1
THE UNIVERSITY OF TRINIDAD AND TOBAGO
SCHOOL FOR STUDIES IN LEARNING, COGNITION AND EDUCATION
BACHELOR OF EDUCATION PROGRAMME
LESSON PLAN- MATHEMATICS SPECIALIZATION ( SECONDARY)
INTRODUCTORY BACKGROUND
NAME:
DATE:
CLASS:
SUBJECT: MATHEMATICS
AGE RANGE:
ABILITY LEVEL:
NO. IN CLASS:
21
NO. PRESENT:
TOPIC/CONCEPT:
DURATION:
SPECIFIC OBJECTIVES/ LEARNING OUTCOMES:
CLASSIFICATION:
2
At the end of the lesson students will be able to:
(Cognitive Domain)
1. Identify items in real life that are shaped like cubes
2. Identify the attributes/properties of a demonstrated cube
3. Describe what is the net of a cube
4. Explain how to derive the net of a given cube
1
2
3
4
5
Knowledge
Analysis
Knowledge
Comprehension
Synthesis /
Precision
6 Synthesis /
Precision
7 Responding
(Cognitive & Psychomotor Domain)
5. Accurately create more than one distinct net of a cube using
concrete cube manipulatives, in a group activity
(Affective Domain)
6. Participate willingly in a group activity to discover the net of a
cube
PREVIOUS KNOWLEDGE, SKILLS AND EXPERIENCES:
1. Students are able to identify prototypes of the 3 dimensional figures: cubes, cuboids,
cylinders, prisms, cones and pyramids.
2. Students know the properties of a square.
3. Students are familiar with the following terms related to a cube: face, edge,
vertex/vertices
MATHEMATICAL PROCESSES:
1. The students have to engage in the activity, in a given amount of time, of creating more
than one examples of net of a cube. Students cooperate to discover ways to get multiple
3
nets. This task involves the problem solving process with the use of concrete
manipulative where students engage in visualisation and inventiveness among other skills
to find more than one solution to the same problem (more than one net of a cube).
Students have the freedom to use more than one strategy to solve the problem.
2. The activity to create more than one net of a cube requires the students to recognize
structures of the nets which may or may not result in a cube. Students are required to give
reason(s) in attempting to distinguish which net gives a cube. This develops their
reasoning skills. The group activity encourages students to critique each other’s
suggestions in their groups and formulate full-proof methods in proving their answers.
Since each group is required also to explain their solutions reasoning skill is further
developed.
3. The lesson builds on students’ prior knowledge of understanding the nature of 3
dimensional figures and how it makes it possible to derive a net from a cube. By referring
to cardboard boxes, which are items in their real life, students will make connections to
what they already know and effectively develop their mathematical understanding. The
new knowledge of “nets of a cube” is not learnt in isolation and will most likely be
imbedded in long term memory.
4. The use of multiple representations of the cardboard box by demonstration (concrete
manipulative) and the diagram of it on the whiteboard provide students with more than
one way of deriving the attributes of a cube. Drawing the discovered nets on the
checkered grids provided when they are given the 3” X 3” cubes provides them with the
opportunity to use representations to record the idea of “nets of a cube”
4
5. Demonstration of solution(s) in the activity and including the journals in the lesson
provides the students with experiences of multiple ways of expressing mathematical
understanding. Apart from demonstrating, students communicate their ideas when they
write and explain their method(s) used in deriving nets of a cube.
RESOURCES:
1 large cardboard box – (cube-shaped)
25 prepared paper cubes – 3”X3”X3”
Large demonstration cube
Adhesive Tape
6 Pairs of Scissors
White board & White board markers
Prepared Written Assessment
Prepared Activity Worksheets
Laptop
Multimedia Projector
Relevant software
Two dice
A Rubik’s Cube
THE LEARNING ENVIRONMENT:
The desks will be arranged linearly however it should accommodate cooperative learning groups
of four or five students. It should also be arranged so that all students are able to see on the
5
whiteboard. The room has proper lighting, good ventilation and an air condition unit. Space is
readily available. The environment includes the following resources: 1 large cardboard box –
(cube-shaped), 25 prepared paper cubes – 3”X3”X3”, large demonstration cube, adhesive tape, 6
Pairs of Scissors, white board & white board markers, prepared written assessment, prepared
activity worksheets, laptop, multimedia projector, relevant software, two dice and A Rubik’s
Cube.
CLASSROOM
MANAGEMENT STRATEGIES:



