Outcomes-Based Teaching Learning Plan in Graph Theory for BSED-Math Students in College

1. GOV. ALFONSO D. TAN COLLEGE
Bachelor of Secondary Education major in Mathematics (BSEd-Math)
Outcomes – Based Teaching and Learning Plan in ME 121
Alfonsos as Lux Mundi: Serving Humanity with Empowered Mind, Passionate Heart and Virtuous Soul
Course Title Graph Theory Course Code ME 121
Credit Units 4 Course Pre-/Co-requisites Previous Math Courses in the Curricular Program
Course Description
(Keijo Ruohonen, 2013)
This course aims to equip the students with knowledge on the different characteristics and algorithms of graphs. The covers the topics on
definition and fundamental concepts of graphs, trees, directed graphs, matrices and vectors of graphs, graph algorithms, drawing of graphs,
and matroids.
Institute Intended
Learning Outcomes
(IILO)
Graduates of BSEd programs are teachers who:
a. Articulate the rootedness of education in philosophical, socio-cultural, historical, psychological, and political contexts
b. Demonstrate mastery of subject matter/discipline
c. Facilitate learning using a wide range of teaching methodologies and delivery modes appropriate to specific learners and their
environment
d. Develop innovative curricula, instructional plans, teaching approaches, and resources for diverse learners
e. Apply skills in the development and utilization of ICT to promote quality, relevant, and sustainable educational practices
f. Demonstrate a variety of thinking skills in planning, monitoring, assessing, and reporting learning processes and outcomes
g. Practice professional and ethical teaching standards sensitive to the local, national, and global realities
h. Pursue lifelong learning for personal and professional growth through varied experiential and field-based opportunities
Program Intended
Learning Outcomes
(PILO)
At the end of this program, graduates will have the ability to:
a. Exhibit competence in mathematical concepts and procedures.
b. Exhibit proficiency in relating mathematics to other curricular areas.
c. Manifest meaningful and comprehensive pedagogical content knowledge (PCK) of mathematics.
d. Demonstrate competence in designing, constructing and utilizing different forms of assessment in mathematics.
e. Demonstrate proficiency in problem-solving by solving and creating routine and non-routine problems with different levels of complexity.
f. Use effectively appropriate approaches, methods, and techniques in teaching mathematics including technological tools.
g. Appreciate mathematics as an opportunity for creative work, moments of enlightenment, discovery and gaining insights of the world.
Course Intended
Learning Outcomes
(CILO)
At the end of this course, the students should be able to:
a. Internalize and apply important proof techniques and problem-solving skills to unfamiliar problems involving graphs.
b. Become inquisitive about graphs and be able to formulate one's own interesting questions about graphs.
c. Recognize the appearance of graphs and understand that certain real-life situations can best be described using graphs.
d. Develop an appreciation for graph theory as an accessible branch of mathematics that secondary educators can share with their
students.

2. MIDTERM Essential Learning
Intended Learning Outcomes
(ILO)
Suggested
Teaching/Learnin
g Activities
(TLAs)
Assessment
Tasks (ATs)Week Content Standards Declarative Knowledge Functional Knowledge
1 – 5
Demonstrate
Knowledge of
Definitions and
Fundamental
Concepts of Graphs
Orientation of Rules and
Mission and Vision of
GADTC and Grading System
Definitions and Fundamental
Concepts of Graphs
 Definitions
 Walks, Trails, Paths,
Circuits, Connectivity,
Components
 Graph Operations
 Cuts
 Labeled graphs and
Isomorphism
Discussing the definitions of
different terminologies of graph
theory
Discussing the meaning and
differences if Walks, Trails,
Paths, Circuits, Connectivity
and Components
Discussing the process of
graph Operations
Discussing the process of
Cutting the graphs
Discussing the labeled graphs
and isomorphism
Identify the different terminologies of
graph
Determine whether a certain graph is a
walk, trail, path, circuit
Determine whether a certain graph is
connected and component of a given
graph
Evaluate the different concepts of Cuts
in the graph
Determine whether a labeled graph is
isomorphic or not
Lecture
Learning Station
Interactive Discussion
Skills Exercises
Paper and Pencil
Test
Assignment
Evaluative Test
Demonstrate
Knowledge of Trees
Tress
 Trees
 Fundamentals of
Circuits and Cut Sets
Discussing Trees and Forests
and their sub-concepts
Discussing the Fundamentals
of Circuits and Cut Sets
Determine whether a graph is a tree or
not
Find the Spanning and Co-spanning of
a tree.
Lecture
Learning Station
Interactive Discussion
Skills Exercises
Paper and Pencil
Test
Assignment
Evaluative Test
5-9
Demonstrate
knowledge of Directed
Graphs
Directed Graphs
 Definition
 Directed Trees
 Acyclic Directed
Determining whether a graph
is a digraph or not
Determining whether a sub-
graph is strongly connected or
not
Determining if a graph is a
directed tree
Determining of a directed
graph is cyclic or acyclic
Determine whether a graph is a
digraph or not
Determine whether a sub-graph is
strongly connected or not
Determine if a graph is a directed tree
Determine of a directed graph is cyclic
or acyclic
Lecture
Learning Station
Interactive Discussion
Skills Exercises
Paper and Pencil
Test
Assignment
Evaluative Test

