SUBJECT
GRADE
LEARNING UNIT
MATHEMATICS
10th
DISCOVER NEW SHAPES AND
USE THE CARTESIAN PLANE.
TITLE OF LEARNING
OBJECT
TO IDENTIFY CONIC SECTIONS IN EVERYDAY OBJECTS.
CURRICULAR AXIS
STANDARD
COMPETENCIES
Spatial thinking and geometric systems.
To identify the characteristics and properties of conic shapes
(ellipses, parabolas, hyperbolas) and use their properties in
problem solving.
To describe conic sections based on the shapes generated from
the intersection of a cone with a specific plane.
1. To identify characteristics of conic sections.
2. To describe a cone based on activities with solid materials.
3. To recognize the circumference as a conic section from
activities with solid material.
4. To identify elliptic shapes in the surrounding environment,
determining that said shape is obtained by cutting a cone.
5. To identify parabolic shapes in the surrounding
environment, determining that said shape is obtained by
cutting a cone.
6. To identify hyperbolic shapes in the surrounding
environment, determining that said shape is obtained by
cutting a cone.
7. To recognize modified conics from activities with solid
materials.
To describe how conic section research began in history.
1. SCO: Establishes characteristics of conic sections
1.1. Identifies a conic section
1.2. Researches historical processes of conic sections and their
uses
1.3. Creates models of cones, cylinders and spheres of different
sizes
1.4. Determines the relation of transversal cuts in cones and
cylinders with conic sections
1.5. Simulates transversal cuts in cones and cylinders using
technology tools
1.6. Builds graphic representations of conic sections in origami
1.7. Generates artistic tridimensional compositions of conic
sections
LEARNING OBJECTIVES
SKILLS/ KNOWLEDGE
2. SCO: Characterizes a cone.
2.1. Identifies cone-shaped elements in his or her surroundings
2.2. Characterizes a cone as a geometric object and identifies
each one of its elements
2.3. Recognizes how a cone is formed originating from a straight
line which crosses a fixed point and moves along the
circumference of a circle.
2.4. Distinguishes a double cone from a single cone.
3. SCO: Recognizes a circumference.
3.1. Builds cones from solid material and identifies the figures
generated when cutting it through a perpendicular plane to
the edge of the cone.
3.2. Recognizes the circumference as the figure obtained when
cutting a cone through a perpendicular plane to the edge of
the cone.
3.3. Identifies the shape of the circumference in everyday
objects such as celestial bodies, decorations, instruments,
among others.
3.4. Identifies the circular shape generated from a lighted space
using lanterns.
3.5. Represents with drawings the figure obtained when cutting
a cone with a perpendicular plane to the axis.
4. SCO: Recognizes an ellipse.
4.1. Builds cones with solid materials and identifies the resulting
figure when cutting it with an oblique plane to the edge
that cuts the generatrix.
4.2. Represents with drawings the figure obtained when cutting
a cone with an oblique plane to the edge and cuts all the
generatrixes.
4.3. Recognizes the ellipse as the figure obtained when cutting a
cone with an oblique plane to the edge and cuts all the
generatrixes.
4.4. Identifies ellipse-shaped objects present in nature, arts,
and everyday-use instruments.
4.5. Identifies the elliptic shape formed by light from lanterns.
6. SCO: Recognizes the parabola
6.1. Builds cones with solid materials and identifies the figure
obtained when cutting it with a plane parallel to the axis
6.2. Represents with drawings the figure obtained when cutting
a cone with a plane parallel to the axis.
6.3. Recognizes the hyperbola as the figure obtained when
cutting a cone with a plane parallel to the axis.
6.4. Identifies objects with hyperbolic shapes present in nature,
mechanics, arts and everyday-use instruments.
6.5. Identifies the hyperbolic shape created from the light of a
lantern.
7. SCO: Identifies the conics modified by cuts.
7.1. Build cones and identifies how a secant plane would cut a
cone to obtain a dot.
7.2. Builds cones and identifies how a secant plane would cut a
cone to obtain two intersecting lines.
7.3. Builds cones and identifies how a secant plane would cut a
cone to obtain a straight line.
LEARNING FLOW
ASSESSMENT
GUIDELINE
Stage
Introduction
Learning
flow
Introduction
8. SCO: Recognizes some historical events in the study of conic
sections.
8.1. Recognizes what problem in history of mathematics
originated the study of conics.
8.2. Identifies some of the processes that developed the
pioneers of conics studies and describes them.
Identifies the uses that conic sections had in some historical
events.
Introduction.
Objectives. The teacher introduces the objectives and suggests
new ones, if needed.
Activities:
Activity 1. Learning the history of conic sections.
Activity 2. Conic Sections.
Activity 3. Construction with solid material.
Activity 4. Conics in our environment.
