The lesson plan outlines a mathematics lesson on cuboids for 8th grade students. The lesson objectives are for students to describe cuboid characteristics, draw cuboid nets, and determine cuboid side lengths. The lesson involves students understanding contextual problems, developing models to solve the problems, and summarizing to learn about cuboid surface area formulas. The teacher guides student understanding through group work and presentations.
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Mathematics is an abstract subject and most of the people hate mathematics. so Mathematics has a great role in developing interest of the students in Mathematics.
Mathematics is an abstract subject and it is necessary to learn it practically. In this sense, comes the necessity of mathematics laboratory. And through these slide you can learn more about mathematics laboratory
Mathematics is an abstract subject and most of the people hate mathematics. so Mathematics has a great role in developing interest of the students in Mathematics.
Mathematics club objectives, need and importance of mathematics club, Mathema...Bhaskar Reddy
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Mathematics club objectives, need and importance of mathematics club, Mathema...Bhaskar Reddy
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Learning Objectives
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conduct appropriate pedagogical processes to help children in achieving the class level learning outcomes
integrate assessment with pedagogical processes to continuously ensure the progress in learning by all children
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
1. LESSON PLAN OF EXPERIMENTAL CLASS 1
Educational Unit : Junior High School
Subject Matter : Mathematics
Class/ Semester : VIII/ 2(Two)
Time Allocation : 2x40 minutes (One Meeting)
Competence Standard: Be able to understand the cube, cuboid, prism, and
pyramid characteristics, and their parts, and also
determine their size
Basic Competence : Be able to indicate the cuboid characteristics and its
parts.
Indicator :1. Be able to describe the characteristics of a cuboid
2. Be able to draw the cuboid nets
3. Be able to determine the length of side of a cuboid
A. Learning Objective
1. Students are able to describe the characteristics of a cuboid
2. Students are able to draw the cuboid nets
3. Students are able to determine the length of side of a cuboid
B. Material
Defenition of a cuboid
The Characteristics of a Cuboid
The Nets of a Cuboid
C. Teaching Method: Discussion, catechising, and group discussion.
Approach : Realistic Mathematics Education
D. Learning Steps
Characteris
tics of RME
Aproach
Activity Time
Allocation
(Minutes)
Teacher’s Activities Students’ Activities
Initial
Preliminary Making class
condition
becomes
conducive then
Students preparingto
studyin order to reacha
conducive learning.
Studentsremember the
10 Minutes
2. giving
motivation and
apperception and
conveying the
objective and
usefulness of the
material.
Conveying the
benefit of
learning space
plane especially
for a cuboid,
such as, students
could make a gift
box by knowing
the
characteristics
and the nets of a
cuboid.
prerequisite
materialandlisten tothe
teacher's explanationof the
purposeandusefulness
ofstudy material
Step 1: Understanding the contextual problem
The use of
contextual
problems
Giving contextual
problem to
students by
distributing the
Student Activity
Sheet
Guiding students
to understand the
contextual
problem in
Student Activity
Sheet
Understanding the
contextual problem in
Student Activity Sheet
Listen teacher carefully in
order that students can
understand the problem
inStudent Activity Sheet
10 menit
Step 2: Solving The Contextual Problems
The use of
model,
student’s
contributio
n, and the
intertwinem
ent of
matter
Teacherassistsand
enhancesthe
results of
thestudentsby
askingquestionsto
lead studentsto
constructtheir
knowledge about
the possibility of
appropriate
model of
Teacher goes
arround from one
Students formulate the
model of and the solution of
contextual problem in group
Students do the activity on SAS-1
then invent their own model of
and how to solve the contextual
problem given.
Contextual problem: students
observe their classroom and
observe the characteristics of it.
Model of: classroom has six
35 menit
3. group to other
groups while
observingandgivi
ngsupporttosolve
problems
Doing interaction
with students
while
observingandgivi
ngsupporttosolve
problems
rectangles
Contextual problem:
Students observe Beng-beng box
Model of: students give label for
each angle point of the box.
Model for: students write down
their observation result on the
table given.
