7 Mathematics First Quarter LEARNING ACTIVITY SHEETS Practice Personal Hygiene protocols at all times. i COPYRIGHT PAGE Learning Activity Sheet in MATHEMATICS GRADE 7 Copyright © 2020 DEPARTMENT OF EDUCATION Regional Office No. 02 (Cagayan Valley) Regional Government Center, Carig Sur, Tuguegarao City, 3500 “No copy of this material shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit.” This material has been developed for the implementation of K to 12 Curriculum through the Curriculum and Learning Management Division (CLMD). It can be reproduced for educational purposes and the source must be acknowledged. Derivatives of the work including creating an edited version, an enhancement of supplementary work are permitted provided all original works are acknowledged and the copyright is attributed. No work may be derived from this material for commercial purposes and profit. Consultants: Regional Director : ESTELA L. CARIÑO, EdD., CESO IV, DepEd R02 Assistant Regional Director : RHODA T. RAZON, EdD,CESO V, DepEd R02 Schools Division Superintendent : CHERRY S. RAMOS, EdD,, CESO V, Santiago City Asst. Schools Division Superintendent: CHERYL R. RAMIRO, PhD, CESE, Santiago City Chief Education Supervisor, CLMD : OCTAVIO V. CABASAG, PhD Chief Education Supervisor, CID : JANETTE V. BAUTISTA, EdD Development Team Writers: JOY ALPHA FLOR C.DELEON, Patul NHS, Stgo City EMERSON R. RESPONZO, CRISEL C. BISTANTE & ROMMEL A. SIMON Patul NHS, Stgo City MARJORIE INGARAN, Sinili, Integrated School, Santiago City ALELI C. VALERIANO, MELY CABUDOL & PRIMAROSE SALES, Cabulay HS, Santiago City GEORGE M. VIBA, GERADINE CANLAS & LEONARD B. SAMBILE, Rizal National HS RANDY B. TOLENTINO,Balintocatoc IS, MARK JOSEPH L. LEAL, San Jose IS LEILANI T. SANTIAGO & MYRNA GUIRING, Santiago City NHS JUN-JUN DARIANO Sagana NHS GEE P. BALTAZAR, Divisoria NHS CRISTOBAL FELIPE, Rosario NHS Content Editors: JACKILYN ALAMBRA, Santiago City National High School, Santiago City EMERITA MAWIRAT, Rosario National High School , Santiago City MARIO P.MABALOT, Principal I, Santiago City ENRIQUE GARCIA, MAI RANI ZIPAGAN Language Editor: PERFECTA BAUTISTA, Education Program Supervisor– English Illustrators: Layout Artists: EARL AARON O. VILLANOZA,Sagana National High School , Santiago City JENELYN B. BUTAC, Division Librarian Focal Persons: NILO A. CANTOR., Division Education Program Supervisor– Mathematics MARIVEL G. MORALES, Division LRMDS Coordinator ISAGANI R. DURUIN, PhD., Regional Education Program Supervisor– Mathematics RIZALINO G. CARONAN, Regional Education Program Supervisor–LRMDS Printed by: Curriculum and Learning Management Division DepEd, Carig Sur, Tuguegarao City Practice Personal Hygiene protocols at all times. i Table of Contents Competency The learner illustrates well-defined sets, subsets, universal sets, null set, cardinality of sets and the difference of two sets Page Number ----- 1-7 The learner solves problems involving sets with the use of Venn Diagram ----- 8-13 The learner represents the absolute value of a number on a number line as the distance of a number from 0 ----- 14-21 ----- 22-40 ----- 41-45 Express rational numbers from fraction form to decimal form and vice versa. ----- 46-54 The learner performs operations on rational numbers. ----- 55-65 The learner describes principal roots and tells whether they are rational or irrational ----- 66-69 ----- 70-76 The learner performs fundamental operations on integers The learner illustrates the different properties of operations on the set of integers. The learner determines between what two integers the square root of a number is The learner estimates the square root of a whole number to the nearest hundredth The learner plots irrational numbers (up to square roots) on a number line. Practice Personal Hygiene protocols at all times. ---- 77-85 ___ 86-89 ii Illustrates the different subsets of real numbers ----- 90-96 The learner arranges real numbers in increasing or decreasing order and on a number line ----- 97-103 The Writes numbers in notation and vice versa scientific ----- 104-107 The learner represents real-life situations and solves problems involving real numbers ---- 108-115 Practice Personal Hygiene protocols at all times. iii MATHEMATICS 7 Name of Learner: ________________________________ Section: _________________________________________ Grade Level: _____ Date: ____________ LEARNING ACTIVITY SHEET The Set Virus Background Information for Learners This activity sheet serves as a self-learning guide for the learners. It facilitates lesson as it specifically aims for students’ mastery on the world of sets. 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 Important Terms to Remember 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. The term well defined means that given a set and an object, one can clearly determine whether that object belongs to the set or not. A set is usually denoted by a capital letter. For example, set of vowels in the alphabet: V = {a, e, i, o, u} 2. The set F is a subset of set A if all elements of F are also elements of A. For example, the even numbers 2, 4 and 12 all belong to the set of whole numbers. Therefore, the even numbers 2, 4, and 12 form a subset of the set of whole numbers. F is a proper subset of A if F does not contain all elements of A. 3. The universal set U is the set that contains all objects under consideration. The set of all letters in the alphabet could be a universal set from which the set {a,b,c,d,…..z} could be taken. 4. The null set ᴓ is an empty set. The null set is a subset of any set. The set of months in a year with 35 days is considered as null set because there is no months with 35 days. 5. The cardinality of a set A is the number of elements contained in A. Supposed set A is the vowels in the alphabet. Its cardinality is 5 because there are just 5 vowels {a, e, i, o, u} in the alphabet. 6. The difference of two sets A and B, denoted by A – B (read as A minus B), is the set that contains all elements of A that are not in B. In some cases, the symbol “\” is also used to mean difference. Suppose set A = {1,3,5} and set B = {2,3,4}, when we take its difference the result will be {1,5}. Practice Personal Hygiene protocols at all times. 1 Learning Competency with code The learner illustrates well-defined sets, subsets, universal sets, null set, cardinality of sets ,union and intersection of sets and the difference of two sets (M7NS-Ia-1,& M7NS-Ia-2) Directions: Different activities were prepared for you to be well versed on the concept of Sets. Activity 1 SET IT UP! Write S if the given group or collection is a set and NS if it is not. Write your answer on the space provided before each number. _______1. Collection of students in your class whose surname starts with letter A. _______2. Countries in Asia affected by covid-19 _______3. Collection of distinct letters of the word “PANDEMIC” _______4. Group of cities in the province of Isabela _______5. Group of enjoyable subjects in high school _______6. Group of students in your class who wear mask _______7. Collection of hygiene kits for sanitation _______8. Group of major TV stations in the Philippines _______9. Group of good schools in Santiago City _______10. Cities in Metro Manila under ECQ(Enhanced Community Quarantine) Activity 2. ARE YOU POSITIVE OR NOT? Draw on the space provided before each item if the given set is a subset of A. If it is not then draw . Given: A = { c,o,r,o,n,a,v,i,r,u,s,o,u,t,b,r,e,a,k} _______1. {c, r, n, v, s, t, k} _______2. {a, e, i, o, u} _______3. {set of all consonants in the alphabet} _______4. {x/ x is a vowel in the alphabet} _______5. {set of even numbers} _______6. {set of odd numbers} _______7. {alcohol, sanitizer, soap} _______8. {USA, China, Italy, Japan, Philippines} _______9. {a, b, c, d, e} _______10. {u, v, w, x, y, z} Practice Personal Hygiene protocols at all times. 2 Activity 3. UNIVERSAL IT IS! A. List all the elements on the universal set for the following sets 1. A = { a, b, c, d, e} B = { a, e, i, o, u} U = ___________________________ 2. C= { letters of the word novel} D = { letters of the word corona} E = { letters of the word virus} U = ____________________________ 3. F = { 2, 4, 6, 8, 10} G = {1, 3, 5, 7, 9} U = ____________________________ 4. H = { N95 mask, gloves, goggles} I = {gowns, aprons, face visors} U = ____________________________________________________________________ 5. J= {set of prime numbers less than 10} K = { set of even numbers less than 10} U = ____________________________________________________________________ B. Identify a possible universal set from which the following sets could be chosen. 