Stare
Touch
Standing at the side of the student/s that are being disruptive while teaching.
ENERGISER/S:

Placing the different nets of the cube found on the board.
THEORETICAL UNDERPINNINGS:
●
Howard Gardener - Cater for multiple intelligences of the students by using audio - visual
approach, manipulatives.
●
Jerome Bruner - modes of representation, concrete (cubes made from Bristol board),
visual/iconic (The different nets of the cube placed on the board)
●
Vygotsky - Social interaction in groups.
●
John Dewey - Learning by Doing.
6
SET INDUCTION:
TIME ALLOCATION 1: 3 Minutes
Bring students to the floor. Ask, “Who can say what an attribute is?” Confirm that an attribute
describes a quality, property, or characteristic of somebody or something.
Call on a student to stand in front of the class and state an attribute/property of the child (the
color of their hair, eyes, shoes, etc.). Ask students, “What are some other attributes (or
properties) of … (name of student). Students contribute suggestions.
MAIN IDEAS/ UNDERSTANDINGS/FOCUS

The properties of a cube are: Cubes have twelve edges, eight vertices and six faces which
are squares

The net of a 3 dimensional object is
STEP- BY STEP PROCEDURES/ACTIVITIES IN THE LESSON
SECTION ONE – 12 Minutes

Introduce the alternative words to “attributes”: properties, characteristics, qualities.

Ask students, “Who can recall the names of the different three dimensional figures you
learnt about in last class?” Pause a few seconds then call on student(s) in class to list
them.

Let students know that the main focus of the lesson is on Cubes, their properties, and
their nets. Show students Figure 1 on the slide show (see Appendix) which shows various
3D shapes and ask, “Which shape shown is a cube?” Ask a student who raises his/her
hand to give an answer.
7

Reveal to students a large cube- shaped cardboard box to demonstrate an example of
where in the real world a cube can be found. Ask students, “What else (in the real world)
has the shape of a cube?” List at least Three (3) examples given by students on the
whiteboard. If students are unable to give examples, three are
 Die (plural Dice)
 Ice cubes
 Rubik’s Cube

Distribute one cube each to the students and ask them to identify the different properties
of the cube, making sure they call the “sides” faces, and “corners” vertices.
Prompt students with the questions, “What can you tell me about
 the faces of the cube
 the edges of the cube
 the vertices of the cube?”

As students identify the properties compile a list on the whiteboard. When all properties
are listed allow students to write them in their math notebooks. Ensure the following
properties are included:
Cubes have
 twelve edges,
 eight vertices and
 six faces
 all faces are squares

To reinforce the properties of a cube show a number of projected images of mixed
examples and non-examples of cubes. Students must analyse which are cubes/not cubes,
and say why. Pose questions to the entire class then randomly choose students to give
responses.
Ask the following questions for each image:
1. Is this a cube?
2. Why do you say so?
8
SECTION TWO – 20 Minutes
Activity

Place students in groups of three’s for the purpose of the activity.

State the objective of the activity – To Investigating the Net of a Cube
Give students the definition of what is a Net. Then ask students, “Given the definition of
a Net, what do you think is the net of a cube?” Write their definition at the top of the
Whiteboard. Allow students to take note of the definition in their notebooks.

Let students know that they will now follow three simple steps in which you start with a
cube and derive its net. They will work in their groups of three’s and use ONE cube per
group. Use the prepared comprehensive steps shown on the power point slides for
students who cannot understand clearly by listening. An instruction sheet is distributed as
well for each student.
INSTRUCTIONS:
Step 1.
Place the cube on a flat surface (the desktop/table-top).
Identify the top flat face of the cube.
Using a pair of scissors, cut three edges around the face to make a flap (see Step 1
diagram)
Step 2.
Cut along the four vertical edges downwards until you reach the base of the cube.
Hold the flap and open outwards (see diagram)
Step 3.
The cube can now be opened completely to the form of its net (see diagram)
Demonstrate how the net is formed back into a cube by folding.

