Republic of the Philippines Department of Education REGION VI – WESTERN VISAYAS SCHOOLS DIVISION OF ILOILO SCHOOLS DISTRICT OF AJUY PUENTE BUNGLAS INTEGRATED SCHOOL AJUY, ILOILO QUARTER I Week 1 – Day 1 Subject: MATH Grade Level: 7 Date: __________________ Session: 1 Content Standard The learner demonstrates understanding of key concepts of sets and the real number system. Performance Standard The learner is able to formulate challenging situations involving sets and real numbers and solve these in a variety of strategies. M7NS-Ia-1 1. Describes well-defined sets, subsets, universal sets, and the null set and cardinality of sets. Competency I. OBJECTIVES • • • Knowledge: Skills: Affective: II. CONTENT Defines sets Illustrates sets Observes the value of cleanliness in illustrating sets SETS III. LEARNING RESOURCES A. References 1. Teacher’s Guide Pages 2. Learner’s Materials Pages 3. Textbook Pages 4. Additional Materials 5. Learning Resources Mathematics – Grade 7 Learner’s Material First Edition, 2013 Pages 1-4 e-Math Intermediate Algebra by Orlando Oronce and Marilyn O. Mendoza, pp. 1-10 Understanding Mathematics Grade 7 by Jose S. Malate & et. al., pp. 1-10 Ruler, pencil, Laptop, and Led TV (LR) portal B. Other Learning Resources IV. PROCEDURES A. Reviewing or presenting the new lesson B. Establishing a purpose for the lesson C. Presenting examples of the new lesson Exploration I. Review the Concepts of Whole Numbers. 1. What are whole numbers? Ans: Positive numbers including zero 2. How are whole numbers represented? Ans: It is represented mathematically by the set: (0,1,2,3,4,5…) II. Recall Roster Method and Rule Method. • What is Roster method or Listing method? (Expected answer: This is a method defining a set by listing all the elements contained in a given set.). • What is Rule Method or Set Builder Notation? (Expected answer: It is a method of defining set by simply describing the elements of a given set clearly) • What is well- defined Set? (Expected answer: A well- defined group of objects, called elements that share a common characteristic. ) About the Lesson: This is an introductory lesson on sets. A clear understanding of the concepts in this lesson will help you easily grasp number properties and enable you to quickly identify multiple solutions involving sets of numbers. Activity A. Identify the objects shown in the pictures. Group them and label each group to answer the given questions. (Prepare this in another sheet) a. How many groups are there? b. Does each object belong to a group? c. Is there an object that belongs to more than one group? What group? D. Discussing new Let us discuss your answers to the questions in Activity A. concepts and practicing new skills #1 1. How many groups are there? There is the group of head covers (hats), the set of trees, the set of even numbers, and the set of polyhedral. But, there is also a set of round objects and a set of pointy objects. There are 6 well-defined sets. 2. Does each object belong to a group? Yes. 3. Is there an object that belongs to more than one set? What groups are these? E. Discussing new concepts and practicing new skills #2 F. Developing Mastery G. Finding practical applications of concepts and skills in daily living H. Making Generalizations and abstractions about the lesson I. Evaluating learning All the hats belong to the group of round objects. The pine trees and two of the polyhedral belong to the group of pointy objects. The teacher discusses the Important Terms to Remember. (Refer to Worksheet –Discusssion) Activity B; I. Use the roster method to give the elements of the set below. a. The set of counting numbers which are multiples of 3 and less than 15. ans. C={ 3,6,9,12 } b. The set of all positive integers greater than 3. ans. O={ 5,7,9,11,13,… } II. Write the rule method of the set with the given elements. a. V= { a, e, i, o, u } ans. V= { vowel of the English alphabet} b. L= { 4,8,12,16,20 } ans. L= { x/ x is counting number divisible by 4 and less than or equal to 20} III. State whether the collection is a well-defined set. a. { a good singer in the Philippines} ans. No, because some people may consider a singer is good while others may not. b. { an even prime number} ans. Yes, because there is only one even prime number which is It is definitely common for us to use the concept of set in everyday experience. • A set of silverware • A set of dishes • A set of tires for car • A set of encyclopedia Give the generalization base on the given examples. 