1. { working pass, travel pass, financial travel pass} Set of _________________________________________ 2. { basketball, volleyball, badminton, futsal, boxing} Set of _________________________________________ 3. { doctors, nurses, police, military, LGU} Set of _________________________________________ 4. { Math, Science, English} Set of _________________________________________ 5. { social distancing, stay at home, hand washing, wear mask, exercise} Set of _________________________________________ Activity 4. MY EMPTINESS AND PHOBIA! “Are you afraid of viruses, germs, bacteria? Then you are ____________” Practice Personal Hygiene protocols at all times. 3 To answer this, cross out the pair of letters that corresponds to null or empty set in the box below. There will be 5 boxes left after. Decode the remaining letter from left to right, top to bottom. Place the letter of your answer on the answer box. One letter per box. AB Set of 3 legged human PH Set of quarantine pass during ECQ MY Set of vowels in the alphabet XY Set of dogs with 6 legs RP Set of cars with 10 doors JR Set of integers which are both even and odd LN Set of vaccines that can treat corona virus EF Set of schools in the Philippines who conducted graduation S.Y. 2019-2020 physically in their respective schools SO Set of even numbers RH Set of newly born babies who can walk CD Set of months with 33 days OB Set of qualified family social status that will be given SAP PS Set of humans living in planet MARS TP Set of humans with multiple lives IA Set of countries affected by covid-19 UV Set of squares with 5 sides Note: Letters that are not crossed out will correspond to the name of the phobia Answer: Activity 5. Where does corona virus outbreak started? __________________ To answer this, identify the cardinality of the following set. Match your answer from the choices on the right and write the corresponding letter of the correct answer in the box at the left of number. 1. {a, e, i, o, u} N1. 2. {set of days in a week} I. 120 3. {set of vowels in the word “PANDEMIC”} H2. 12 4. { set of non-repeated consonant letters in the word H1. 3 Practice Personal Hygiene protocols at all times. 9 4 “FRONTLINERS”} 5. {rice, coffee, powdered milk, sugar, noodles, sardines, corned beef, soap, alcohol} C. 0 6. {empty set} U. 7 7. {set of months in a year} A1. 6 8. {100,200, 300, …….12000} W. 5 9. {USA, Italy, Spain, Germany, China, France, Iran, United Kingdom, Switzerland, Turkey} A2. 11 10. {N95 mask, surgical gloves, goggles, medical gowns, aprons, face visors, face shields, respirators, protective clothing, helmets, biohazard bags } N2. 10 Answer: _______________________________________________________________ Activity 6 THE HIDDEN MESSAGE What is the hidden message written below despite this pandemic outbreak of corona virus? To answer, shade the elements of the result of the difference of two sets on each of the following number. 1. A= { c, o, r, o, n, a} - B= {v, i, r, u, s} C O O R A c v o r a c v n n a 5. A = { r,e,p,a,c,k} -B = {r,e,l,i,e,f} P A A L K p r a f k p e c c k 2. A = {a, e, i, o, u} -B = {a, b, c, d ,e} i a a a a i o o u u i e e e e f n f w s 2 4 4 6 6 2 1 6 3 7 2 8 8 10 10 7.A = {1,2,3…10} -B = {2,4,6…10} 6. A = {f, a, k, e} -B = {n, e, w, s} f a a a a 3. A= {2,4,6,8,10} -B = {1,3,5,7,9} f k k k k 1 3 3 5 5 1 2 7 6 10 1 4 9 8 10 4. A = {w, e, a, r} -B = {m, a, s, k} w w m m a a e e r r w w s k k 8. A = {4,8,12…40} -B = {2, 4, 8…64} 12 12 28 28 40 20 4 36 16 40 24 8 36 32 40 Reflection Complete this statement: I have learned that … Practice Personal Hygiene protocols at all times. 5 ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ __________________________________________________________________________. References Math 7 Teaching Guide Oronce, O. & Mendoza, M.(2012) E-Math Malvar, M. et al. (2014) Simplified Math https://www.who.int/medical_devices/meddev_ppe/en/ https://www.pharmaceutical-technology.com/features/covid-19-coronavirus-top-ten-mostaffected-countries/ Answer Key Activity 1 1. S 2. S 3. S 4. S 5. NS 6. NS 7. S 8. S 9. NS 10. S 2. sports 3. frontliners 4. major subject 5. rules during covid-19 outbreak Activity 2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Activity 3 A. 1. {a,b,c,d,e,i,o,u} 2. { a,c,e,i,l,n,o,r,s,u,v} 3. {1,2,3,4,5,6,7,8,9,10} 4. {aprons, facemask, gloves, goggles, gowns, N95 mask} 5. {2,3,4,5,6,7,8} B. 1. quarantine pass Practice Personal Hygiene protocols at all times. 6 Activity 4 X X AB Set of 3 legged human MY Set of vowels in the alphabet SO Set of even numbers CD Set of months with 33 days PH Set of quarantine pass during ECQ XY Set of dogs with 6 legs UV Set of squares with 5 sides JR Set of integers which are both even and odd LN Set of vaccines that can treat corona virus RH Set of newly born babies who can walk TP Set of humans with multiple lives OB Set of qualified family social status that will be given SAP PS Set of humans living in planet MARS IA Set of countries affected by covid-19 X X X RP Set of cars with 10 doors X EF Set of schools in the Philippines who conducted graduation S.Y. 2019-2020 physically in their respective schools X M Y S X X X Answer: P H O Activity 5 1. W 2. U 3. H1 4. A1 5. N1 O X B I A 6. C 7. H2 8. I 9. N2 10. A2 Activity 6 1. c o o r a 2. c v o r a c v n n a 5. 3. i a a a a i o o u u i e e e e 6. p a a l k p r a f k p e c c k 4. 2 4 4 6 6 2 1 6 3 7 2 8 8 10 10 7. f a a a a f n f w s f k k k k w w m m a a e e r r w w s k k 12 12 28 28 40 20 4 36 16 40 24 8 36 32 40 8. 1 3 3 5 5 1 2 7 6 10 1 4 9 8 10 Prepared by: JOY ALPHA FLOR C. DE LEON EMERSON R. RESPONZO T-III, Patul National High School 7 MATHEMATICS 7 Name of Learner: ________________________________ Grade Level: _____ Section: ________________________________________ Date: ____________ LEARNING ACTIVITY SHEET SOLVE PROBLEMS INVOLVING SETS USING VENN DIAGRAM Background Information for Learners This learning activity sheet is about solving problems involve using Venn diagram. The activity encourages students to learn, to help direct students’ learning out-of-class and a good way to choose practice or drill their skills on the concepts of Venn diagram. A Venn diagram is used to organize a list of data. Set can be represented in a Venn diagram. Circle are drawn inside a rectangle representing the universal set. The overlapping region in the Venn diagram is called the “Intersection” of the set while the “Union” is the combination of all elements of A and B (or the circle inside the rectangle). In a simplest manner, A Venn diagram is a diagram with one or more circles on closed regions representing sets. A rectangle can be drawn around the Venn diagram to represent the universal set. The figures below are the models for representing the operations on sets which is somewhat similar to the basic operations on numbers. Four Basic Operations on Sets 1. Union of sets A and B A U B = set of all elements found in A or B or both Example : A = {a, b, c, d, e} , B = {b, c, f, g, h} = { a, b, c, d, e, f ,g } In General, A U B = {a, b, c, d, e, f ,g} 2. Intersection of Sets A and B A ∩ B = Set of all elements common to set A and Set B Example : A ={ 1, 2, 3, 4 } , B={3, 4,5, 6,} = { 3,4} In General A ∩ B = { 3,4} 3. Complement of a set A A’ = Set of all elements in the universal set but not found in A Example: A = {1,2}, U= {1,2,3,4,5 } A’= {3,4,5} In General = A’ U U= {3,4,5} Practice Personal Hygiene protocols at all times. 8 4. Difference of Sets A and B A-B = Sets of all elements in A but not in B B-A = Sets of all elements in B but not in A Example : A= {4,5,6,7}, B= {1,6,7,8,9) A-B {4,5} , B -A {1,8,9} Example : Soaring with 95% In a class of 40 students ; 25 got an average of 95 in English ; 17 have an average of 95 in Mathematics , 7 have an average of 95 in Mathematics and English U = 40 English 18 Mathematics 7 10 5 This Photo by Unknown Author is licensed under CC BY-NC-ND a. How many students have an average of 95 in English only? b. How many students have an average of 95 in Math Only? c. How many student do not have an average of 95 in Math and English? Solution : a. For Students who have an average of 95 in English only 25-7 = 18 students have an average 95 in English only b. For Students who have an average of 95 in Math only 17-7 = 10 students have an average of 95 in Math only c. Students that does not have an average of 95 in both English and Math 40 - [18 +7 +10 ] = 5 students does not have an average of 95 in both Math and Science Learning Competency (Quarter 1, Week 2) Solve problems involving sets with the use of Venn Diagram. (M7NS-Ib-2) Practice Personal Hygiene protocols at all times. 