DAILY LESSON LOG OF M10AL-1b-c-1 (Week Two – Day Tw0)

School Grade Level 10

Teacher Learning Area Mathematics
Teaching Date and Time Quarter First
I. OBJECTIVES
A. Content Standards The learner demonstrates understanding of the key concepts of sequences.

B. Performance Standards The learner is able to formulate and solve problems involving sequences in different
disciplines through appropriate and accurate representations.
Learning Competency: Determines arithmetic means and nth term of an arithmetic
Sequence. (M10AL-1b-c-1) day 2
Learning Objectives:
C. Learning Competencies/ 1. Determine the nth term of an arithmetic sequence.
Objectives 2. Find the unknown term in an arithmetic sequence; and
3. Cooperate patiently with groupmates in answering the assigned tasks.

II. CONTENT Arithmetic Sequence

III. LEARNING RESOURCES Teachers’ Guide, Learners’ Module
A. References
1. Teacher’s Guide pages 18- 19
2. Learner’s Materials pages 19-21
3. Textbook pages
4. Additional Materials from Grade 10 Mathematics Patterns and Practicalities By: Gladys C. Nivera,Ph.D. , et. al.
Learning Resource (LR) portal
B. Other Learning Resources
IV. PROCEDURES
The teacher asks the students:
Have I given you assignment yesterday?
What was it? Can anyone read the assigned problem?
“The second term of an arithmetic sequence is 24 and the fifth term is 3. Find the first
Term and the common difference.”
Guide Questions:
1.What are given in the problem?
2. What is/are ask in the problem?
A. Review previous lesson or 3. How did you go about finding the a1 and the d in the problem?
presenting the new lesson Answer key:
1. a2 =24 and a5 = 3
2. a1 and d
3. From an=a1 + (n-1) d; substitute 3 for an, 24 for a1,and 4 for n
In solving for d : 3 = 24 + (4-1)d
3 – 24 = 3d
-21=3d
-7=d
In solving for a1: 24-7 = 13
Let us now have more challenging problems involving arithmetic sequence to analyze
B. Establishing a purpose for
and solve.
the lesson
The teacher says be with your group now and answer the following problems.
1.Find the nth term of the sequence 3,7,11,15, …
C. Presenting examples/ 2.How many terms are there in an arithmetic sequence with a common difference of 4
instances of the new and with first and last terms 3 and 59, respectively.
lesson 3.The 4th term of an arithmetic sequence is 34 and the 10 th term is 22. Find a1, d, and
the nth term.

D. Discussing new concepts The teacher asks:

and practicing new skills #1 1.What is ask in problem 1? What is your answer?
2.What about problem 2, what are given? What is ask? What is your answer?
3.What are given in problem 3? What are you going to find?( the teacher here will
guide
the students with some mathematical manipulations to find what is ask in the
problem)
Answer Key:
1. nth term; 4n-1
2. d=4, a1= 3, an = 59
n=?
n=15
3. a4=34, a10=22
a1 =? d=? nth term=?
 To find d: since a4=34 and a10 =22,let us add d 6 times to 34 to get to
34 +6d = 22
6d = -34 +22
d = -12/6 = -2
to find a1: subtract d from a4 three times since d should be subtracted (n-1)
times from an in order to find a1
a1 = a4 – (n-1) d
= 34 – (3) (-2)
= 34+6
a1 = 40
to find the nth term: let’s use an=a1 +(n-1) d
an= 40+(n-1) (-2)
an = 40 -2n +2
an = -2n +42
Thus; a1 = 4, d = -2, and an= -2n + 42

The teacher presents this problem and let them answer this within their group:
Find k so that the numbers 7k + 2, 5k +12, 2k -1, … form an arithmetic sequence.
Hint: identify the a1, a2, and a3, then equate them this way
a2 – a1 = a3 – a2
E. Discussing new concepts The teacher here can explain farther depending on the need of the students and can
and practicing new skills #2 also
ask the students to write out the terms of the sequence and identify the common
difference.
Answer key: k = -13
The terms are: -89, -53,-27 and the common difference is 36
The teacher lets the students to try working with the problems below individually.
1.Find the 16th term of the arithmetic sequence sequence 1,5,9,13,…
2.What is the nth term of the arithmetic sequence 7,9,11,13,…?
3.What must be the value of k so that 5k-3, k+2, 3k-11 will form an arithmetic
Sequence? Write out the terms of the sequence and find d.
F. Developing mastery (leads
Answer key:
to formative assessment 3)
1. 61
2. 2n + 5
3. K =3
The sequence: 12,5,-2,…
D = -7
Perez family saved Php1000 in January, Php1200 in February, Php1400 in March, and so
G. Finding practical
on. How much will they save by December?
applications of concepts
Answer key:
and skills in daily living
Php3400
H. Making generalizations How do we solve problems involving arithmetic sequence?
and abstractions about the
lesson
The teacher let the students answer the problems below.
1.Find the value of k so that k+2, 4k, and 6k +1 are term of an arithmetic sequence.
Write out the terms.
2.Give the arithmetic sequence of 5 terms if the first term is 8 and the last term is 100.
3. Find the nth term of the arithmetic sequence 50,45,40,35,…
Answer key:
I. Evaluating Learning
1. 4k- (k+2) = 6k + 1 -4k
K=3
Terms: 5,12, 19
2. 8, 31, 54, 77, 100
3. an = -5n + 45

The teacher lets the students study about arithmetic means and answer this:
1. Insert 4 arithmetic means between 5 and 25.
2. Find the arithmetic mean between 8 and 20.
J. Additional activities or
Answer key:
remediation
1. 9,13,17and 21
2. (8 + 20) / 2 = 14

V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80% of
the evaluation
B. No. of learners who require
additional activities for
remediation who scored below
80%
C. Did the remedial lesson work? No.
 of learners who have caught up
with the lesson.
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these work?
F. What difficulties did I encounter
which my principal or supervisor
can help me solve?
G. What innovation or localized 1V: G
materials did I use/ discover which
I wish to share with other teachers