DAILY LESSON LOG in Statistics and Probability (3rd Quarter)
I. Objectives:
LC: Illustrates a normal random variable and its characteristics.
At the end of the lesson, the learners should be able to:
- Illustrates a normal random variable and its characteristics.
II. Content: Illustrating a normal random variable and its characteristics
III. Learning Resources: Statistics and Probability Alternative Delivery Mode Quarter 3 – Module 3: The Normal Distribution
First Edition, 2020
IV. Procedures:
A. Reviewing previous lesson or presenting the new lesson:
- Ask the students to recall what they have learned in the previous lesson related to probability and statistics.
- Introduce the new lesson by telling them that they will learn about normal random variables and their characteristics.
B. Establishing a purpose for the lesson:
- Tell the students that they will learn how to illustrate normal random variables and their characteristics.
C. Presenting illustrative examples/instances of the lesson:
- Give examples of real-life situations where normal distributions occur, such as height, weight, and test scores.
- Provide handouts with examples of normal distributions and z-scores to help them understand the concept.
Height: The distribution of human height is often described as a normal distribution, with most people falling within a certain range of heights and very few people being much taller or much shorter than average.
Weight: Similarly, the distribution of human weight can also be described as a normal distribution, with most people falling within a certain range of weights and very few people being much heavier or much lighter than average.
Test scores: The scores on many standardized tests, such as the SAT or ACT, are often distributed in a normal distribution, with most students scoring around the average and very few scoring extremely high or extremely low.
Reaction times: The distribution of reaction times for a given task can often be described as a normal distribution, with most people having a reaction time within a certain range and very few people having a significantly faster or slower reaction time.
IQ scores: The distribution of IQ scores across the population is also often described as a normal distribution, with most people having an average IQ and very few people having an exceptionally high or low IQ.
D. Discussing new concepts and practicing new skills #1:
- Divide the students into pairs or groups and assign each group a set of problems related to normal distributions and z-scores.
Instructions:
- Divide the students into pairs or groups. Each group should have at least two students and no more than five.
- Assign each group a set of problems related to normal distributions and z-scores. The problems can be found in the textbook or worksheets that you have prepared.
- Encourage the students to discuss the problems among themselves. They can ask each other questions, share their ideas and strategies, and work collaboratively to solve the problems.
- After the students have completed the problems, ask each group to present their work to the class. This can be done by having each group write their solutions on the board, prepare a PowerPoint presentation, or give a brief oral report.
- While the groups are presenting, ask questions to assess their understanding of the concepts. These questions can be open-ended, such as "How did you arrive at that solution?" or "Can you explain why you used that formula?" Alternatively, they can be more specific, such as "What is the formula for calculating the z-score?" or "What is the standard deviation of a normal distribution?
- Provide feedback to each group on their presentation and problem-solving skills. Encourage them to ask questions if they are unsure about anything and to work collaboratively with their peers
- Collect the assignments and assess them for accuracy and completeness. Provide individual feedback to each student on their strengths and areas for improvement.
By following these instructions, the students will have an opportunity to work collaboratively, develop problem-solving skills, and demonstrate their understanding of the concepts related to normal distributions and z-scores.
E. Discussing new concepts and new skills #2:
- Ask the students to continue discussing new concepts related to normal distributions and z-scores.
- Prepare at least five higher-order thinking questions to deepen their understanding and application of the concepts.
- Let the students present their output in front of the class and assess their responses.
F. Developing mastery (guides formative assessment):
- Give individual sample questions where students can practice solving problems related to normal distributions and z-scores.
- Provide detailed instructions and examples for the activity.
- Allow the students to use calculators to solve problems.
- How can the concept of a normal distribution be applied to real-life situations?
- What are some factors that can affect the shape of a normal distribution?
- Can a data set have more than one normal distribution? Why or why not?
- How can z-scores be used to compare data sets with different means and standard deviations?
- How can understanding the properties of a normal distribution be useful in hypothesis testing or decision-making?
G. Making generalizations and abstractions about the lesson:
- Ask the students to answer questions that will help them crystallize their learning and demonstrate their skills.
H. Finding practical applications of concepts and skills in daily living:
- How can the concept of a normal distribution be applied to real-life situations?
I. Evaluation of Learning:
- Give a five-item multiple-choice quiz to assess their learning.
1. What is the standard deviation of a standard normal distribution?
a. 0
b. 1
c. 2
d. 3
Answer: b
2. What is the formula for calculating the z-score of a data point?
a. (data point - mean) / standard deviation
b. (data point + mean) / standard deviation
c. (mean - data point) / standard deviation
d. (mean + data point) / standard deviation
Answer: a
3. Which of the following is not a characteristic of a normal distribution?
a. It is symmetrical.
b. It is bell-shaped.
c. It has a mean of 0.
d. It has a standard deviation of 2.
Answer: d
4. If a data point has a z-score of 1.5, what percentage of the data falls below this point in a standard normal distribution?
a. 6.68%
b. 22.76%
c. 93.32%
d. 97.72%
Answer: c
5.In a normal distribution, approximately what percentage of the data falls within one standard deviation of the mean?
a. 34%
b. 50%
c. 68%
d. 95%
Answer: c
J. Additional activities for application or remediation:
- Conduct a research project: Have students choose a topic of interest that can be analyzed using normal distribution data (such as the height of NBA players or the IQ scores of a particular group). Have them collect and analyze the data using normal distribution concepts and present their findings to the class. This activity will help them apply the concepts learned in class to a real-life situation and develop their research skills.
(alert-passed) The lesson plan can be adjusted based on the grade level and the available resources. The teacher may also use different strategies to achieve the objectives.