9 Activity 1. WEBINAR ! NEW NORMAL Directions/Instructions: Let us try to solve the following problem: Venn diagram is already drawn for you, just fill up your answer on the given illustrations below ,and answer the following questions. SCIENCE MATH In a group of 35 students who joined the online activity in Math and Science webinar 28 of these students are in Science club and 20 of them are in Math club a. How many have joined in Science club only? b. How many have joined in both Club? Guide Questions: 1. In evaluating the sets what method did you use? _______________ Why? 2. Did you compare set A and Set B? What relationship exists between the two sets? How? 3. What symbol did you use to emphasize the intersection? Why? 4. What can you conclude regarding on the operation of sets? Why? Practice Personal Hygiene protocols at all times. 10 Activity 2. I CAN MAKE IT!, BELIEVE ME I CAN ! This Photo by Unknown Author is licensed under CC BY-SA-NC (Option A) (Option B) This Photo by Unknown Author is licensed (Option C) under CC BY-SA-NC Direction : A Venn diagram is already drawn for you just fill in the empty sets to correspond your answer inside the universal set. Online Actual 50 students was surveyed through social media bout their option of classes they most prefer for this coming opening of school year , 15 of the students wants online schooling 20 of the students wants actual face to face schooling 7 students want both option. a. b. c. d. How many students want online schooling only? How many students want actual face to face schooling only? How many students want at least two scheme of classes? How many students do not want any of the two option? Guide Questions: 1. How did you evaluate the problem? 2. How did you make the intersection of set? 3. Does set A, Set B and Set C related with one another? 4. What operation did you used in finding the intersection of the three sets? Practice Personal Hygiene protocols at all times. 11 Activity 3: CONGQUER MY TALENT! (Dancing) This Photo by Unknown (Singing) Author is licensed under CC BY-NC This Photo by Unknown ( Painting) Author is licensed under CC BY-SA Directions: A Venn diagram is already drawn for you just fill in the empty sets to correspond your answer inside the universal set. 100 students were enrolled in Special Performing Arts Class, 27 are inclined in singing 42 are inclined in dancing 35 are inclined in painting 15 are both inclined in singing and painting 18 are both inclined in dancing and singing 20 are both inclined in painting and dancing 10 are all inclined into the three performing arts a. b. c. d. e. f. g. h. i. j. How many are into singing only? How many are into dancing only? How many are into painting only? How many students are both inclined in both singing and dancing but not painting? How many students are both inclined in both painting and dancing but not singing? How many students are both inclined in both singing and painting but not dancing How many students are both inclined into either singing or dancing? How many students are both inclined into either dancing or painting? How many students are both inclined into either singing or painting? How many students are not into any of the tree performing arts ? *** both inclined in singing and dancing both inclined in painting and dancing Guide Question: 1. How did you evaluate the problem? 2. What method did you use in identifying sets? 3. How did you make the intersection of the set? 4. Does set A, Set B and Set C related with each other? How? 5. What operation did you used in finding the intersection of the three sets? Practice Personal Hygiene protocols at all times. 12 Activity 4: Sporty Venn Diagram Directions/Instructions: The diagram below shows the different outdoor sports played by ten (10) students last month. Use the Venn diagram to answer the questions. Reference: Volleyball (V) Basketball (B) Sepak Takraw (S) V B Anne Bing Rona Rey Ben Kris Fe Al Rob Bill S Questions: 1) How many students played Volleyball and Basketball? _____ 2) How many students played Basketball and Sepak Takraw? _____ 3) How many students played Volleyball and Sepak Takraw? _____ 4) How many students played ONLY Volleyball? _____ 5) How many students played ONLY Basketball? _____ 6) How many students played ONLY Sepak Takraw? _____ 7) V ∪ B _______________________________________________ 8) (V ∩ B ) ∪ S _______________________________________________ 9) V – B _______________________________________________ 10)V ∩ B ∩ S _______________________________________________ Reflection I have learned that ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ References Curriculum Guide in Grade 7 Mathematics Learning Modules in Grade 7 Mathematics Books : College Algebra with Recreational Mathematics by Benjamin Concepcion, Chastine Najjar, Prescilla Altares, Sergio Ymas, E-Math Worktext in Mathematics by Orlando Oronce and Marilyn O. Mendoza Prepared by:JULIE BACTAD AGCAOILI-Rosario NHS/ JHOANNA D. BALAYANSaganaNHS Practice Personal Hygiene protocols at all times. 13 MATHEMATICS 7 Name of Learner: ________________________Grade Level: ______________ Section: _______________________________ Score: ___________________ LEARNING ACTIVITY SHEET ABSOLUTE VALUE Background Information for Learners A number line is a line with numbers placed in the right order. It is an infinite line which points represent the real numbers. It is divided into two symmetric halves by the origin that is the number zero. The absolute value of a number is the distance on the number line between the number and zero without any regard to its direction. Since you are only counting the distance, absolute values are always positive values. Absolute value bars surround the number being evaluated. Two vertical bars | | denote the absolute value of a number. For example: |5| = 5 and |-5| = 5. The absolute value of a positive number is the number itself. The absolute value of a negative number is the opposite of the negative number and the absolute value of zero is zero. This is best illustrated on the number line below: Expressions with absolute value symbol can be simplified. The absolute value of a number is the number of units it is away from 0 on the number line. For example: |x| = 2. Using the number line, the distance from 0 to x is 2 units. Therefore x = -2 and x = 2. Practice Personal Hygiene protocols at all times. 14 Furthermore, to solve and illustrate |x - 4| = 3 using the number line, x must be a number whose distance from 4 is 3. Thus, think of starting at 4 and moving 3 units in both directions on the number line. The solutions can be illustrated as the figure below: Therefore, x is equal to 1 or 7. The diagram shows that |x - 4| = 3 is equivalent to: |x - 4| = 3 x – 4 = -3 x = -3 + 4 x=1 or |x - 4| = 3 x–4=3 x=3+4 x=7 Learning Competency with code Represents the absolute value of a number on a number line as the distance of a number from 0 (M7NS-Ic-1) Directions/Instructions Exercises 1. GIVE ME MY VALUE! Give the absolute value of each of the following. Each correct answer corresponds to 1 point. 1. 2. 3. 4. 5. |10| |13| |48| |-74| |-85| 6. |93| 7. |-103| 8. |-127| 9. |133| 10. |165| Exercises 2. THE SANTIAGO CITY BARANGAY TOUR. Tell whether how far a barangay in Santiago City from the other barangay as shown in the picture below. Each correct answer corresponds to 1 point. Practice Personal Hygiene protocols at all times. 15 1. How far would Calao West be from Dubinan East? 2. How far when you travel from Calao West to Malvar given the route above? 3. If you are from Plaridel and you would like to visit your mom in Malvar, how far would you travel from your place? 4. Ana travelled from Dubinan West to Calao West while Robert travelled from Plaridel to Malvar. Who travelled the greater distance, Ana or Robert? Why? 5. What is the total distance travelled by Ana and Robert? Exercises 3. COME AND ILLUSTRATE. Illustrate using the number line. Each correct illustration corresponds to 2 points each. Practice Personal Hygiene protocols at all times. 16 Exercises 4. SOLVE AND PROVE. Solve and illustrate using the number line. 1. |x - 2| = 5 2. |x + 6| = 3 3. |x + 8| = 6 4. |x - 5| = -8 5. |x + 1| = -10 Reflection Complete the statement below. I have learned that ____________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________ Practice Personal Hygiene protocols at all times. 