Republic of the Philippines

Department of Education
Region XII
Kidapawan City Division
Kidapawan City

A Semi- Detailed Lesson Plan in Mathematics IX

Prepared by:

REY MARK V. RAMOS

Applicant

MARCH 2021
 Republic of the Philippines
Department of Education
Region XII
Kidapawan City Division
Kidapawan City

A Semi- Detailed Lesson Plan in Statistics and Probability

Grade 11

Prepared by:

REY MARK V. RAMOS

Applicant

MARCH 2021
 A Semi- Detailed Lesson Plan in Mathematics IX

I. Objective

At the end of the period, at least 75% of the students should be able to:

a. Determine trigonometric ratios involving special angles.

b. Relate problems involving the concept of special right triangle in real
life situation

II. Subject Matter

Topic: Trigonometric Ratios of Special Angles

Reference: Learner’s Material in Mathematics 9, Module 7, pp. 451 – 453
Materials: laptop, projector, and meta strips
ICT Application: PowerPoint presentation
Values Integration: cooperation, teamwork, neatness of work, accuracy
and honesty

III. Procedure

A. Preliminary Activities
a. Prayer
b. Greetings
c. Checking of Attendance
d. Passing of Assignment
e. Review of Previous Lesson on Trigonometric Ratios through Drill

Determine the trigonometric ratio of the following:

opposite hypotenuse
a. d.
hypotenuse opposite
adjacent hypotenuse
b. e.
hypotenuse adjacent
opposite adjacent
c. f.
adjacent opposite

B. Motivation
(Ask the students)
What makes you special?

Lesson Proper

a. Activity
1. Board work

Match the measures of the sides of the 45°-45°-90° and 30°-60°- 90°
triangle.
 a √2 2a 60°

a a

45° 30°

a a √3
2. Group work
Find the values of the six trigonometric ratios of the special

triangles.

Group I – trigonometric ratios of 30°

Group II – trigonometric ratios of 45°

Group III – trigonometric ratios of 60°

Rubrics:
Cooperation – 10 pts
Accuracy – 30 pts ( 5 points each Trigonometric expression)
Presentation – 10 pts
Speed - 10 pts

b. Analysis
1. How did you find the values of the trigonometric ratios?
2. Are the numerical values is in simplified form? Why? Why not?
3. How can you simplify these values?
4. What did you observe about the values you obtained?

c. Abstraction
1. Complete the table of values of the trigonometric ratios.

Possible Answers:

√3 √ 31 1 √2
2 2 2
√3

2 √3 √3 √2 √ 3 2√ 3
2
3 3 2 3 3

31
1 √ 2 √2 √ 2
2 2

TRIGONOMETRIC RATIOS
θ sin θ cos θ tanθ csc θ sec θ cot θ
30°
45°
60°
2. What if a numerical expression is given as2− √3 , what
expression in trigonometric ratios can be obtained?
 3. What if a numerical value is given as ( √ 2 ) ( 23√3 ), what
expression in trigonometric ratios can be obtained?
4. Why do you think these angles are special?
5. Do you think these concepts are important? Why?
6. How will you use these concepts in real – life situation?

d. Application
(Group Activity)
1. Group the students into three to four members.
2. Each group will be given numerical expression.
3. The group will determine the equivalent expression in trigonometric
ratios and write it on the given meta strips.
4. The students in each row will post the expressions on the board.

IV. Evaluation
Determine the numerical value of the following trigonometric ratios
involving special angles on a ¼ sheet of paper.

1. sin 30° 5. cot 60°

2. cos 45° 6. sec 30°
3. tan 60° 7. tan 45°
4. csc 45° 8. cos 60°

V. Assignment
Compute the numerical values of trigonometric expressions involving
special angles on a ¼ sheet of paper.

1. ( sin 30° ) ( cot 30° )

2. tan 45 ° - cos 60°
3. ( tan 60° ) ( cot 30° ) + csc 30 °
4. ( sec 60° + csc 30° ) ( cos 60° )
5. ( sin 30° ) ( tan 45° ) + ( tan 30° ) ( sin 60° )

Semi-detailed Lesson Plan in Statistics and Probability

Grade-11
 I. Objectives
At the end of the period, at least 75% of the students should be able to:

a. Formulate the appropriate null and alternative hypothesis on a population

mean
b. Computes for the test- statistic value (probability value)
c. Draws conclusion about the population mean based on the test-statistic value
and the rejection region.