Abstract
Homework
Evaluation
Vocabulary box
Bibliography
English review topic
With the development of the following LO, the student will be
able to identify and describe conic sections in his or her
environment. Furthermore, he or she will be able to characterize
each one of them based on the transversal intersection of a plane
with a conic section or cylinder, using different methods such as
using pencil and paper, hand work with origami and solid
materials.
Teaching/Learning Activities
Recommended
Resources
Multimedia support,
With the aid of the platform, share the platform resources.
suggested animation regarding conic
sections in real life.
Suggestion: Ask some
situations in which the
Ask the students if they know the name of students think conic
some of the geometric figures shown in sections may appear.
the images.
Development
Activity 1: Learning the history of Platform resources for
conic sections
the explication of the
The
teacher
material.
presents the Show the suggested video. Then share
topic
with the students which are the principal Printable resource.
pioneers of conic sections as well as the
contribution of each one of them.
Present the activity related to the study
of the two classic problems that
originated research of conic sections.
Finally, the activity suggests the
completion of two learning points. The
first one is based on the video, and for
this, the student must create a timeline
with the information of the video. For
the second activity, the student must
research what was the second classic
problem that originated research of
conic sections.
Activity 2. Conic Sections
Support
Present the introductory infographic where (images)
how a conic surface and its principal platform.
elements are created is explained.
material
in
the
With the aid of the platform resource,
cover the different types of intersections Printable resource.
that can be done to a cone and a cylinder
with a plane, which will generate each
type of conics (circumference, ellipse,
parabola,
hyperbola)
as
well
as
degenerate conics (dots, lines)
Show the conic sections based from the
intersection of the plane with a conic
surface.
Suggested activity where the objective is
that the student identifies each one of the
conics, through association of the
intersection of a plane with a cone and the
type of conic section it generates.
Finally, a table in which the students can
see the results of the intersection of a
plane with a cylinder, and the student
must suggest the resulting conic, as well
as completing the sentences.
material
Activity 3. Construction with solid Support
(images)
in
the
material
platform.
Guide this activity with help from the
platform. In it, the construction of conics
using origami, clay, lanterns and
Printable resource.
mathematical software is covered.
The suggested learning activity presents
the construction of conic surfaces, using
clay and an acetate sheet that serves as a
plane. The resulting figures must be
stored for an artistic display later on.
Activity 4. Conics in our environment
Support
material
(images)
in
the
Present the images to the students,
platform.
encouraging them to identify the conics he
or she sees. After covering the rest of the
unit, the results should be much better in
comparison to the beginning of the
Printable resource.
chapter.
Suggest the activity using lanterns or
flashlights. If needed, ask for assistance to
the physics or mathematics teachers.
Abstract
Assignment/
homework
Share the annexed diagram in this file that Printable resource.
show the summary of the contents.
Activity 1.
Suggest that, in pairs, the students solve
two activities.
1. Search elements with the shape of
conic sections, take a picture and
classify them according to each
type.
2. Generate an artistic tridimensional
display with the figures created
during the previous activity.
Evaluation
Glossary
Vocabulary
box
Bibliography
Evaluation:
Platform resource.
Perform the evaluation that contains three
types of questions: multiple choice with
unique answer, fill in the blanks with the
appropriate word or words and TRUE or
FALSE.
The following words are defined: Conic Printable resource.
Section,
Generatrix,
Circumference,
Ellipse, Parabola and Hyperbola.

Circumference: Originated when a
plane cuts a conic surface
horizontally.
 Ellipse: Obtained when the plane is
slightly inclined or oblique, and cuts
a conic surface.
 Generatrix: Straight line that spins
on an axis to create a surface.
 Hyperbola: Intersection of a vertical
plane to a generatrix of a conic
surface.
 Parabola:
Product
of
the
intersection of a parallel plane to a
generatrix of a conic surface.
 Conic section: Intersection of a
conic surface with a plane.
Alegría,
P.
(2012).
Las
cónicascónicas
y
sus
aaplicaciones. Retrieved from:
http://www.ehu.eus/~mtpalez
p/conicas.pdf
Sorando,
J.
(2013).
Cónicas.
Retrived
from:
http://catedu.es/matematicas_
mundo/FOTOGRAFIAS/fotografi
a_conicas.htm
Stern, D. (2012). Las tres leyes de
Kepler.
Retrieved
from:
http://www.phy6.org/stargaze
/Mkepl3laws.htm
Universo
Arquitectura.
(s.f.).
Retrieved
from:
http://www.universoarquitectu
ra.com/the-apeiron-en-dubai/
English
review topic
Villaseco,
T.
(2013).
Cónicas.
Retrieved
from:
https://www.emaze.com/@ACRTCLZ
I/conicas
Past Narrative Tenses (Past Simple,
Past Perfect and Past Continuous)
Annexed 1. Conceptual Map Abstrac