17 References A. Books 1. Orance, O. and Mendoza, M., 2015. E- Math 7. 1st ed. 586 Nicanor Reyes St., Sampaloc Manila: Rex Book Store, pp.35-38. 2. De Leon, C. and Bernabe, J., 2002. Elementary Algebra. 1281 Gregorio Araneta Avenue, Quezon City: JTW Corporation, pp.32-33. 3. 2013. Mathematics Grade 7 Teacher's Guide. 1st ed. 2nd Floor Dorm G, Philsports Complex, Meralco Avenue, Pasig City, Philippines 1600: Department of Education, pp.94-100. 4. Aseron, E., Armas, A., Canonigo, A. and Garces, I., 2013. Mathematics – Grade 7 Learner’S Material. 1st ed. 2nd Floor Dorm G, Philsports Complex, Meralco Avenue, Pasig City, Philippines 1600: Department of Education, pp.70-75. B. Website Arias, L., 2019. Positive And Negative Numbers, Oh My!. [online] Google Books. Available at: <https://books.google.com.ph/books?id=TQXDwAAQBAJ&printsec=frontcover&dq=absolute+value+of+a+number&hl=en&sa= X&ved=0ahUKEwim09GS_cvpAhWuBKYKHd_bB94Q6AEIJjAA#v=onepage&q=a bsolute%20value%20of%20a%20number&f=false> [Accessed 24 May 2020]. 2. Kolby, J., 2020. ACT Math Prep Course. [online] Google Books. Available at: <https://books.google.com.ph/books?id=NQ_CBgAAQBAJ&pg=PA131&dq=absolut e+value+of+a+number&hl=en&sa=X&ved=0ahUKEwim09GS_cvpAhWuBKYKHd _bB94Q6AEIdzAJ#v=onepage&q=absolute%20value%20of%20a%20number&f=fal se> [Accessed 20 May 2020]. 3. Aufmann, R. and Lockwood, J., 2020. Course Companion For Basic College Mathematics: Powered By Enhanced Webassign. [online] Google Books. Available at: <https://books.google.com.ph/books?id=BoXbkVg325sC&pg=RA34. Marshall, S., n.d. Rubric For Short-Answer Math Problems. [online] Hosting.astro.cornell.edu.Available at: <http://hosting.astro.cornell.edu/~seanm/Sean_Marshall_rubrics.pdf> [Accessed 20 May 2020]. 1. Others: 1. STARBOOKS. 2020. Absolute Value of A Number. 2. Word Search 3. Google Map Practice Personal Hygiene protocols at all times. 18 Answer Key Exercises 1. Give Me My Value 1. 10| 6. 93 2. 13 7. 103 3. 48 8. 127 4. 74 9. 133 5. 85 10. 165 Exercises 2. The Santiago City Barangay Tour 1. 2.5 km 2. 10.9 km 3. 5.3 km 4. Robert; 5.3 km > 3.7 km 5. 10.1 km Exercisers 3. Come and Illustrate. Practice Personal Hygiene protocols at all times. 19 Exercises 4. SOLVE AND PROVE. Solve and illustrate using the number line. 1. |x - 2| = 5 |x - 2| = 5 x - 2 = -5 x = -5 + 2 x = -3 or |x - 2| = 5 x-2=5 x =5+2 x=7 or |x + 6| = 3 x+6=3 x =3-6 x = -3 or |x + 8| = 6 x+8=6 x=6–8 x = -2 Therefore: 2. |x + 6| = 3 |x + 6| = 3 x + 6 = -3 x = -3 - 6 x = -9 Therefore: 3. |x + 8| = 6 |x + 8| = 6 x + 8 = -6 x = -6 – 8 x = -14 Therefore: 4. |x - 5| = -8 Practice Personal Hygiene protocols at all times. 20 |x - 5| = -8 x - 5 = -8 x = -8 + 5 x = -3 or |x - 5| = -8 x-5=8 x=8+5 x = 13 or |x + 1| = -10 x + 1 = 10 x = 10 – 1 x=9 Therefore: 5. |x + 1| = -10 |x + 1| = -10 x + 1 = -10 x = -10 – 1 x = -11 Therefore: Prepared by: Gee P. Baltazar Teacher III Practice Personal Hygiene protocols at all times. Mely C. Paulino Teacher III 21 MATHEMATICS 7 Name:_____________________________________ Section:____________________________________ Grade Level_______ Date:____________ LEARNING ACTIVITY SHEET Addition of Integers Background Information for Learner/Concepts Integers are whole numbers that are positive or negative including zero. Negative integers are numbers less than zero found at the number line from the left of zero and hold a negative sign. Examples are -1, -5, -8, -12, -18, etc. while positive integers are numbers greater than zero located at the right side of zero in the number line. This sign(+) indicates positive integer. However, the sign is not always needed. Numbers like +3 or 3, +6 or 6, +9 or 9, +13 or 13, etc. are examples of positive integers. Zero on the otherhand is located in between the positive and negative integers in the number line. A number line is a horizontal line with numbers that are placed equal distance apart and are sequentially numbered. Below is an illustration of negative and positive integers using the number line. Rules for Adding Integers RULE # 1 In adding two integers having the same sign, add the numbers and copy their common sign. Examples: 1. 9 + 3 = 12 2. 17 + 6 = 23 3. -5 + -9 = -14 4. – 4 + - 15 = - 19 Number 1 and 2 are both positive while 3 and 4 are negative. Examples: 1. -10 + 4 = -6 The difference is 6 and the sign of the In adding two integers larger number is negative, so the sign of the with different sign, sum is negative. Rule # 2 subtract and copy the sign 2. -5 + 8 = 3 of the larger number. The difference is 3 and the sign of the larger number is positive, so the sign of the sum is positive 3. 15 + (-6) = 9 Practice Personal Hygiene protocols at all times. 4. -25 + 17 = -8 22 Addition of Integers using the number line 1. Use the number line to find the sum of 3 and 7. ( 3 & 7 are both positive) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 On the number line start with point 3 and count 7 units to the right. At what point on the number line does it stops? It is at point 10, hence, 3 + 7 = 10. 2. Find the sum of -2 and -5. ( -2 & -5 are both negative) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 On the number line start with point -2 and count 5 units to the left. At what point on the number line does it stops? It is at point -7, hence, -2 + -5 = -7. 3. Find the sum of -8 and 4. ( adding a negative, a larger number and a positive number, the smaller number) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 On the number line start with point -8 and count 4 units to the right. At what point on the number line does it stops? It is at point -4, hence, -8 + 4 = -4. 4. Find the sum of -4 and 9.(adding a negative number, smaller and a positive which is larger number) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 On the number line start with point -4 and count 9 units to the right. At what point on the number line does it stops? It is at point 5, hence, -4 + 9 = 5. SUMMARY: Addends ┼ Addends ┼ Sum ┼ ┼ ┼ ┼ LEARNING COMPETENCY and Code Performs fundamental operations on integers Practice Personal Hygiene protocols at all times. ( M7NS-Ic-d-1) 23 ACTIVITY I. SHOW ME THE WAY: integers. 1. 3 + 6 -4 -3 -2 -1 Use the number line to find the sum of the following 0 1 2 3 4 5 6 7 8 9 10 2. -4 + -1 -7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7 3. -7 + 2 -7 -6 4. 8 + -3 -5 -4 -3 -1 0 1 2 3 4 5 6 7 -2 -1 0 -3 -2 -1 3 1 2 3 4 5 6 7 8 9 10 5. 10 + -5 II. III. Name 1. 2. 3. 4. 5. 0 1 2 3 4 5 6 7 8 9 10 Find the sum of each of the following. 1. 3 + 8 = _____________ 6. -9 + -10 = _________ 2. -4 + -2 = _____________ 7. -20 + 7 = __________ 3. -10 + 15 = _____________ 8. – 5 + 12 = __________ 4. 7 + -10 = _____________ 9. 13 + -6 = __________ 5. 15 + 9 = ______________ 10. -4 + 0 = _________ BEYOND COMPARE: The table shows the scores obtained by the five players in a game. Following the rules in adding integers find the total score of each player. Round 1 Round 2 Total Score Beth 19 8 Zeny -2 12 Aida -5 -7 May 23 -11 Jona 16 -7 Practice Personal Hygiene protocols at all times. 24 Use the table to answer the following questions: 1. 2. 3. 4. IV. Find the total score for each player. Whose player had the lowest score? Whose player has the highest score? Who was the best player? LEARN ON ME. : The integers -10, -8, -6, -4, -2, 0, +2, +4, +6, and +8 are assigned to the letters W, L, E, O, A, T, M, E, H, V respectively. A word is formed by using these letters. Find the sum of the integers in the word formed. (Letters can be used more than once) W(-10) L(-8) E(-6) V(8) E(4) H(6) T(0) O(-4) Example: WE ----------------V. GO for MASTERY: M(2) A(-2) -10 + 4= -6 Solve the following problems. Show your solutions. 1. It will be 380 tomorrow. The weatherman predicts it will increase 2 0 in the afternoon. What will be the new temperature? 2. A submarine was situated 700 feet below sea level. I it goes up 300 feet, what is its new position? 3. Leny bought 2 pieces of jeans at 850 pesos each. How much did she pay to the cashier? 4. Rubric for rating Activity I and II Score Descriptions 4 The computations are accurate. A wise use of the rules of addition of integers are evident. 3 The computations are accurate. Use of the rules of addition of integers are evident. 2 The computations are erroneous and show some use of the rules of addition of integers . 