Let students know that it is possible to get eleven (11) distinct nets of a cube.

Students in each group now work together to create different nets of a cube, Each group
is allowed three cubes. Instructions given:
 Students can cut ONLY edges
 ALL faces must be joined together by at least one edge each
9
 Every student must participate
 Groups are given five (5) minutes to create their nets.

Observe students on-task
Presentation of Findings

Students, in their groups, display their nets by sticking them on different sections of the
whiteboard. Label each group’s work.

Possible questions to ask group members:
 How do you know that you have created a net of a cube?
 Was there any special method that you used to arrive at your nets?
 Did you make any other observations when you
 Can you draw a net of a cube without using the cube?
 Is it possible to create a new net of a cube without using the cube? How?
 Why do you think we need to learn about Nets?

Confirm that all nets are accurate. Allow students to draw the different nets of a cube that
they created, on the Grid Sheet provided.

Students will attempt Worksheet #1 which is an assessment of the entire lesson
QUESTIONING STRATEGIES
Setting
Recall of prior knowledge at

the start of the lesson
Question
Who can recall the names of
the different three
dimensional figures you
learnt about in last class?
Question asked during the set

What are some other
induction when students have
attributes (or properties) of …
to identify attributes of a
(name of student).
selected student from the class
Students are shown a real
world example of a cube

What else (in the real world)
has the shape of a cube?
Level of Questioning
10
Students are given concrete

cubes to analyse.
What can you tell me about
the faces of the cube, the
edges of the cube, the vertices
of the cube?
Students are shown pictures of

Is this a cube?
examples and non-examples

Why do you say so?

How do you know that you
of cubes, some of which are
real world examples
Questions asked during
presentation of findings in the
Activity
have created a net of a cube?

Was there any special method
that you used to arrive at your
nets?

Did you make any other
observations when you

Can you draw a net of a cube
without using the cube?

Is it possible to create a new
net of a cube without using
the cube? How?