1. Boat, car, bus, airplane 2. Carabao, cow, pig, goat Activity C; I. List the elements of set using roster method. a. The set of counting numbers less than 10. ans. C={ 1,2,3,4,5,6,7,8,9 } b. The set vowels of the word “MISSISSIPPI”. ans. W={ I } II. Write the rule method of the set with the given elements. a. D= { 5,10,15,20,25 } ans. D= { x/ x is counting number divisible by 5 and less than or equal to 25} J. Additional Activities for application or remediation III. State whether the collection is a well-defined set. a. { collection of all Math teachers in a particular school} ans. Yes, because we can identify all Math teachers in a particular school. Activity E; A. Use the roster method to specify the elements of the set given below. a. A= {vowels of the word “Mathematics” }. ans. A={ A,E,I } b. B={ x/ x is a prime number less than ten} ans. B={ 2,3,5,7 } B. Write each of the following using set-builder notations. a. R= { Saturday, Sunday } ans. R={x/ x is a week end day} C. Let A={ x/ x is a whole number less than or equal to 10} Classify each statement as TRUE or FALSE. a. 0 ∈ A ans. FALSE b. 10∈A c. 5∈A V. VI. ans. TRUE ans. TRUE d. -5∈A ans. FALSE e. 12∈A ans. FALSE REMARKS REFLECTION A. No. of learners who earned 80% in the evaluation B. No. of learners who require additional activities for remediation C. Did the remedial lessons work? No. of learners who have caught up the lesson D. No. of learners who continue to require remediation E. Which of my teaching strategies worked well? Why did these work? A. ____ No. Learners who earned 80% in the evaluation B. ____ No. Of learners who require additional activities for remediation. C. Did the remedial lessons work? ____ No. Of learners who have caught up the lesson. D.___ No. Of learners who continue to require remediation. Strategies used that work well: ____ Group collaboration ____ Games ____ Powerpoint Presentation ____ Answering preliminary activities/ exercises ____ Discussion ____ Case Method ____ Think- Pair- Share (TPS) ____ Rereading of Paragraphs/Poems/Stories ____ Differentiated Innnstruction ____ Role Paying/Drama ____ Discovery Method ____ Lecture Method Why? ____ Complete IMs ____ Availability of Materials ____ Pupil’s eagerness to learn ____ Group member’s Cooperation in doing their tasks F. What difficulties did I encounter which my principal and supervisor help me solve? G. What innovation or localized I used/discover which I wish to share with other teacher? ___ Bullying among Pupils ___ Pupil’s behavior/attitude ___ Coloful IM’s ___ Unavailable Technology Equipment (AVR/LCD) ___ Science /Computer/ Internet Lab ___ Additional Clerical works ___ Reading Readiness ATTACHMENT Session: 1 (1 day) Content: SETS DISCUSSIONS: The following are terms that you must remember from this point on. 1. A set is a well- defined group of objects, called elements that share a common characteristic. For example, 3 of the objects above belong to the set of head covering or simply hats (ladies hat, baseball cap, hard hat). 2. Uppercase letters will be used to name sets and lowercase letters will be used to refer to any element of a set. For example, let H be the set of all objects on that cover or protect the head. We write H = {ladies hat, baseball cap, hard hat} This is the listing or roster method of naming the elements of a set. 3. Another way of writing the elements of a set is with the use of a descriptor. This is the rule method. For example, H = {x| x covers and protects the head}. This is read as “the set H contains the element x such that x covers and protects the head.” SUPPLEMENTARY ACTIVITIES Note: The activities included here will be used only when needed. Do the following exercises. 1. Give 3 examples of well-defined sets. ans. Example only a. The set of days in a week 2. Name two subsets of the set of whole numbers using both the listing method and the rule method. Ans. a. A= (1,2,3,4,5) A={ x/x is a counting number from 1 to 5} b. B= (6,12,18,...,48) B={ x/x is a number multiples of 6 from 6 to 48} 3. Let B = [1, 3, 5, 7, 9 }. List all the possible subsets of B. Ans. a. A= (3,6,9) and many more possible subsets