1 The computations are erroneous and do not show some use of the rules of addition of integers . Rubric for rating Activity III and IV Score Descriptions 4 Student explains the rules of adding integers and be able to apply in solving problems.. 3 Student demonstrates an understanding the rule of adding integers. 2 Student understands the rule of operations but is inconsistent in solving 1 Student needs assistance in adding integers. Practice Personal Hygiene protocols at all times. 25 Rubric for rating the Solving Problem Score Descriptions 4 The problem is properly modelled with appropriate mathematical concepts used in the solution and a correct final answer is obtained. 3 The problem is properly modelled with appropriate mathematical concepts partially used in the solution and a correct final answer is obtained. 2 The problem is not properly modelled other alternative mathematical concepts are used in the solution and a correct final answer is obtained. 1 The problem is not properly modelled by the solution presented and the final answer is incorrect. Reflection Complete this statement: I have learned in this activity that… ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ __________________________________________________________________________. References: 1. Callanta, Melvin T.(2015). Mathematics 10 Learners Module 2. https://www.mathsisfun.com/whole-numbers.html 3. https://brilliant.org/wiki/integers/ Answer Key I. Addition of Integers Use the number line to find the sum of the following integers. 1. 3 + 6 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 (Starts at 3 and move 6 units to the right, it stops at 9 which is the sum) 2. -4 + -1 -7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7 (Starts at -4 and move 1 space to the left, it stops at -5, hence the sum is -5) 3. -7 + 2 -7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7 (Starts at -7 and move 2 spaces to the right, it stops at -5, hence the sum is -5) 4. 8 + -3 3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 (Starts at 8 and move 3 spaces to the left, it stops at 5, hence the sum is 5) 5. 10 + -5 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 (Starts at 10 and move 5 spaces to the left, it stops at 5, hence the sum is 5) Practice Personal Hygiene protocols at all times. 26 I. 1. 11 2. -6 3. 5 4. -3 5. 24 II. IV. V. 1. Beth 2. Zeny 3. Aida 4. May 5. Jona 6. -19 7. -3 8. 7 9. 7 10 -4 ---------------------- 27 10 -12 12 9 1. 3. Beth 2. Aida 4. Beth LET --------------- -8 + (-6) + (0) = -14 ME __________ ( 2) + ( -6 ) = -4 VOTE ___________ 8 + (-4) + (0) + (-6) = -2 (Sample words only) 1. 400 2. 1000 feet 3. 1700 pesos Prepared by OFELIA V. CAGUIN Cabulay High School Practice Personal Hygiene protocols at all times. 27 MATHEMATICS 7 Name:__________________________________________ Section:___________ Section:_________________________________________ Date:_____________ LEARNING ACTIVITY SHEET Subtraction of Integers Background Information for Learner/Concepts Integers are whole numbers that are positive or negative including zero. Negative integers are numbers less than zero found at the number line from the left of zero and hold a negative sign. Examples are -1, -5, -8, -12, -18, etc. while positive integers are numbers greater than zero located at the right side of zero in the number line. This sign(+) indicates positive integer. However, the sign is not always needed. Numbers like +3 or 3, +6 or 6, +9 or 9, +13 or 13, etc. are examples of positive integers. Zero on the other hand is located in between the positive and negative integers in the number line. The number line is used as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations. Subtraction of an integer is just by adding its opposite. Rules in subtracting integers: 1. Copy the first number(minuend) 2. Change the operation from subtraction to addition. 3. Get the opposite sign of the second number(subtrahend) 4. Proceed with the addition of integers. Example: 1. What is -13 minus 4? Subtraction -13 - Minuend 4 = -13 + - 4 = 17 Subtrahend Subtraction of integers is just the opposite of adding integers. It can be done by adding the opposite. 2. Using the number line -8 -7 -6 -5 -4 a. 5 - 3 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 5 + -3 = 2 Start at point 5, then move 3 units to the left, so it stops at 2. b. -4 – 4 -4 + -4 = -8 Practice Personal Hygiene protocols at all times. Start at point -4, then move 4 units to the left, it stops at -8, hence the difference is -8. 28 Learning Competency and Code Performs fundamental operations on integers. M7NS-Ic-d-1 DIRECTIONS: Different activities were given for you to measure how deep is your understanding on how to subtract integers. Activity 1. IN WHAT WAY? Find the difference using the number line. -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 1. -6 - (+3) = _______________ 6. -5 - (+7) = __________ 2. 9 - (-4) = _______________ 7. 8 – (-6) = __________ 3. -8 – (+5) = _______________ 8. 10 – (3) = __________ 4. 10 - (-6) = _______________ 9. 1 – (-5) = __________ 5. 7 - ( +2) = _______________ 10. -7 – ( -7) = __________ I. 1. 2. 3. 4. 5. II. Subtract the following. (Show your solutions) 26 - (15) = ___________ 6. 12 - (0) =___________ -50 - (-32) = __________ 7. -63 – (-14) = __________ 46 - (20) = __________ 8. 87 - (-52) = __________ 100 - (-150) = __________ 9. -69 – (84) = __________ -33 - (18) = ___________ 10. -26 – (-12) = __________ FITS ME WELL: Subtracting Squares(Show your solutions). Minuend Subtrahend 8 10 -4 1. 2. -7 3. 4. 14 10 -9 12 III. 9 10 11 -15 5. 7. -6 6. 8. -18 9. 11. 20 10. 12. I AM BRAVE!: Find the difference, then determine the letter that matches your answer. When you are done you will be able to decode the word and proved you are really brave. R O G T U E 1 2 3 4 5 6 -8 - (6) 12 - (-4) -10 - (8) 13 - (10) 0 – (-14) -8 - (1) Practice Personal Hygiene protocols at all times. 29 C A IV. 7 8 6 - (-5) -11 - (-7) ____ ____ ____ ____ ____ ____ ____ 11 16 14 -15 4 -18 -9 Solve what is being asked: 1. Henry prepared 50 glasses of orange juice to sell. He sold 32 glasses. How many glasses of orange juice does he have left? 2. Mary Ann’s cat gave birth to 5 kittens, and she gave 2 to her friends. How many kittens he have now? 3. Peter saved 500 pesos and he spent 175 pesos in buying his shirt. How much money does Peter have now? 4. It will be 380 tomorrow. The weatherman predicts it will be 20 colder by night. What will be the temperature by night tomorrow? 5. The table below shows the amount of money donated by the faculty and staff of a certain school and the amount spent to purchase relief goods for the needy families. Amount Collected Amount Spent 3,245.00 2,875.35 Question: Find the amount of money left, if one staff needs to buy 1 pack of plastic bag to be used in the packaging of relief goods that costs 40.50. Rubric for rating Activity I and II Score Descriptions 4 The computations are accurate. A wise use of the rules of subtraction of integers are evident. 3 The computations are accurate. Use of the rules of subtraction of integers are evident. 2 The computations are erroneous and show some use of the rules of subtraction of integers . 1 The computations are erroneous and do not show some use of the rules of subtraction of integers . Rubric for rating Activity III and IV Score Descriptions 4 Student explains the rules of subtracting integers and be able to apply in solving problems.. 3 Student demonstrates an understanding the rule of subtracting integers. 2 Student understands the rule of operations but is inconsistent in solving 1 Student needs assistance in subtracting integers. Rubric for rating the Solving Problem Score Descriptions 4 The problem is properly modelled with appropriate mathematical concepts used in the solution and a correct final answer is obtained. 3 The problem is properly modelled with appropriate mathematical concepts partially used in the solution and a correct final answer is obtained. 2 The problem is not properly modelled other alternative mathematical concepts Practice Personal Hygiene protocols at all times. 30 1 are used in the solution and a correct final answer is obtained. The problem is not properly modelled by the solution presented and the final answer is incorrect. Reflection Complete this statement: I have learned in this activity that … ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ________________________________________________________________________. References: 1. https://www.chilimath.com/lessons/introductory-algebra/subtraction-of-integers/ 2. http://www.math.com/school/subject1/lessons/S1U1L11DP.html 3. Callanta, Melvin T.