Do you get it, class?
Now that we have mentioned noncollinear points in defining the
plane. There are 4 types of points.
This are Collinear and NonCollinear points and Coplanar and
Non-Coplanar points.
Collinear points are points that lie
on the same line, while noncollinear points do not lie on the
same line.
For example, consider this set of
points
H
I
R
(Student’s raises hand)
They line on the same line
They are collinear points
S
Where do points I, R and S lie?
Yes, (student’s name)
No, ma’am
(Student raises hand)
Because, line H does not lie on the
line.
Therefore?
It is a non-collinear point.
Very good, how about point H, is
point H collinear with the other
three points?
Yes, ma’am
How do you say, so?
What can you conclude then about
point H?
Very good! Do you understand
what collinear and non-collinear
points is?
We, then, proceed now to
Coplanar and Non-coplanar points.
Now, these points are just the same
with Collinear and Non-Collinear
only that this point are found on a
plane.
Therefore, Coplanar points are
points found on the same plane
while Non-Coplanar points do not
lie on the same plane.
For example,
(Students raises hands)
Points A, B, C, and D are coplanar,
while points F and E are noncoplanar.
The figure above shows a plane,
containing points A, B, C, D, E, F.
Can someone identify what are the
coplanar and non-coplanar points?
It is because points A,B,C, and D lies
on the same plane while points F and
E does not lie on the plane.
Yes, (student’s name)
Yes, ma’am.
How do you say so?
Very good, class. Were you able to
understand our lesson for today?
E. Application
However, let us try to see whether
you have really mastered our
lesson for today. You will be
grouped into 4. We will do the
grouping by count of.
Your task is to be an aspiring
architect or designer. You have to
make a sketch and design a cabinet
or divider for the sala set of your
teacher. Your design should show
points, lines and planes. So, I
expect you to be creative. You are
given 15 minutes to do the activity,
afterwards you pick on
representative of your group to
present your work in front of the
class.
Teachers and students create 4
groups.
Your work will be graded by the
following rubric:
Any clarifications for the activity?
If none, then proceed to your
respective groups.
A point is a specific location that has
no size and no dimension.
F. Generalization
A line is of infinite length but it has
You have shown expended mastery of no width, or no thickness.
our lesson for today. Let’s recall,
a. What is a point?
A plane is a flat surface that has no
thickness.
b. What is a line?
c. What is a plane?
Collinear points are points that lie on
the same line while non-collinear
points are points that do not lie on the
same line.
d. Differentiate collinear and Points are said to be coplanar if they
non-collinear points.
lie on the same plane while noncoplanar points do not lie on the same
plane.
e. Differentiate coplanar and
non-coplanar points.
IV. Evaluation
A. Knowledge: Name me!
Identify what is asked on the following:
1. It is a flat surface that extends infinitely in all directions.
2.
3.
4.
5.
Points that lie on the same line.
It is a specific location in space that has no dimensions.
Points that lie on the same plane.
It is of infinite length but it is no width and no thickness.
B. Process
Tell whether each represents a point, a line or a plane.
1. Your desktop
2. The surface of the page of a notebook.
3. The string on a guitar.
4. The ceiling of a room.
5. A broomstick.
6. Electric wire.
7. The floor.
8. A hair strand.
9. A rope.
10. A needle point.
C. Understanding
Draw and describe the intersection of the following:
A. intersection of two lines
B. intersection of two planes
C. intersection of a line and a plane
V.Assignment
Research on the following:
1. Postulate about points, lines, and planes.
2. Postulate about intersection of lines and planes.