Formal Mathematics: from the
above table, students conclude
that cuboid is regular space plane
which is limited by six rectangles
and for each pair of faced flate
plane is congruent.
the characteristics of a cuboid:
a. Sides of a cuboid is rectangle
b. The parallel edges have the
same length
c. Each face diagonal on the
faced side has the same
length
d. Each space diagonal in a
cuboid has the same length
e. Each diagonal plane on a
cuboid has rectangle shape
Step 3: Comparing or discussing the answer
The
interactive
Teacher asks one
of students to
present model of
and its solution in
front of the class
One of students presents
model of and its solution in
front of the class
15 minutes
4. Teacher gives
opportunity to
students to
present different
model of
Teacher gives
opportunity to
students to
respond and
choose the
appropriate
model of
Teacher does
negotiation,
cooperative
intervention,
explanation,
reflection, and
evaluation to
guide students till
understand the
concept of formal
mathematics
One of the other students
presents different model of
Respond and choose the
appropriate model of and
discuss it with their own
group
Listen and respond
teacher’s explanation
Step 4: Summarizing
Summarizin
g
Teacher helps
students to make
summary and
conclusion
Students make summary
and conclusion
10 minutes
E. Learning Reference(s) and Instrument(s)
References :
- e-book MatematikaKonsepdanAplikasinya 2
- e-book MudahBelajarMatematika 2
- e-book Contextual Teaching and Learning Matematika SMP
Instruments :
- Student Activity Sheet 1
- Visual Aid
- Posttest
5. LESSON PLAN OF EXPERIMENTAL CLASS 2
Educational Unit : Junior High School
Subject Matter : Mathematics
Class/ Semester : VIII/ 2(Two)
Time Allocation : 2x40 minutes (One Meeting)
To know,
Principal of SMPN 1
LubukPakam
( .......................................................)
NIP/NIK ………..……………….
LubukPakam........... 2014
Researcher
(Maria PriscillyaPasaribu)
IDN. 4103312018
6. Competence Standard: Be able to understand the cube, cuboid, prism, and
pyramid characteristics, and their parts, and also
determine their size
Basic Competence : Be able to calculate the surface area and volume of a
cuboid
Indicator :1. Be able to calculate the surface area of a cuboid
2. Be able to calculate the volume of a cuboid
A. Learning Objective
1. Students are able to calculate the surface area of a cuboid
2. Students are able to calculate the volume of a cuboid
B. Material
- The surface area of a cuboid
- The volume of a cuboid
C. Teaching Method : Debriefingand group discussion.
Approach : Realistic Mathematics Education
D. Learning Steps
Charac
teristics
of
RME
Aproac
h
Activity Time
Allocation
(Minutes)
Teacher’s Activities Students’ Activities
Initial
Prelimi
nary
Making class
condition
becomes
conducive then
giving
motivation and
apperception and
conveying the
objective and
usefulness of the
material.
Conveying the
benefit of
learning space
plane especially
for a cuboid,
such as, students
Students preparingto studyin
order to reacha conducive
learning. Studentsremember the
prerequisite materialandlisten
tothe teacher's explanationof
the purposeandusefulness
ofstudy material.
5 Minutes
7. could know how
much paint that
will be used for
painting the wall
which is shaped
like a cuboid.
Step 1: Understanding the contextual problem
The use
of
context
ual
proble
ms
Giving contextual
problem to
students by
distributing the
Student Activity
Sheet
Guiding students
to understand the
contextual
problem in
Student Activity
Sheet
Understanding the contextual
problem in Student Activity
Sheet 1
Listen teacher carefully in order
that students can understand the
problem inStudent Activity
Sheet
10 menit
Step 2: Solving The Contextual Problems
The use
of
model,
student
’s
contrib
ution,
and the
intertw
inemen
t of
matter
Teacherassistsand
enhancesthe
results of
thestudentsby
askingquestionsto
lead studentsto
constructtheir
knowledge about
the possibility of
appropriate
model of
Teacher goes
arround from one
group to other
groups while
observingandgivi
ngsupporttosolve
problems
Doing interaction
with students
while
observingandgivi
ngsupporttosolve
problems
Students formulate the model of
and the solution of contextual
problem in group
Students do the activity on SAS-2 then
invent their own model of and how to
solve the contextual problem given.
