Grades 1 to 12 School Taligaman National High School Grade Level 11

DAILY LESSON LOG Teacher Jeriel V. Cortez Learning Area Precalculus

Day 1 Day 2 Day 3 Day 4

C. Learning Competencies/ illustrate the Principle of Mathematical apply mathematical induction in apply mathematical induction in proving illustrate Pascal’s Triangle in the expansion
Objectives Induction (STEM_PC11SMI-Ih-4) proving identities (STEM_PC11SMI- identities (STEM_PC11SMI-Ih-i-1) of (x+y)n for small positive integral values of
Write the LC code for each Ih-i-1) n
II. CONTENT

III. LEARNING RESOURCES

A. References
1. Teacher’s Guide pages Precalculus Teacher’s Guide, selected Precalculus Teacher’s Guide, Precalculus Teacher’s Guide, Precalculus Teacher’s Guide, selected
pages selected pages selected pages pages
2. Learner’s Materials pages
3. Textbook pages
4. Additional Materials from
Learning Resource (LR)
portal
B. Other Learning Resources Precalculus for Senior High School by Danilo De Guzman
IV. PROCEDURES

A. Reviewing previous lesson Say: We have derived and used formulas Review the previous lesson Review the previous lesson In this lesson, we study two ways to expand
or presenting the new for the terms of arithmetic and geometric (a + b)n, where is a positive integer. The first,
lesson sequences and series. These formulas which uses Pascal’s Triangle, is applicable if
and many other theorems involving n is not too big, and if we want to determine
positive integers can be proven with the all the terms in the expansion. The second
use of a technique called mathematical method gives a general formula for the
induction. expansion of (a + b)n for any positive integer
n.
B. Establishing a purpose for There are many mathematical results that This formula is useful especially when n is
the lesson can be proven using mathematical large because it avoids the process of going
induction. In this lesson, we will focus on through all the coefficients for lower values of
three main categories: summation n obtained through Pascal’s Triangle.
 identities, divisibility statements, and
inequalities.
C. Presenting The Principle of Mathematical Induction is Present more examples in proving
examples/instances of the often compared to climbing an infinite equations using Mathematical induction
new lesson staircase. First, you need to be able to
climb up to the first step. Second, if you
are on any step (n = k), you must be able
to climb up to the next step (n = k + 1). If
you can do these two things, then you will
be able to climb up the infinite staircase.
D. :Discussing new concepts We now consider some examples on the Proving Divisibility Statements Discuss: Pascal’s Triangle and the Concept
and practicing new skills #1 use of mathematical induction in proving of Combination
summation identities.
E. Discussing new concepts Give an illustrative example Give an illustrative example
and practicing new skills #2

F. Developing mastery (leads Provide a practice exercise in proving Sample exercises involving problem Use Pascal’s Triangle to expand binomial
to Formative Assessment 3) using mathematical induction solving algebraic expression
G. Finding practical
applications of concepts and
skills in daily living
H. Making generalizations and
abstractions about the
lesson
I. Evaluating learning Short Quiz Seatwork/Homework Assignment Short Quiz

J. Additional activities for Give activity sheets for practice Give activity sheets for practice
application or remediation
V. REMARKS
VI. REFLECTION

A. No. of learners who earned 80%