Polynomials, Inductive and Deductive Reasoning, Axiomatic Structure, Lecture notes of Mathematics

Download Polynomials, Inductive and Deductive Reasoning, Axiomatic Structure and more Lecture notes Mathematics in PDF only on Docsity! Republic of the Philippines Department of Education Region XII Division of Cotabato Amas, Kidapawan City DAILY DETAILED LESSON PLAN School: MATALAM HIGH SCHOOL – JUNIOR HIGH SCHOOL Subject: MATHEMATICS 7 Teacher: ELLEN JOY TORMIS DATE: 02/20-21/2023 CLASS/SECTION / TIME: 7C : MW 1:00 – 3:00 7A : TTH 1:00– 3:00 I. OBJECTIVES A. Content Standar ds demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Perform ance Standar ds Is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions, and solve these problems accurately using a variety of strategies. C. Learnin g Compet encies/ Objectiv es Cognitive: a. Differentiate a polynomial from an algebraic expression; b. Define a polynomial c. Classify degree of a polynomial and the number of terms Psychomo tor: Affective: d. Show appreciation of the concept of polynomials in real life situation. II. CONTENT/SUBJE CT MATTER Polynomials III. LEARNING RESOURCES A. References 1. Teacher’s Guide pages 2. Learner’s Material pages 3. Textbook pages 4. Additional Materials from Learning Resource Portal B. Other Learning Resources Grade 8 LCTG Laptop, LED TV, Powerpoint IV. PROCEDURE A. Reviewing Review: Previous Lesson or Presenting the New Lesson Supply the messing answer in table by identifying parts of an algebraic expression. Given Numerical Coefficient Literal Coefficient Variables Constant 1. 4mn 2. 5x + 10 3. 5x3y4 - 11 4. 7x 5. m3p5 Please do not forget about the LEADING COEFFICIENT and the EXPONENTS in an algebraic expression. B. Establishing a Purpose for the Lesson I. A. Activity 1: Word Hunt Find the following words inside the box BASE CUBIC COEFFICIENT LINEAR DEGREE QUADRATIC EXPONENT QUINTIC TERM QUARTIC CONSTANT BINOMIAL MONOMIAL In the term 3x2, 3 is called the numerical coefficient and x2 is called the literal coefficient. In the term –x has a numerical coefficient which is -1 and a literal coefficient which is x. The term 5 is called the constant, which is usually referred to as the term without a variable. Similar Terms are terms having the same literal coefficients. 3x2 and -5x2 are similar because their literal coefficients are the same. 5x and 5x2 are NOT similar because their literal coefficients are NOT the same. 2x3y2 and -4x2y3 are NOT similar because their literal coefficients are NOT the same. *Note: when you have similar terms in a polynomial, you can combine them by combining their numerical coefficient and copying the literal coefficient. Kinds of Polynomial according to the number of terms 1) Monomial – is a polynomial with only one term 2) Binomial – is polynomial with two terms 3) Trinomial – is a polynomial with three terms 4) Polynomial – is a polynomial with four or more terms Kinds of Polynomials according to degree: 1. Constant – polynomial of degree 0. 2. Linear – degree 1 3. Quadratic – degree 2 4. Cubic – degree 3 5. Quartic – degree 4 6. Quintic – degree 5 7. 6 or more  we call them “polynomial of degree ___ (the degree of the given polynomial) A polynomial is in Standard Form if its terms are arranged from the term with the highest degree, up to the term with the lowest degree. If the polynomial is in standard form the first term is called the Leading Term, the numerical coefficient of the leading term is called the Leading Coefficient and the exponent or the sum of the exponents of the variable in the leading term the Degree of the polynomial. The standard form of 2x2 – 5x5 – 2x3 + 3x – 10 is -5x5 – 2x3 + 2x2 + 3x – 10. The terms -5x5 is the leading term, -5 is its leading coefficient and 5 is its degree. It is a quintic polynomial because its degree is 5 TRY THIS: E. Discussi ng New Concept s and Practici ng Skills # 2 F. Develop ing Mastery (leads to Formative Assessment ) FIND A PAIR! G. Finding Practical Applications of Concepts and Skills in Daily Living - Can you tell some instances where we can apply polynomials in real life? - How important are these? - H. Making Generalizations and Abstractions about the Lesson Generalization: Ask the students the following questions: 1. What are polynomials? 2. How do we say that an expression is a polynomial or not? 3. How do we differentiate a polynomial from an algebraic expression? 4. What are the classification of polynomials according to t=number of terms? How about according to the degree? I. Evaluating Learning Choose the letter of the correct answer. 1. What is the value of a non – zero polynomial raised to 0? a. constant b. zero c. undefined d. cannot be determine 2. It a kind of algebraic expression where each term is a constant, a variable or a product of a constant and variable in which the variable has a whole number (non-negative number) exponent. a. Algebraic expression b. polynomial c. variables d. terms 3. which of the following is TRUE about polynomials and rational algebraic expressions? a. All rational algebraic expressions are polynomials, but not all polynomials are algebraic expressions. b. All algebraic expression are polynomials and vice versa. c. All polynomials are algebraic expressions but not all algebraic expressions are polynomials. d. All polynomials are algebraic expressions and vice versa. 4. Which of the following is a trinomial? a. 3x + y b. 5c – 3d + 4a c. 3a – 2a + 7c d. 3abc 10 5. Which of the following is a quadratic polynomial? a. 3x2 + 2y -10 b. 2x – 11 c. 7abc d. 2x2 - x2 + 10 J. Additional Activities for Application or Remediation Classify the following algebraic expression according to its degree and number of terms. 1. 2x + 7 6.-8x + 3 2. 7x2 -4x + 3 7.x2 -9 3. 10 8.x5 -2x +13 4. x4 + -5x3 + -x2 + 2x -1 9. 100x3 5. 5x5 + 3x3 + -x 10.x4 + 2x3 + -4x2 -6 V. REMARKS VI. REFLECTION A. No. of learners who earned 80% in the evaluation STEM 8_____ 8 A ______ 8 F _____ B. No. of learners who require additional activities for remediation who scored below 80% STEM 8_____ 8 A ______ 8 F _____ C. Did the remedial lesson work? No. of learners who have caught up with the lesson ____ YES STEM 8_____ 8 A ______ 8 F _____ ____ NO D. No. of learners who continue to require remediation STEM 8_____ 8 A ______ 8 F _____ E. Which of my teaching strategies worked well? Why did these work? Teaching Strategies that work well ___Games ___ Peer Teaching ___Group Activities/Group Collaboration ___ 4A’s Approach ___Convergent & Divergent Thinking ___Think-Pair-Share ___ Problem-based Learning ___ Experiential Learning ___ Reciprocal Teaching ___ Differentiated Instruction ___ Inquiry-based Learning ___ Discussion ___Chalk & Talk Method (Lecture Method) ___ Case Method ___ Power Point Presentation ___ Role Playing/Drama Why? ___ Complete IMs ___ Availability of Materials ___ Learners’ eagerness to learn ___ Group members’ cooperation in doing their tasks F. What difficulties did I encounter which my principal or ___ Bullying ___ Learners’ behaviour/attitude ___ Colorful IMs ___ Unavailable Technology ___Equipment (AVR/LCD) ___ Reading Readiness ___ Additional Clerical Work ___ Science Computer/Internet Lab