SUBJECT
GRADE
9TH GRADE
MATH
LEARNING UNIT
DISCOVER MEASUREMENTS
BASED ON GEOMETRICAL SHAPE
TITLE OF LEARNING
OBJECT
To solve problems related with cylindrical shapes.
CURRICULAR AXIS
STANDARD
COMPETENCIES
Spatial thinking, numerical reasoning.
 Establish valid calculation procedures to find the area of flat
sections and the volume of solid objects.
 Select and use methods and instruments to measure lengths,
surface areas, volumes and angles with appropriate precision.
 To develop problem solution processes related to shape, surface
area and volume of cylinders.
 To recognize cylindrical shapes based on the elements that form
them.
 To characterize elements with cylindrical shape based on the
surface area.
 To characterize cylindrical objects based on its volume.
SCO: Describes cylindrical shapes present in their surroundings.
LEARNING OBJECTIVES
SKILLS/ KNOWLEDGE
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Identifies the lateral face, the bases and the height of a
cylinder.
Builds the concept of a cylinder.
Recognizes the shape of an oblique cylinder
Identifies the difference between a right cylinder and an
oblique cylinder
Recognizes cylindric sections.
SCO: Recognizes the area of the surface of cylinders.
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Recognizes the figures that make up the surface of a cylinder.
Calculates the area of the bases of a cylinder.
Calculates the area of the lateral face of a cylinder.
Calculates the total area of the surface of a cylinder.
Builds cylinders from the area measurements of the surface.
Finds the expense of material in the construction of a cylinder
by identifying the surface area.
Identifies the figures contained in the surface of oblique
cylinders.
Expresses and supports procedures and strategies for area
calculation.
Recognizes the figures contained in the surface of right
cylinders.
SCO: Recognizes the volume of a cylinder.
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LEARNING FLOW
ASSESSMENT
GUIDELINE
Stage
Learning
Flow
Introducti
on
Introduct
ion
Objective
s
Objectiv
es
Interprets the volume measurement of a geometrical shape.
Identifies the height of a right cylinder.
Relates the height of a cylinder with the area of the bases
when calculating volume.
Establishes strategies to determine the volume of an oblique
cylinder.
Recognizes the formula to find the volume of a cylinder.
Calculates the volume of cylinders.
Establishes strategies to find the volume of a cylindric section.
Introduction: Geometrical objects with cylindrical shapes.
Objectives
Activities.
Activity 1: Cylinders
Activity 2: Areas and volumes of cylinders
Abstract
Homework
Evaluation
Glossary
With the completion of the following LO the student will acquire the
ability to identify, classify and relate cylindrical objects. The student
will have the ability to solve problems related to surface areas of
faces and volumes of different types of cylinders (straight, oblique
and cylindric sections)
Teaching/Learning Activities
Recommen
ded
Resources
The teacher introduces an animated resource in Animated
which the different cylindrical objects are resource
presented from two different perspectives: the
first as a classification as an irregular geometrical
object and the second from the use as everyday
aspects.
Dialog
Animated
resource
Content
The
teacher
introduc
es the
topic
Activity 1: Cylinders and types of cylinders.
Animated
Resource
The teacher presents an animation with the
objective of characterizing cylinders, focusing on
the elements that compose cylinders and the
different types of cylinders.
Next we will find an individual activity regarding
the construction of a straight cylinder using the
printable resource. It is also suggested to have
an activity of characterization through the
identification of each of the elements of the
cylinder.
A group activity is encouraged to work with
oblique cylinders, mainly by practical work using
coins. Then, a series of questions will follow
aiming for the students to generate conclusions
around the relation of the characteristics of
cylinders.
Map
infographic
In the printable resource we can find an activity to
build a cylindric section. Additionally, we will find
a series of questions about characterization and
information extraction.
The purpose of this activity is to have the
students explore and build the object, to identify
its parts and find the values of the different
heights and radii of the bases (as main elements
for further development). The values will depend
on the size of the object from the printable
resource. To reach an agreement, class Image
teamwork and the higher number of elements
detected will be taken into account.
-------------------------------------------------------------------------Activity 2. Areas and volumes of cylinders.
The student will be presented an animated
resource in which specific topics about the
elements of cylinders, the calculation of surface
areas and the volume of straight cylinders will be
explained. Additionally a video will be shown.

YouTube. Volume of a cylinder (Geometry
#272). Inquiry date March 22nd, 2016Url:
https://www.youtube.com/watch?
v=bfg83Y8gTuY
In the video, it is indicated that the volume of a
straight cylinder and an oblique cylinder is
calculated the same way. It is therefore asked to
the student to answer in his or her words, why
does he/she think this phenomenon happens?
It is expected that the student consults and see
the video and relating it to activity 1 (the coin
activity), conclude that: the sections of oblique
cylinders can be rearranged to form a straight
cylinder; as a result, the volume of an oblique
cylinder can be found inversely to the volume of a
straight cylinder. Furthermore, the relationship of
the volume is directly proportional to the height
and not the generatrix.
Lastly, in the explicative section, we can find
additional information about the calculation of the
volume of a cylindric section.
Up next, a problem is presented with the
objective of the student matching theoretical
concepts with the context. Then, we will find 2
situations that the student must solve.
A reinforcement activity in pairs follows, with the
objective to build cylindric sections with different
values and the action to relate heights.
Finally, a free activity is presented in which the
students must fill in the blanks with theoretical
concepts.
Abstract
The following chart is presented:
Text
Printable
resource
Homewor
k
The following homework is suggested:
1. In groups of 2 or 3 students, identify in your
surroundings round geometrical objects,
relating them to the three different types of
cylinders. Draw them and label each one of
their elements.
Share with your classmates the elements found
and point out the most common ones.
2. Mathematical challenge
Suggest a development strategy and share it in
class.
The tires of a car are straight cylinders supported
on a curved surface. Is it possible to know the
distance a car has traveled based on an
established number of revolutions of one tire?
Suggest a strategy and solve the following
problem.
 A car is travelling along a road; it is known
that its tires have spun 200 times. If the
radius of the tire is 30cm, what distance
has the car travelled?
o If it spun 500 times, what distance
did the car travel?
o If it spun n times, what distance
did the car travel?
Theoretical-experimental activity.
 Get a glass, a barrel, a soda can or any
Printable
Resource
Evaluatio
n
Glossary
other object that has a cylinder shape.
o Obtain its measurements and
calculate its volume.
o Check that its capacity in cm3 is the
same as indicated in the label. If the
cylinder does not have a capacity
label, fill it with water and verify the
amount using a measured container
such as a blender cup to calculate
the amount of water used to fill it.
o Remember that 1 liter equals to 1000
milliliters and 1 milliliter is 1cm3. (Keep in
mind that the amounts used are estimated
and the results may have a small error
percentage).
An evaluation activity is presented with three
different types of questions. The first type is
embedded questions, the second type is short
answer, and the third type is a problem solution
problem with multiple choice and only answer.
Definitions for the following keywords are
presented: Straight cylinder, oblique cylinder,
cylindric section, circle, circumference, radius, Pi,
geometrical object, face, axis, generatrix, area,
volume
Interactive
Resource.
Printable
Resource
Printable
Resource.