Why do you think we need to
learn about Nets?
SECTION 1: Teaching
TIME ALLOCATION 2:
11
CONTENT
METHODOLOGY
TEACHING POINTS
TEACHING STRATEGIES
An attribute is a property or CLASS DISCUSSION
characteristic
of
an
object
(person, thing etc).
The teacher asks the students what
LEARNING ACTIVITIES
Students contribute
suggestions of what they
think an attribute is.
they think an attribute is. After
discussion the class confirms that
an attribute describes a quality,
property or characteristic of
something or someone. The teacher
then asks a student to stand at the
front of the class and the class then
states an attribute of that student.
The teacher now establishes other
synonyms for “attributes” and lets
Other synonyms for “attribute” students know that the main focus
are quality, characteristic, trait, of the lesson is on Cubes, their
feature aspect and element.
“attributes”, and their nets.
Cubes found in the real world
are :
 Television
 Dice
 Blocks
 Ice block
DEMONSTRATION
The teacher will reveal to students a
large cube- shaped cardboard box
to demonstrate an example of
Students give examples of
cubes found in the real
be found. At least three examples of world.
where in the real world a cube can
cubes found in the real world, given
by students, will be displayed on
the whiteboard.
USE OF MANIPULATIVES
12
The properties of a cube
 It is a three –
dimensional solid
 It bounded by six square
faces, twelve edges, with
three meeting at each
vertex.
 It has eight vertices
 It has eleven nets
Distribute one cube each to the
students and ask them to identify
the different properties of the cube,
making sure they call the “sides”
faces, and “corners” vertices.
A list of the properties will be
complied on the whiteboard. When
Students will identify
different properties of the
cube and write them in their
math notebooks.
all properties are listed, students
will be allowed to write them in
their math notebooks.
USE OF VISUALS
Show students on the slide show,
various 3D shapes consisting of
examples and non- examples of
Students answer questions
based on examples and nonexamples of cubes.
cubes. Pose questions to the entire
class based on the various 3D
shapes then randomly choose
students to give responses.
QUESTIONING
-“Who can recall the names of the
different three dimensional figures
you learnt about in last class?”
-“What are some other attributes (or
properties) of … (name of student).
Students actively participate
in formative questioning
13
-“What else (in the real world) has
the shape of a cube?”
-“What can you tell me about the
faces of the cube, the edges of the
cube, the vertices of the cube?”
-Is this a cube?
-Why do you say so?
SECTIONAL REVIEW 1/ VERIFICATION OF LEARNING DURING THE LESSON 1:
14
SECTION 2: Activity
TIME ALLOCATION 3:
CONTENT
TEACHING POINTS
METHODOLOGY
TEACHING STRATEGIES
COOPERATIVE LEARNING
Students will be placed in groups of four or
five
A net is a twodimensional figure that
can be cut out and
folded up to make a
threedimensional
solid.
LEARNING
ACTIVITIES
Allow students to take
note of the definition in
their notebooks.
Teachers will give students the definition of a
net and then ask them what they think the net
of the cube is. Their definition will be written
on the whiteboard. Teacher will let students
know that they will now follow three simple
steps to derive the net of a cube. They will
work in their groups and use ONE cube per
group. After deriving one net, they will try to
derive other nets of the cube. Each group is
allowed three cubes.
Teacher will demonstrate how the net is
Working in cooperative
learning groups
students will start with
a cube and derive its
net.
Students, in their
groups, display their
nets by sticking them
on different sections of
the whiteboard.
formed back into a cube by folding.
They will also observe students on-task and
confirm that all nets are accurate.
Allow students to draw
the different nets of a
cube that they created,
on the Grid Sheet
provided.
15
EXPLANATION
Students accurately
Teacher will use the procedure shown on the
follow teacher’s
power point slides for students who cannot
instructions
understand clearly by listening. An instruction
sheet will also be provided for each student.
QUESTIONING
 How do you know that you have
created a net of a cube?
 Was there any special method that
you used to arrive at your nets?
 Did you make any other
observations when you
 Can you draw a net of a cube
without using the cube?
 Is it possible to create a new net of
a cube without using the cube?
How?
 Why do you think we need to learn
about Nets?
16
CLOSING ACTIVITIES: - 5 Minutes
SUMMARY &CLOSURE
Pay special attention to the presentation of materials on the whiteboard which serves as a visual
representation of the concepts learned. Students can take notes in their journals in a similarly organized
fashion.
17
ASSESSMENT ACTIVITIES:
Assessments: 1) Authentic
This assessment involves
 Problem-solving tasks
 Observations
 Presentations
Make observations of individuals during open-class interactions, when on task in the group
activity and group presentations. Special attention is made to the following:

Class Participation

Class Behaviour

Group Listening Skills

Sensitivity to Others

Group Contributions
Each student is rated in the different areas using a Rubric.
18
Participation Rubric
NAME__________________________
FORM__________ DATE_________
Criteria
3
Class
Participation
Consistently
and actively
contributes
knowledge,
opinions, and
skills, and asks
questions.
Class
Behaviour
Group
Listening
Skills
2
1
0
Student
rarely offer
ideas, and
asks
questions
sometimes.
Contributes to
the group with
occasional
prompting.
Student never
contributes
ideas and ask
questions
Student
almost never
displays
disruptive
behaviour
during class.
Values the
knowledge,
opinion and
skills of all
group
members.
Student rarely
displays
disruptive
behaviour
during class
Student
almost always
displays
disruptive
behaviour
during class
Student does
not listen
when others
talk and often
interrupts
when others
speak.
Sensitivity to
Others
Student is
sensitive to the
feelings and
learning needs
of all group
members all
the time
Student
shows
sensitivity to
the feelings
of others
sometimes
Group
Contributions
Student
willingly
volunteers
ideas and
encourages
contribution
from group
member(s)
Student
volunteers
ideas
sometimes
TOTAL
____/13
Student listens
sometimes
when others
talk and
sometimes
interrupts
when others
speak
Student needs
occasional
reminders to
be sensitive to
the feelings of
others
Student
contributes to
group only
when
prompted by
other members
Student does
not display
sensitivity to
the feelings of
others
Student
works in
isolation and
makes little or
no attempt to
share ideas
when
prompted
Points
Awarded
19
Traditional Assessment
Worksheet #2
NAME______________________________
FORM______________________
Time 10 mins.
INSTRUCTIONS:
Answer all questions.
SECTION A
Read each of the following questions and circle the letter which gives the best response:
1) Which statement below describes a NET?
A) A net is a two-dimensional figure that cannot be cut out and folded up to make a
three-dimensional solid.
B) A net is a three-dimensional figure that can be cut out and folded up to make a twodimensional solid.
C) A net is a three-dimensional figure that cannot be cut out and folded up to make a
two-dimensional solid.
D) A net is a two-dimensional figure that can be cut out and folded up to make a threedimensional solid.
(1 Mark)
2) Which of the following is NOT a property of a cube?
A) A cube has 6 faces
B) A cube has 6 vertices
C) All the edges of a cube are the same length.
D) ALL the faces of a cube are squares with the same areas
(1 Mark)
20
SECTION B
Read each of the following questions and answer them in the spaces provided.
All working must be shown clearly where necessary:
3) How many identical squares would be needed to make three cubes of the same sizes?
(2 Marks)
4) Draw two different nets that would form a cube.
(2 Marks)
5) Can the net below be folded to form a cube?
____________________ (Yes or No?)
(1 Mark)
6) Can the net below be folded to form a cube?
____________________ (Yes or No?)
(1 Mark)
21
Traditional Assessment - SOLUTIONS
NAME______________________________
FORM______________________
Time 10 mins.
INSTRUCTIONS:
Answer all questions.
SECTION A
Read each of the following questions and circle the letter which gives the best response:
1) Which statement below describes a NET?
A) A net is a two-dimensional figure that cannot be cut out and folded up to make a
three-dimensional solid.
B) A net is a three-dimensional figure that can be cut out and folded up to make a twodimensional solid.
C) A net is a three-dimensional figure that cannot be cut out and folded up to make a
two-dimensional solid.
D) A net is a two-dimensional figure that can be cut out and folded up to make a threedimensional solid.
(1 Mark)
2) Which of the following is NOT a characteristic of a cube?
A) A cube has 6 faces
B) A cube has 6 vertices
C) All the edges of a cube are the same length.
D) ALL the faces of a cube are squares with the same areas
(1 Mark)
22
SECTION B
Read each of the following questions and answer them in the spaces provided.
All working must be shown clearly where necessary:
3) How many identical squares would be needed to make three cubes of the same sizes?
No. of square faces in one cube
=
6
No. of square faces in three cubes
=
3x6
=
18
Therefore 18 identical squares will be needed
(2 Marks)
4) Draw two different nets that would form a cube.
ANSWER:
Any two from the set:
(2 Marks)
5) Can the nets below be folded to form a cube?
NO___________________ (Yes or No?)
(1 Mark)
6) Can the nets below be folded to form a cube?
YES___________________ (Yes or No?)
(1 Mark)
23
Table of Specification/Mark Scheme
Distribution of Items by Strand and Skill Level
SKILL LEVEL
KC
AT
PS
TOTAL
GEOMETRY
2 (ques. 1,2)
2 (ques. 2,3)
1 (ques. 4)
4
TOTAL
2
2
1
4
STRAND
Distribution of Marks
MARKS
Per Item
TOTAL
Knowledge/comprehension 1
1
1
Algorithm Thinking
2
2
4
Problem Solving
1
3
3
TOTAL
4
LEVELS
NO. OF
ITEMS
8
24
ADAPTATIONS OF THE LESSON:
TEACHER’S LESSON APPRAISAL/ REFLECTION ON THE LESSON:
CONTINUATION/ FOLLOW –UP:
CO-OPERATING TEACHER’S COMMENTS:
25
PRACTICUM ADVISOR’S COMMENTS:
APPENDIX: FOUR COLUMN LESSON PLAN
Overall goal:
Materials needed:
Steps of the Lesson:
Expected student
Teacher’s Responses
Goals and Method(s)
Learning Activities
Reactions or
to Student
of Evaluation
and Key Questions
Responses
Reactions/ Things to
Remember
26
Steps of the Lesson:
Expected student
Teacher’s Responses
Goals and Method(s)
Learning Activities
Reactions or
to Student
of Evaluation
and Key Questions
Responses
Reactions/ Things to
Remember
27
Matthew, M.E. et al (2009). Using Lesson Study and Four- Column Lesson Planning with
Pre-service Teachers. Mathematics Teacher 102(7).pp.504-509.