(2015). Mathematics 10 Learners Module ANSWER KEY Subtraction of Integers 1. -9 2. 13 3. -13 4. 16 5. 5 6. -12 7. 14 8. 7 9. 6 10. 0 II. 1. 11 2. -18 3. 26 4. 250 5. -21 6. 12 7. -49 8. 139 9. -153 10 -14 III.1.-12 2.-14 3. -15 4. -17 5. 29 6. 20 7. 25 8. 16 9. 9 10. -29 11. 30 12. -8 IV. R O G T U 1 2 3 4 5 -8 - (6) 12 - (-4) -10 - (8) 13 - (10) 0 – (-14) Practice Personal Hygiene protocols at all times. -14 16 -18 3 14 31 E C A 6 7 8 -8 - (1) 6 - (-5) -11 - (-7) -9 11 4 __C__ _O_____U__ __R_ __A__ __G__ _E___ 11 16 14 -15 -14 -18 -9 V. Solving Problem: 1. 18 2. 3 3. 325 4. 400 5. 329.15 Prepared by OFELIA V. CAGUIN Teacher - III Cabulay High School Practice Personal Hygiene protocols at all times. 32 MATHEMATICS 7 Name of learner : _______________________________________ Section : ______________________________________________ Grade Level ___________ Date : ________________ LEARNING ACTIVITY SHEET Multiplying Integers Background of Information for Learners In multiplying integers you just do as multiplying whole numbers, but you should be aware of the signs. We have to remember the rules, the product of two positive integers is Positive. The product of two negative integers is Positive. The product of a positive integer and a negative integer is Negative. And remember too that any number multiplied by zero is equal to zero. Examples. 1. 2. 3. 4. (15) ( 10) (-25) (- 8) (-12) ( -30) (-345) (0 ) = = = = 150 200 - 360 0 Learning Competency with Code: Performs fundamental operations on integers M7NS-1c-d-1 Activity 1. POSITIVE OR NEGATIVE? DIRECTIONS : Tell whether the product of the integers is Positive or Negative. Write your answer on the space before each number. ______________ 1. ( 7) ( 9 ) ______________ 2. ( - 10) ( 8) ______________ 3. ( - 5) ( -3) ______________ 4. ( - 63) ( 2) ( --9) ______________ 5. ( -8 ) ( -7) ( 5 ) ( - 4) ______________ 6. ( 11)(6)(-2) _______________7. ( 31) (- 117) _______________8.( 140)(12) _______________9. (-13)(-406)(0) _______________10.( 22)(-7)(-102) Practice Personal Hygiene protocols at all times. Hi, here are some activities for you to master multiplication of integers. 33 Activity 2 Let us see if you can find the products? Direction: Find the products of the following : 1. ( 6) ( -3) = __________ 2. (- 4) ( -8) = __________ 3. ( 12 ) ( 9) = __________ 4. ( - 7) ( 10) = __________ 5. ( 42) ( - 15) = __________ 6. ( -11) (-112) = __________ 7. ( 5) ( 13) = __________ 8. ( - 9) ( -5) = __________ 9. ( 14) ( -130) = ___________ 10. ( -6) ( - 74) = __________ 11. ( 89)(-7)( 2) = __________ 12. (-10)(-51)(-4) = __________ 13. ( 920)(0)( 11) = __________ 14. (- 12)(8)(-2) (31)= _________ 15. ( 320) ( - 167) = __________ Activity 3. GUESS WHAT? . Direction: What was the mathematical name for # (number sign)? To answer this, find the products of the integers then write the letter inside the box that corresponds to their products. - 60 H. T. C. P. R. O. E. 63 42 -60 42 - 96 - 60 80 -120 -180 ( 6) (4) (-4) ( 3) (- 7) ( -2) ( 7) ( -1 ) ( -9) ( 2) ( -6) ( 1) ( 10) ( 16) ( 5) ( 5) ( 4) ( -3) ( -15) ( -3) ( -2) ( 2) Practice Personal Hygiene protocols at all times. 34 Rubrics for Scoring 0 mistakes 1-2 mistakes 3-4 mistakes 5- above mistakes Outstanding Very Good Good Try again Reflection: Now ,Rate yourself, put a check . Score 35 34-26 25-15 0-14 Remarks Outstanding Very Good Good Try Again Try to ponder on this: When something good (+) happens to someone good (+), it is Good (+). When something good (+) happens to someone bad (-), it is Bad (-). When something bad (-) happens to someone good (+), it is Bad (-). When something bad (-) happens to someone bad (-), it is Good (+). How will you deal with your negative attitudes? ______________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ __________________________________________________ References: Learner’s Module Grade 7, Math Lesson 4.3 : Fundamental Operation on Integers: Multiplication of Integers Book : e – Math edition 2012 revised edition 2015 by Orlando A. Oronce and Marilyn O Mendoza. Internet : byjus.com>videos Answer Key Activity 1 1. 2. 3. 4. Positive Negative Positive Positive Practice Personal Hygiene protocols at all times. 35 5. Negative 6. Negative 7. Negative 8. Positive 9. Negative 10. Positive Activity 2 1. 2. 3. 4. 5. – 18 32 108 -70 – 15 11. – 1246 12. 2040 13. 0 14. 5952 15.53,440 6. 22 7. 65 8. 45 9. -1820 10. 444 Activity 3 O - 60 C 63 T 42 O - 60 T 42 H O - 96 - 60 R 80 P -120 E -180 Prepared by ALELI C. VALERIANO Teacher - III Cabulay High School Practice Personal Hygiene protocols at all times. 36 MATHEMATICS 7 Name of Learner :___________________________________________ Grade level :_________ Section: ___________________________________________________ Date: ______________ LEARNING ACTIVITY SHEET Dividing Integers Background of Information for Learners If multiplication is spreading of numbers, division is the distribution of numbers. Dividing integers is opposite operation of multiplication. But the rules for division of integers are same as multiplication rules. Though, it is not always necessary that the quotient will always be an integer. Rule 1: The quotient of two positive integers will always be positive. Rule 2: The quotient of two negative integers will always be positive. Rule 3: The quotient of a positive integer and a negative integer will always be negative. Examples: 1. ( 45) ÷ ( 9) = 5 2. ( -100) ÷ ( -5) = 20 3. ( 88) ÷ ( -4) = -22 4. ( -14) ÷ (7) = -2 Learning Competency with Code: Performs fundamental operations on integers M7NS-1c-d-1 Activity 1. TRUE OR FALSE ? Directions: Identify whether the given expression below is TRUE or FALSE. Write T if it is true and F if it is false. _____ 1. (- 9) ÷ ( - 3 ) = 27 _____ 2. ( 42) ÷ ( - 7) ÷ ( -6) = 1 _____ 3. ( 85 ) ÷ ( - 17 ) = 5 _____ 4. ( - 112) ÷ ( 16 ) = 7 _____ 5. ( 20) ÷ ( - 2) ÷ ( 5) = 2 _____ 6. ( 81) ÷ ( 9)÷ (- 1) = 9 _____ 7. ( - 36) ÷ ( -6) = -6 _____ 8. ( 515) ÷ (- 5) = 103 _____ 9. ( 24) ÷( 3) ÷(4) = -2 _____10. ( -60) ÷ ( -6) = 10 Practice Personal Hygiene protocols at all times. Ready for this? 37 Activity 2 Direction: Find the quotient of the following: Looks like easy, you can do it. 1. ( 18) ÷ ( 9) = _____ 2. ( -75) ÷ ( - 5) = _____ 3. ( - 40) ÷ (- 4) = _____ 4. ( -156) ÷ ( 12) = _____ 5. ( 66) ÷ ( -11) = _____ 6. (- 84) ÷ ( 7) ÷ ( - 3) = _____ 7. ( 78) ÷ ( -13) ÷( 2) = _____ 8. ( -64) ÷( 4) ÷ ( -8) = _____ 9 .( 162) ÷ (-9) ÷ (-6) = _____ 10. (- 136) ÷ (17) ÷(-2)=_____ Activity 3 What was the division slash (/) called? DIRECTION: To find the answer , , match the letter in column II with number that corresponds to the numbers in column I. ____1. ( 322) ÷ ( 14) U.–7 ____2. ( -198) ÷ ( 22 ) E. 7 ____3. (186) ÷ ( 6) G. 53 ____ 4. ( -212) ÷ ( -4) I. – 9 ____5. ( 280) ÷ ( -40) R. 31 ____ 6. (720) ÷ ( 9) ÷( -8) V. 23 ____ 7. (560) ÷ ( 8) ÷ ( 10) L. – 10 Want to discover? Solve the problem. B. – 23 Rubrics for Scoring 0 mistakes 1-2 mistakes 3-4 mistakes 5 – above mistakes Outstanding Very Good Good Try again Reflection: Now ,Rate yourself, put a check . Score 22 21- 16 15 -11 0-10 Remarks Outstanding Very Good Good Try Again Practice Personal Hygiene protocols at all times. 38 Try to ponder on this: When something good (+) happens to someone good (+), it is Good (+). When something good (+) happens to someone bad (-), it is Bad (-). When something bad (-) happens to someone good (+), it is Bad (-). When something bad (-) happens to someone bad (-), it is Good (+). Do you have any experience which have the same result like the above statement? Can you share it? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ ________________________________________________________________ References: .Learner’s Module Grade 7 Math Lesson 4.3 : Fundamental Operation on Integers: Multiplication of Integers Book : e – Math edition 2012 revised edition 2015 by Orlando A. Oronce and Marilyn O Mendoza. Internet : byjus.com>videos Answer Key Activity 1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. T F F F F F F F F T Activity 2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2 15 10 – 13 –6 4 -2 2 3 –4 Practice Personal Hygiene protocols at all times. 39 Activity 3 1. 2. 3. 4. 5. 6. 7. V I R G U L E Prepared by: ALELI C. VALERIANO Teacher – III Cabulay High School Practice Personal Hygiene protocols at all times. 