DETERMINING THE FORMULA
OF SURFACE AREA OF A CUBOID
Contextual problem: students
observe the soap box they have
Model of: students cut the soap box in
order to get the nets of box and give
label for each flat plane on the nets.
35 menit
8. Model for: students give label for each
plane and angle point on the nets they
have as follows.
Flat plane that they have is rectangle
Studentsgroupped the congruent plane.
Sisiatas = sisibawah or
EFGH = ABCD
Sisibelakang = sisidepan or
DCGH = EFAB
Sisikiri = sisikanan or
ADEH = CBGF
Students formulate the surface area of
soap box nets
The surface area of a soap box = the
sum of six flat planes on nets
= LEFGH + LABCD + LDCGH + LEFAB +
LABEH + LCBGF
= 2 x (p x l) + 2 x (p x t) + 2 x (l x t)
Formal Mathematics: students
formulate the surface area of a cuboid
Surface area of a cuboid = 2 (pl + pt +
lt)
DETERMINING THE FORMULA
OF VOLUME OF A CUBOID
Contextual Problem: students
observe two different boxes and
certain unit cubes
Model of: students put unit cubes into
two different boxes till full of the box
9. then write the result into the given
table:
Model for:students find the
relationship between the multiplication
of the length, width, and height of a
box and the amount of unit cubes that
is used for fill two different boxes
given.
Volume of box I acquired from the
multiplication of the length, width, and
height of box I (4cm x 3cm x 1cm).
Volume of box II acquired from the
multiplication of the length, width, and
height of box II (5cm x 3cm x 2cm).
Formal Mathematics: students
formulate the volume of a cuboid.
Volume of a cuboid = p x l x t cm3
Step 3: Comparing or discussing the answer
The
interact
ive
Teacher asks one
of students to
present model of
and its solution in
front of the class
Teacher gives
opportunity to
students to
present different
model of
Teacher gives
opportunity to
students to
respond and
choose the
appropriate
model of
Teacher does
negotiation,
cooperative
intervention,
explanation,
reflection, and
evaluation to
guide students till
One of students presents model
of and its solution in front of the
class
One of the other students
presents different model of
Respond and choose the
appropriate model of and
discuss it with their own group
Listen and respond teacher’s
explanation
20 minutes
10. understand the
concept of formal
mathematics
Step 4: Summarizing
Summa
rizing
Teacher helps
students to make
summary and
conclusion
Students make summary and
conclusion
10 minutes
E. Learning Reference(s) and Instrument(s)
References :
- e-book MatematikaKonsepdanAplikasinya 2
- e-book MudahBelajarMatematika 2
- e-book Contextual Teaching and Learning Matematika SMP
Instruments :
- Student Activity Sheet 2
- Visual Aid
- Posttest
To know,
Principal of SMPN 1
LubukPakam
( .......................................................)
NIP/NIK ………..……………….
LubukPakam........... 2014
Researcher
(Maria PriscillyaPasaribu)
IDN. 4103312018
11. LESSON PLAN OF CONTROL CLASS 1
Educational Unit : Junior High School
Subject Matter : Mathematics
Class/ Semester : VIII / 2(Two)
Time Allocation : 2x40 minutes (One Meeting)
Competence Standard: Be able to understand the cube, cuboid, prism, and
pyramid characteristics, and their parts, and also
determine their dimensions
Basic Competence : Be able to indicate the cuboid characteristics and its
parts.
Indicator :1. Be able to describe the characteristics of a cuboid
2. Be able to draw the cuboid nets
3. Be able to determine the length of side of a cuboid
A. Learning Objective
1. Students are able to describe the characteristics of a cuboid
2. Students are able to draw the cuboid nets
3. Students are able to determine the length of side of a cuboid
12. B. Material
THE CUBOID
There are so manythingsaround youthathave the shape ofa cuboid. For
example, boxes of match, boxes ofmineralwater, instantnoodleboxes, bricks,
and others. Why are those objects called like a cuboid?Toanswer it, try to
pay attentionandlearnthe following description.
