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This is a lesson notes regarding Mathematical system., Lecture notes of Mathematics

West Visayas State University (WVSU)Mathematics
Prof. Mary Ann Dela Vega

The curriculum begins with the foundational elements of set theory and logic, establishing the underlying language and framework for subsequent topics. These foundational concepts are then applied to the study of relations and functions, analyzing their properties and classifications within the context of sets. The notes' overall structure reflects a well-defined mathematical system itself, with each section logically building upon the previous one to create a comprehensive and cohesive understanding of the subject matter.

Typology: Lecture notes

2023/2024

Uploaded on 01/30/2025

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MATHEMATICS / QUARTER 3 / GRADE 8 / Day 1 of Week 3
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content Standards The learners should demonstrate understanding of key concepts of axiomatic structure of geometry and triangle
congruence.
B. Performance
Standards By the end of the quarter, the learners can formulate and organize plan to handle a real-life situation.
C. Learning
Competencies
and Objectives
1. The learners describe a mathematical system.
The learners describe mathematical system in general and its components.
D. Content Mathematical System
E. Integration
II. LEARNING RESOURCES
*Mathematics 8- Most Essential Learning Competencies (MELCS)
*Grade 8 Mathematics Quarter 3 Self-Learning Module: Describing Mathematical System. https://depedtambayan.net/grade-8-mathematics-
module-describing-mathematical-system/
*Mathematical System|Grade 8| Week 1. https://www.youtube.com/watch?v=IskSuV8dvlY
*Mathematical System|Basic geometry: Language and labels.
https://www.khanacademy.org/math/8th-grade-philippines/xa5b1424237e0f2b8:3rd-quarter/xa5b1424237e0f2b8:mathematical-system/v/
language-and-notation-of-basic-geometry
III. TEACHING AND LEARNING PROCEDURE
A. Activating Prior “Word Warp” Instructions:
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MATHEMATICS / QUARTER 3 / GRADE 8 / Day 1 of Week 3 I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES A. Content Standards The learners should demonstrate understanding of key concepts of axiomatic structure of geometry and triangle congruence. B. Performance Standards By the end of the quarter, the learners can formulate and organize plan to handle a real-life situation. C. Learning Competencies and Objectives

  1. The learners describe a mathematical system. The learners describe mathematical system in general and its components. D. Content Mathematical System E. Integration II. LEARNING RESOURCES *Mathematics 8- Most Essential Learning Competencies (MELCS) *Grade 8 Mathematics Quarter 3 Self-Learning Module: Describing Mathematical System. https://depedtambayan.net/grade-8-mathematics- module-describing-mathematical-system/ *Mathematical System|Grade 8| Week 1. https://www.youtube.com/watch?v=IskSuV8dvlY *Mathematical System|Basic geometry: Language and labels. https://www.khanacademy.org/math/8th-grade-philippines/xa5b1424237e0f2b8:3rd-quarter/xa5b1424237e0f2b8:mathematical-system/v/ language-and-notation-of-basic-geometry III. TEACHING AND LEARNING PROCEDURE A. Activating Prior “Word Warp” Instructions:

Knowledge

  1. Group the learners per column based on their sitting arrangement.
  2. Give them the envelope with jumbled letters to form a significant word priory known to Mathematics.
  3. One at a time, learners from each group come up to the chalkboard to paste the word/s they have formed.
  4. Once all words are pasted, discuss as a class how well the learners did. Time to unwarp the word/s they have created. Jumbled letters:  ednfiuend trmes (Undefined terms)  defiened trmes (Defined terms)  oximsa (Axioms)  utsolapte (Postulates)  orehmset (Theorems) B. Establishing Lesson Purpose
  5. Lesson Purpose Observing Systems in Barangay
  6. In your locality/ barangay, which of the following systems do you think is present and how does this system operates/ works? Choose from the following or you can give your own. o Irrigation System: Designing a more efficient system for distributing water to farmlands. This could involve considering water flow, distances, and equitable distribution. o Waste Management: Creating a system for collecting and disposing of waste in an environmentally friendly way, considering factors like distance to recycling centers or landfills. o Community Garden: Designing a community garden, considering plot allocation, crop rotation, and shared resources. o Transportation Network: Improving transportation within the barangay, perhaps considering walking paths, tricycle routes, and accessibility for everyone. o Cooperative System (e.g., palay buying): Designing a system for a cooperative that fairly prices and distributes rice or other agricultural products.
  7. Allow the learners to share their ideas explaining their choices and how their system demonstrates the characteristics of a mathematical system. They should also discuss the challenges and considerations specific

D. Making

Generalizations

Generalization questions for group discussion:

  1. Can you think of real-world examples of systems (not necessarily mathematical) that share similar characteristics to the mathematical systems we've studied? How do these systems use rules, defined terms, and predictable outcomes?
  2. Why are axioms or postulates considered fundamental to a mathematical system? What would happen if we changed or removed an axiom from a system we've studied (e.g., the rule about the sum of angles in a triangle)?
  3. Why is it important to define terms precisely in a mathematical system? What are the potential problems that could arise if terms were not clearly defined? IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER’S REFLECTION A. Evaluating Learning Multiple Choice: Choose the correct answer for each number.
  4. Which of the following is an example of an undefined term? a. angle c. circle b. point d. ray
  5. Which of the following statements is an axiom in Euclidean geometry? a. The sum of the angles in any triangle is 180 degrees. b. A line segment can be extended indefinitely in a straight line. c. The area of a rectangle is length times width. d. The Pythagorean theorem (a² + b² = c² for right-angled triangles). 3.Suppose you are standing in a room with a group of people, and by sight, you see one of them is the tallest. Which of the following best describes the statement that the person is the tallest among the others? Support your answer. a. The statement that is always false. b. The statement cannot be proven to be true or false. c. The statement needs to be formally proven to be accepted as true. d. The statement does not need to be formally proven to be accepted as true.

GLAIZA M. SAROL

Teacher I

Observed:

___________________________

Date of Observation: ___________________________