40 MATHEMATICS 7 Name: _____________________ Date: ______________________ Grade Level: ____ Score: _________ LEARNING ACTIVITY SHEET Properties of Real Numbers Background Information for Learners Understanding the properties of real numbers will help us simplify numerical and algebraic expressions, solve equations, and more as you progress in studying algebra. For clarity, “properties” in this context refer to the characteristics or behaviors of real numbers under the operations of addition and/or multiplication that are accepted even without proof. Here are the main properties of the Real Numbers: 1. Commutative a. a + b = b + a b. ab = ba Example 2+6=6+2 4×2=2×4 2. Associative a. (a + b) + c = a + ( b + c ) b. (ab)c = a(bc) Example (1 + 6) + 3 = 1 + (6 + 3) (4 × 2) × 5 = 4 × (2 × 5) 3. Distributive a. a × (b + c) = ab + ac b. (b+c) × a = ba + ca Example 3 × (6+2) = 3 × 6 + 3 × 2 (6+2) × 3 = 6 × 3 + 2 × 3 Real Numbers are closed (the result is also a real number) under addition and multiplication: 4. Closure a. a+b is real b. a×b is real Example 2 + 3 = 5 is real 6 × 2 = 12 is real Adding zero leaves the real number unchanged, likewise for multiplying by 1: 5. Identity a. a + 0 = a b. a × 1 = a Practice Personal Hygiene protocols at all times. Example 6+0=6 6×1=6 41 For addition the inverse of a real number is its negative, and for multiplication the inverse is its reciprocal: 6. Additive Inverse Example 6 + (−6) = 0 a + (−a ) = 0 7. Multiplicative Inverse Example 6 × (1/6) = 1 a × (1/a) = 1 *But not for 0 as 1/0 is undefined Multiplying by zero gives zero (the Zero Product Property): 8. Zero Product If ab = 0 then a=0 or b=0, or both Example a × 0 = 0 × a = 05 × 0 = 0 × 5 = 0 Learning Competency and Code The learner illustrates the different properties of operations on the set of integers. (M7NS-Id-2) Activity 1 Directions: Each of the given instructions is about two things. In column II, the order has been changed around. Put a check before the number if the results in the two columns are the same. A 1. Put on your socks and then put on your shoes. 2. Kill the snake and then pick it up. 3. Walk 10 paces south and then two paces north. 4. Add 7 and 12 5. Divide 6 by 3. B Put on your shoes and then put on your socks. Pick up the snake and then kill it. Walk two paces north and then 10 paces South. Add 12 and 7 Divide 3 by 6. Activity 2. Directions: Do the following calculations in the quickest way you can find. 1. 2. 3. 4. 5. 18 + 6 + 4 65 + 35 + 19 17 + 129 + 1 19 x 5 x 2 1 5 2 + 2 + 13 2 Practice Personal Hygiene protocols at all times. 42 Activity 3 Directions: Identify if the following instructions is commutative or not. Write C if commutative, NC if not commutative. __________1. __________2. __________3. __________4. __________5. Wash the shirt and the iron it. Fetch water and turn on the TV Find x if 3 is a factor of 12. Find x if 12 is a factor of 3. Eat dinner and clean the bathroom. Attend the review class and take the exam. Activity 3.1 Directions: Complete each statement to illustrate the indicated property. 1. 2. 3. 4. 5. 6. 7. 3 + ( 2 +11) = 3 + (11 +____) 3∙ ( 8 + 12 ) = 3∙ ( 12 + ____ ) (15 + 8) + 7 = _____ + (8 + ____) 11∙ ( 9 + 2 ) = 11∙ 9 + 11∙ ____ 11 + ____ = 11 -17 + 17 = _______ 7 3 × Commutative Property Commutative Property Associative Property Distributive Property Identity Property Inverse Property =1 Inverse Porperty 8. 19 × 0 = _____ Zero Property Activity 4 Directions: Identify the real number property that justifies each statement. 1. 2. 3. 4. 19 + x = x + 19 7(x – 6) = 7x – 42 17 + (-17) = 0 7 7 0+3=3 5. (0.1)(10) = 1 6. xy + y = y(x + 1) ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Activity 5 Directions: Complete each statement using the indicated property. 1. 2. 3. 4. 5. 6. 7. 8. a + b = ____________________ 7x + 7 = _______________________ 19(bc) = _______________________ (p + 9) + 1 = _____________________ 0.13 + (____) = 0 4 (___) = 1 25 + ______ = 25 13 13 𝑘 + 9 = ______________________ 9 Practice Personal Hygiene protocols at all times. Commutative Distributive Associative Associative Inverse Property Multiplicative Inverse Identity Distributive 43 REFLECTION In this lesson, I learned ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___ REFERENCES Oronce, O & Mendoza, M (20156). E-Math: Workbook in Mathematics. Rex Printing Company.), ANSWER KEY Activity 1 Directions: Each of the given instructions is about two things. In column II, the order has been changed around. Put a check before the number if the results in the two columns are the same. A 1. Put on your socks and then put on your shoes. 2. Kill the snake and then pick it up. 3. Walk 10 paces south and then two paces north. 4. Add 7 and 12 5. Divide 6 by 3. / B Put on your shoes and then put on your socks. Pick up the snake and then kill it. Walk two paces north and then 10 paces South. Add 12 and 7 Divide 3 by 6. Activity 2. Directions: Do the following calculations in the quickest way you can find. 1. 2. 3. 4. 5. 18 + 6 + 4 = 28 65 + 35 + 19 = 119 17 + 129 + 1 = 147 19 x 5 x 2 = 190 1 2 + 5 2 2 + 13 = 5 Activity 3. Directions: Identify if the follwing instructions is commutative or not. Write C if commutative, NC if not commutative. NC 1. Wash the shirt and the iron it. NC 2. Fetch water and turn on the TV NC 3. Find x if 3 is a factor of 12. Find x if 12 is a factor of 3. C 4. Eat dinner and clean the bathroom. Practice Personal Hygiene protocols at all times. 44 NC 5. Attend the review class and take the exam. Activity 3.1 Directions: Complete each statement to illustrate the indicated property. 1. 2. 3. 4. 5. 6. 7. 3 + (2 +11) = 3 + (11 + 2) 3∙ (8 + 12) = 3∙ ( 12 + 8) (15 + 8) + 7 = 15 + (8 + 7) 11∙ (9 + 2) = 11∙ 9 + 11∙ 2 11 + 0 = 11 -17 + 17 = 0 7 3 × 7 =1 3 Commutative Property Commutative Property Associative Property Distributive Property Identity Property Inverse Property Inverse Porperty 8. 19 × 0 = 0 Zero Property Activity 4. Directions: Identify the real number property that justifies each statement. 1. 2. 3. 4. 19 + x = x + 19 7(x – 6) = 7x – 42 17 + (-17) = 0 7 7 0+3=3 COMMUTATIVE DISTRIBUTIVE INVERSE IDENTITY 5. (0.1)(10) = 1 6. xy + y = y(x + 1) INVERSE DISTRIBUTIVE Activity 5. Directions: Complete each statement using the indiciated property. 1. 2. 3. 4. 5. 6. 7. 8. a+b=b+a 7x + 7 = 7(x+ 1) 19(bc) = (19b)c (p + 9) + 1 = p+(9+1) 0.13 + (-0.13) = 0 4 (1/4) = 1 25 + 0 = 25 13 13 13 𝑘 + 9 = 9 (𝑘 + 1) 9 Commutative Distributive Associative Associative Inverse Property Multiplicative Inverse Identity Distributive dule Fourth Year · Triangle Trigonometry, Mo, Module 2 (LPrepared by: GERALDINE S. CANLAS Teacher Practice Personal Hygiene protocols at all times. 45 MATHEMATICS 7 Name: _____________________ Date: ______________________ Grade Level: ____ Score: _________ LEARNING ACTIVITY SHEET THE TRANSFORMER! Express rational numbers from fraction form to decimal form (vice versa). Background Information for Learners This activity sheet serves as a supplement learning material guide for the learners. It will direct the students to familiarize in expressing rational numbers from fraction form to decimal form (vice versa) to be used in solving real life activity. The steps in expressing rational numbers from fraction form to decimal form (vice versa) can be modified using the operations on whole number. Always remember that any rational number can be changed from fractional form to decimal form by dividing the numerator by the denominator. On the other hand, a decimal can be changed to a fraction using the power of 10 as the denominator. Then, reduce it to its simplest form. Learning Competency with code Express rational numbers from fraction form to decimal form and vice versa. (M7NS-Ie-1) Activity 1: Hunt me if you can! Instruction: Encircle all terminologies use in expressing rational number from fraction form to decimal form (vice versa). Words can be spelled forward, backward, diagonally up or down. Practice Personal Hygiene protocols at all times. 46 Activity 2: TRANSFORM ME! Express the given fraction to decimal. 3 1. 4 = ______ 2 1 2. = ______ 3. = ______ 5 3 4. 10 4 3 = ______ 5. = ______ 8 1 6. = ______ 7. 8 3 8. = ______ 9. 5 10. 3 16 4 10 15 60 = ______ = ______ = ______ Activity 3: GETTING TO KNOW! State wether the following fraction are terminating or nonterminating decimals 4 _____________ 1. _____________ 3. _____________ 5. _____________ 7. 5 3 7 9 20 3 15 Practice Personal Hygiene protocols at all times. 7 _____________ 2. _____________ 4. _____________ 6. _____________ 8. 