Defenition of a cuboid
The plane shape ofABCD.EFGHabovehasthree pairs ofoppositesides ofthe
sameshapeanddimension, in whicheach side isrectangular. Itis called
acuboid. The following arethe elementsthatare ownedbythe cuboid
ofABCD.EFGH.
a. Faces
Cuboid faceisthe plane that is bounded a cuboid. From the above figure,
it can be seen that cuboidABCD.EFGHhas6rectangularfaces.
Thesixfaces areABCD(bottom side), EFGH(upper side), ABFE(front
side), DCGH(back side), BCGF(left side), andAdhe(right side).
Acuboidhas threepairs ofoppositesides ofthe
sameshapeanddimension.The three pairs ofsidesareABFEwithDCGH,
ABCDtoEFGH, andBCGFwithADHE.
b. Edges
It is the same with a cube, cuboid of ABCD.EFGH has 12 edges. The
edges of cuboid ABCD. EFGH are AB, BC, CD, DA, EF, FG, GH, HE,
AE, BF, CG, and HD.
c. Vertices
From the above figure, it can be seen that cuboid of ABCD.EFGH has 8
vertices, i.e. A, B, C, D, E, F, G, and H.
d. Face Diagonal
ACline segmentwhich crossesbetween two opposite angle
pointsontheface, i.e.vertex AandC, calledface diagonal of ABCD.EFGH.
e. Diagonal Plane
There are twoparalleldiagonalplanes, i.e.diagonal plane of HFandDB.
Both ofthese planesand two parallelcuboid’s edges, i.e.DHandBFformed
diagonal plane e. BDHF plane is the diagonal plane of
cuboidABCD.EFGH.
13. The Characteristics of a Cuboid
a. The face of a cuboid is rectangular.
b. The parallel edges have similar length.
c. Eachface diagonalonthe opposite sidehas thesamelength.
d. Each space diagonal of a cuboid has the same length.
e. Each diagonal plane of a cuboid has shape of rectangular.
The Nets of a Cuboid
Similarly with thecube, cuboidnetsobtained byopeningthecuboidso that
thewholesurface area of a cuboid is visible. Notice the following flow to
make the nets of a cuboid.
The nets isobtainedfromimage(c) is composedofa series
ofsixrectangularpieces. The seriesconsists ofthreepairs ofrectangles
thateachpairhasthe sameshape anddimension.
C. Teaching Method : Catechising
Approach : Conventional approach
D. Activity Steps
Teacher’s Activity Student’s Activity Time
Allocation
1. Preliminary
Teacher does apperception
1. Preliminary
Students listen teacher’s
10 minutes
14. and gives motivation to
students and conveys the
learning objectives
Teacher reminds the
prerequisite matter to
students
explanation
Students remember the
prerequisite matter
2. Core Activity
Teacher explains the
concept of cuboid parts and
make cuboid’s nets
Teacher gives problem
example and guide students
to solve the problem
together
Teacher gives excercise to
students and asks students
to solve the problem in
front of the class
Teacher asks students
whether they did’nt
understand what he/she
explained
2. Core Activity
Students listen teacher’s
explanation
Students take a note of the
problem example and
listen teacher’s
explanation of problem
solving
Students solve the
problem that teacher given
in front of the class
Students ask if they didnt
understand what teacher
explained
60 minutes
3. Closing Activity
Teacher makes a summary
from his/her explanation
Teacher gives homework to
students
3.Closing Activity
Students take a note of
what teacher summarized
Students take a note of
their homework
10 minutes
E. Learning Reference(s) and Instrument(s)
References :
- e-book MatematikaKonsepdanAplikasinya 2
- e-book MudahBelajarMatematika 2
- e-book Contextual Teaching and Learning Matematika SMP
.