II. Subject Matter

Topic: Hypothesis testing About One Population Mean
References:
 Zorilla,R.et al.2016.Statistics and probability. Malabon City.
Mutya Publishing House Incorporated
 Walpole,R. &Myers R. 1993.Probability and Statistics for
Engineers and Scientists. Macmillan Publishing Company
Incorporated
 Ocampo,S &Tresvalles R. 2017.Probability,Statistics, and
Applications. ABIVA Publishing House Inc.
 https://onlinecourses.science.psu.edu/stat500/node
Materials: laptop, projector, and meta strips
ICT Application: powerpoint presentation
Values Integration: cooperation, teamwork, neatness of work, accuracy
and honesty

III. Procedure
A. Preliminary Activities
a. Prayer
b. Greetings
c. Checking of Attendance
d. Passing of Assignment
e. Review of Previous Lesson on the concept statistical inferences
B. Motivation

(Chain-Question Challenge). Teacher will provide one question in

which the first student who can give the correct answer will
automatically receive points for class participation. In return, he will
also ask question to his classmates and will call somebody to give
the answer correctly. This process will be repeated within 3 minutes
only.

A. Lesson Proper
a) Activity
The students will answer the following problems by group for 20
minutes.
 Problem No. 1
A TV manufacturer claims that the life span of its regular TV sets is longer
than 10 years with a standard deviation of 1.5 years. Using a random
sample of their 16 TV sets, the average life span is found to be 11.5 years.
Test the hypothesis that the TV sets’ life span is longer than 10 years at α
= 0.01.

Problem No. 2
A report states that the mean monthly salary of call center agents is Php
22,000 a month. A random sample of the salaries of 81 call center agents
showed a mean monthly salary of Php 23,500 with a standard deviation of
Php 3,000. Is there a significant difference between the reported mean
and sample mean of the salaries of the call center agents? Use α= 0.05

1. Determine if the given problem is a one tailed or two tailed test.

2. Formulate the null and alternative hypotheses.
3. Decide on an appropriate statistical testing procedure. Specify the level of
significance.
4. Find the critical value or tabulated value.
5. Compute the test-statistic or the probability value (p-value).
6. Make a statistical decision.
7. State the conclusion.

Rubrics:
Cooperation – 10 pts
Accuracy – 35 pts ( 5 points each question)
Presentation – 10 pts
Speed - 5 pts

(b) Analysis
1. How will you know that a given problem is a one-tailed or two tailed test?
2. How did you construct the null and alternative hypothesis?
3. What is your basis on determining the statistical testing procedure of the
problem? What is the level of significance?
4. How did you find the t- critical and z-critical value?
5. What process did you used in finding the t- computed?
6. How did you make your conclusion on the problem?

(c) Abstraction
In order for you to come up a correct decision in z-test and t-test using one
population mean, follow the following steps:
1. Identify whether the given problem is a one-tailed or two-tailed test.
(Refer to your guide table)
2. Do the process in hypothesis testing.
2.a Formulate the null and alternative hypotheses.
2.b Decide on an appropriate statistical testing procedure. Specify
the level of significance.
2.c Find the critical value or tabulated value.
2.d Compute the test-statistic or the probability value (p-value).

One-sample mean
 X−μ ( √ n )
z=
δ

X−μ ( √ n )
t=
s

2.e Make a decision

|z computed| ¿ |z critical|
Reject Null Hypothesis

|z computed| ¿ |z critical|
Do not reject Null Hypothesis
2.f Make a conclusion

(d) Application

Compute for the test statistics and draw a conclusion by showing the steps in
hypothesis testing.
1. A supermarket owner believes that the mean income of its customers is Php
50,000 per month. One-hundred customers are randomly selected and asked
of their monthly income. The sample mean is Php 48,500 per month and the
standard deviation is Php 3,200. Is there sufficient evidence to indicate that
the mean income of the customers of the supermarket is Php 50,000 per
month? Use α= 0.05
2. Angel heard that the average grade in Mathematics of her class is at least
88%. She was not convinced by this, and so decided to use hypothesis
testing to check if this claim was true. She got a random sample of 10
classmates who gave their grades in Mathematics as follows: 90, 93, 85, 77,
88, 80, 78, 83, 95, 90. Assume that the distribution of the grades is normal.
Based on this sample data, what would Angel’s conclusion be on the average
grade in Mathematics of her class?

IV. Evaluation
Formulate the appropriate hypotheses on the given situation. Compute for the
test statistics and based from the result draw a conclusion.
1. It is reported that the average monthly salary of accounting graduates
in the accounting field is Php 18,000. A dean of a certain university
conducted a survey of 60 accounting graduates and found their
average salary at Php 20,500 per month with a standard deviation of
Php 1,500 per month. Using α= 0.05, did he find the reported average
salary incorrect?

V. Assignment

Compute for the test statistics and draw a conclusion by showing the
steps in hypothesis testing.
1. The average cost per househould owning a brand new car is 10,000
according to the survey. A group of 45 households has a sample mean
of Php15,000, sample standard deviation of 1,500. Is the average cost
greater than 10,000? Test at 0.01 level of significance.