3. Demonstrate
Knowledge of Matrices
and Vector Spaces of
Graphs
Matrices and Vectors
Spaces of Graphs
 Matrix Representation of
Graphs
 Cut Matrix
 Circuit Matrix
Constructing a matrix based
on the given graph
Determining the cuts of the of
a directed graph
Determining the circuits of a
directed graph
Construct a matrix based on the given
graph
Determine the cuts of the of a directed
graph
Determine the circuits of a directed
graph
Lecture
Learning Station
Interactive Discussion
Skills Exercises
Paper and Pencil
Test
Assignment
Evaluative Test
FINALS
10-13
Demonstrate
Understanding on
Graph Algorithms
Graph Algorithms
 Reachability: Warshall’s
Algorithm
 Depth-First and Breadth –
First Searches
 The Lightest Path: Dijkstra’
Algorithm
 The Lightest Path: Floyd’s
Algorithm
 The Lightest Spanning
Tree: Kruskal’s and Prim’s
Algorithms
 The Lightest Hamiltonian
Circuit (Travelling
Salesman’s Problem): The
Annealing Algorithm and
the Karp-Held Heuristics
 Maximum Matching in
Bipartite Graphs: The
Hungarian Algorithm
 Maximum Flow in a
Transport Network: The
Ford-Fulkerson Algorithm
Discussing the different Graph
Algorithms’ and their uses in
solving problems in Graph
Theory.
Use each algorithm in solving and
simplifying problems in Graph theory.
Lecture
Board work
Problem Sets
Quiz
Assignment
Evaluative Test
14-18
Demonstrate
Understanding on
Planarity and Planar
Embedding
Planarity and Planar
Embedding
 Euler’s Polyhedron
Formula
 The Linear Bound
 The Minimum Degree
Bound
 Kuratowski’s Theorem
 The Four-Color Theorem
 Heawood’s Theorem or
The Five-Color Theorem
 The Davidson-Harel
Algorithm
Discussing the theorems used
in Planarity and Planar
Embedding
Simplify specific cases using the
applicable Theorems
Lecture
Board work
Problem Sets
Quiz
Assignment
Evaluative Test

4. Demonstrate
Understanding on
Matroids
Matroids
 Hereditary Systems
 The Circuit Matroid of a
Graph
 Other Basic Matroids
 Greedy Algorithm
 The General matroid
 Operations on Matroids
Discussing the different types
and operations of Matroids
Use each property to determine the
Hereditary system of sets
Explain other basic Matroids
Perform the operations of Matroids
Lecture
Board work
Problem Sets
Quiz
Assignment
Evaluative Test
Basic Readings
Extended Readings RuohonenK. (2013).GraphTheory.
Course Assessment As identifiedin the Assessment Task
Course Policies LanguageofInstructions
English
Attendance
 As identifiedin the student handbook
Homework,Quizzes,Written Reports,ReactionPapersand Portfolio
Special Requirement
GradingSystem
Summative Quizzes - 30%
SummativePerformance - 40%
Periodical Exam - 30%
100%
Classroom RulesandRegulations
 Respect
Committee Members CommitteeLeader : Alemar C. Mayordo
Members : Elton John B. Embodo
ZarleneM.Tigol
RogielouP. Andam
Clint Joy Quije
Consultation Schedule FacultyMember :
ContactNumber :
E-mailaddress :
ConsultationHours:
TimeandVenue :

5. Course
Title
A.Y. Term of
Effectivity
Prepared by Checked by Noted by Approved by Pages
Graph Theory Summer 2021 ELTON JOHN B. EMBODO, MAED
Instructor
ELTON JOHN B. EMBODO, MAED
Program Coordinator
ALEMAR C. MAYORDO, MAED
OIC-Dean
LOVE H. FALLORAN, Ph.D. 5