To know,
Principal of SMPN 1 LubukPakam
LubukPakam........... 2014
Researcher
15. ( .......................................................)
NIP/NIK ………..………………. (Maria PriscillyaPasaribu)
IDN. 4103312018
Appendix 6. Lesson Plan of Control Class 2
LESSON PLAN OF CONTROL CLASS 2
Educational Unit : Junior High School
Subject Matter : Mathematics
Class/ Semester : VIII/ 2(Two)
Time Allocation : 2x40 minutes (One Meeting)
Competence Standard: Be able to understand the cube, cuboid, prism, and
pyramid characteristics, and their parts, and also
determine their dimensions.
Basic Competence : Be able to calculate the surface area and volume of a
cuboid.
Indicator :1. Be able to calculate the surface area of a cuboid
2. Be able to calculate the volume of a cuboid
A. Learning Objective
1. Students are able to calculate the surface area of a cuboid
2. Students are able to calculate the volume of a cuboid
B. Material
The Surface Area of A Cuboid
16. The way to calculate the surface area of a cuboid is the same with a cube,
i.e. by calculating the whole area of its nets. Notice this following figure.
Let the vertices of a cuboid are p (length), l (width),and t (height). So that
the surface area of a cuboid is:
surface area of a cuboid = surface area of rectangular 1 + surface area of
rectangular 2 + surface area of rectangular 3 +
surface area of rectangular 4 + surface area of
rectangular 5 + surface area of rectangular 6
= (p × l) + (p × t) + (l × t) + (p × l) + (l × t) + (p × t)
= (p × l) + (p × l) + (l × t) + (l × t) + (p × t) + (p × t)
= 2 (p × l) + 2(l × t) + 2(p × t)
= 2 ((p × l) + (l × t) + (p × t)
= 2 (pl+ lt + pt)
So, the surface area of a cuboid can be denoted by this following formula:
surface area of a cuboid= 2(pl + pt + lt)
Volume of A Cuboid
To determine the volume of a cuboid, notice this following figure. This
figure shows a unit cube with the length of 1unit length.
Figure (b)shows a unit cuboid with
Length dimension = 4 unit of length, width = 2 unit of length, and
height = 2 unit of length.
Volume of a cuboid = length of a unit cube xwidth of a unit cube x height of
a unit cube
= (4 x 2 x 2) unit of volume
= 16 unit of volume
So, the volume of a cuboid (V) with the dimensions (p x l x t) is formulated
as.
Volume of a cuboid = p x l x t
(a) (b)
17. C. Teaching Method : lecturing
Approach : Conventional approach
D. Activity Steps
Teacher’s Activity Student’s Activity Time
Allocation
1. Preliminary
Teacher does apperception
and gives motivation to
students and conveys the
learning objectives
Teacher reminds the
prerequisite matter to
students
1. Preliminary
Students listen teacher’s
explanation
Students remember the
prerequisite matter
10 minutes
2. Core Activity
Teacher explains the
formula of surface area and
volume of a cuboid
Teacher gives problem
example and guide students
to solve the problem
together
Teacher gives excercise to
students and asks students
to solve the problem in
front of the class
Teacher asks students
whether they did’nt
understand what he/she
explained
2. Core Activity
Students listen teacher’s
explanation
Students take a note of the
problem example and
listen teacher’s
explanation of problem
solving
Students solve the
problem that teacher given
in front of the class
Students ask if they didnt
understand what teacher
explained
60 minutes
3. Closing Activity
Teacher makes a summary
from his/her explanation
Teacher gives homework to
students
3. Closing Activity
Students take a note of
what teacher summarized
Students take a note of
their homework
10 minutes
E. Learning Reference(s) and Instrument(s)
References :
- e-book MatematikaKonsepdanAplikasinya 2
- e-book MudahBelajarMatematika 2
- e-book Contextual Teaching and Learning Matematika SMP
18. To know,
Principal of SMPN 1
LubukPakam
( .......................................................)
NIP/NIK ………..……………….
LubukPakam........... 2014
Researcher
( Maria PriscillyaPasaribu )
IDN. 4103312018