8 8 11 1 6 1 3 47 12 _____________ 9. _____________10. 42 5 6 Activity 4: Follow Stictly! To answer this, you will express the rational number from decimal form to fraction form. Match your answer from the choices on the right and write the corresponding answer on the left before the number. Then decode the message below. ( Clue:It is the deliverate increase of physical space between people to prevent them spreading illness.) _________1. 0.75 G _________2. 0.328 L _________3. 0.8 C _________4. 0.625 I _________5. 0.25 D _________6. 0.88 T _________7. 0.35 N _________8. 0.825 A _________9. 0.152 J ________10. 0.365 M ________11. 0.175 O ________12. 0.78 B ________13. 0.142 U ________14. 0.18 S ________15. 0.98 P 71 500 4 5 5 8 3 4 41 125 7 20 19 25 7 40 49 50 39 50 22 25 1 4 33 40 73 200 9 50 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 10 6 4 1 11 3 2 1 Practice Personal Hygiene protocols at all times. 10 7 11 9 4 1 9 13 48 Activity 5: Make Me Simple! Express the repeating, nonterminating decimals to fraction. The illustrative example were shown for your reference. Rubric for scoring is given below. Illustrative example: Express 0.44… to fraction. a. 0.44… Let x = 0.44 10x= 4.44 - x= 0.44 9x = 4 9x = 4 9 9 x= 1. 0.33… Solution 4. 0.1212… Solution 7. 0.135135… Solution 𝟒 𝟗 2. 0.66… Solution 5. 0.3232… Solution 8. 0.123123… Solution Practice Personal Hygiene protocols at all times. 3. 0.55… Solution 6. 0.1515… Solution 9. 0.125125… Solution 49 CRITERIA OUTSTAND ING (4) SATISFACTOR Y (3) Representation Represent the problem into equation. Represent the problem into equation with missing parts. The representation is not clear. Doesn't understand enough to get started or make progress. Solution Shows correct computation. Proficient evidence in expressing decimals to fraction. Work is clear and organize. 80% of the problem got correctly. There is basic evidence in expressing decimal to fraction. 50% of the problem got correctly. There is basic evidence in expressing decimal to fraction. Work is fairly neat. There is no evidence of computation. Neatness Work is clear but not organize. DEVELOPIN G (2) BEGINNING (1) Work is not clear and lack of organization. Reflection I have learned that____________________________________________ Practice Personal Hygiene protocols at all times. 50 Answer key Activity 1: Hunt me if you can! Practice Personal Hygiene protocols at all times. 51 Activity 2: TRANSFORM ME! 3 1. 4 = _0.75_ 2 1 2. = __0.4__ 3. = _0.25_ 5 3 4. 4 3 = __0.3__ 5. = _0.375 = _0.125__ 7. 8. = __0.6__ 9. 6. 10 1 8 8 3 5 10. 3 16 4 10 15 60 = __0.4__ = __0.25__ = _0.1875_ Activity 3: GETTING TO KNOW! 4 __Terminating__ 1. Nonterminating 3. __Terminating__ 5. __Terminating__ 7. Nonterminating 9. 5 3 7 9 20 3 15 12 42 Practice Personal Hygiene protocols at all times. 7 __Terminating__ 2. 8 8 Nonterminating 4. Nonterminating 6. Nonterminating 8. 11 1 6 1 3 Nonterminating 10. 5 6 52 Activity 4: Follow Stictly! ____ I ___ 1. 0.75 G ____D____2. 0.328 L ____L ___ 3. 0.8 C ____C____4. 0.625 I ____B____5. 0.25 D ____O____6. 0.88 T ____T____7. 0.35 N ____U____8. 0.825 A ____N____9. 0.152 J ___ S____10. 0.365 M ___ A____11. 0.175 O ___M____12. 0.78 B ____G__ 13. 0.142 U ____P___ 14. 0.18 S ____J ___15. 0.98 P _S_ _O_ _C_ _I_ _A_ _L_ 10 6 4 1 11 3 71 500 4 5 5 8 3 4 41 125 7 20 19 25 7 40 49 50 39 50 22 25 1 4 33 40 73 200 9 50 _D_ _I_ _S_ _T_ _A_ _N_ _C_ _I_ _N_ _G_ 2 1 10 7 11 9 4 1 9 13 Activity 5: Make Me Simple! 1. 0.33… 2. 0.66… Solution Let x = 0.33 10x= 3.33 - x= 0.33 9x = 3 9x =3 9 9 x= x= 3 9 𝟏 𝟑 4. 0.1212… Solution Let x = 0.66 10x= 6.66 - x= 0.66 9x = 6 9x = 6 9 9 x= x= 6 9 𝟐 3. 0.55… Solution Let x = 0.55 10x= 5.55 - x= 0.55 9x = 5 9x =5 9 9 x= 𝟏 𝟑 𝟑 5. 0.3232… Practice Personal Hygiene protocols at all times. 6. 0.1515… 53 Solution Solution Solution Let x = 0.12 100x= 12.12 - x = 0.12 99x = 12 99x = 12 99 99 Let x = 0.32 100x =32.32 - x = 0.32 99x = 32 99x = 32 99 99 Let x = 0.15 100x =15.15 - x = 0.15 99x = 15 99x = 15 99 99 x= x= 12 99 𝟒 x= 𝟑𝟑 7. 0.135135… x= 135 999 𝟒𝟓 𝟗𝟗 x= Let x = 0.123 1000x= 123.123 - x= 0.123 999x = 123 999x = 123 999 999 x= 15 99 𝟓 𝟑𝟑 9. 0.125125… Solution Solution Let x = 0.135 1000x= 135.135 - x= 0.135 999x = 135 999x = 135 999 999 x= 𝟑𝟐 8. 0.123123… Solution x= Let x = 0.125 1000x= 125.125 - x= 0.125 999x = 125 999x = 125 999 999 𝟏𝟐𝟑 𝟗𝟗𝟗 x= 𝟏𝟐𝟓 𝟗𝟗𝟗 𝟑𝟑𝟑 References Mathematics 7 Teaching Guide, p. 61 - 63 Bernabe, J. & De Leon, C. (2002). Elementary Algebra https://www.everydayhealth.com/coronavirus/coronavirus-glossary-key-terms-about-thepandemic-explained/ Prepared by ROMMEL A. SIMON/PRIMAROSE A. SALES Teacher III Practice Personal Hygiene protocols at all times. 54 MATHEMATICS 7 Name: ________________________________________ Grade Level: _____ Section: _______________________________________ Date: ____________ LEARNING ACTIVITY SHEETS Operations on Rational Numbers Background Information for Learners This activity sheet serves as a self-learning guide for you. It is expected that you will learn or master operations on rational numbers. How do you operate using rational numbers? We have learnt about fractions earlier, and we saw how different operators can be used on different fractions. Well, all the rules and principles that govern fractions can also be applied to rational numbers. The one thing to be kept in mind is that rational numbers also include negatives. So, while 1/5 is a rational number, it is also true that −1/5 is also a rational number. Rational Integers Whole Numbers Practice Personal Hygiene protocols at all times. 55 To understand the concept of negative rational numbers, we need to understand a number line. A number line is simply a line on which numbers are marked at equal intervals. A number line can be extended infinitely in both directions. One of the points of a number line is zero. All points to the right of the zero mark are positive numbers, while all the numbers to the left of zero are negative numbers. A number line also makes it very easy to visualize additions and subtractions of positive numbers and negative numbers. For example, if we wish to add −3−3 with +2,+2, then it means that the first number is three spaces to the left of zero, while the second number is two spaces to the right of zero. Therefore, their sum will be just one space to the left. Addition of Rational Numbers As we saw above, a rational number is a ratio of two numbers p and q, where q is non-zero number. Here p is called the numerator and q is called the denominator. When it comes to addition of two such rational numbers, there can be four possible variations. First, both the rational numbers could have the same denominator. For example, when we wish to add ⅓ and ⅔, the answer is simply the sum of 1 and 2, divided by the common denominator 3. So ⅓+⅔ = (1+2)/3 = 3/3 Next, the two rational numbers could have the same denominator, but one of them could be negative. So, when you need to add 3/5 and −1/5, then we can write the calculation in this way 3/5+(−1/5)=(3+(−1)/5=(3−1)/5=2/5 The third variant is when the two rational numbers to be added have different coefficients. Like we have seen earlier, we will make the two numbers similar to each other by taking the lowest common multiple of both denominators as the denominator of the answer. So, to add 5/6 and 7/9, we first need to find the LCM of 6 and 9, which is 18. So, we can write 5/6 as 15/18 and 7/9 as 14/18. Then the addition of these two rational numbers can be expressed in the following way 5/6+7/9=15/18+14/18=(15+14)/18=29/18 Practice Personal Hygiene protocols at all times. 56 The final variant is when one of the two rational numbers with different denominators is negative. So, if we need to add 5/6 and −7/9, then the addition can be carried out in the following manner 5/6+(−79)=15/18+(−14/18)=(15+(−14)/18=1/18 Subtraction of Rational Numbers If you can understand the concept of additive inverse, then you do not need to understand anything extra outside the addition we saw above, when we need to subtract two rational numbers. The additive inverse of a fraction is the number which when added to it gives a result zero. So, if you have a variable x, and its additive inverse is i, then x+i = 0, = > i = −x. So, when expressed simply, the additive inverse of any number is the same number with a negative sign. Now let us see how we can express how to subtract 3/7 from 5/7. The additive inverse of 3/7 is −3/7 So, the subtraction can be expressed as the addition to additive inverse. Therefore, 5/7−3/7=5/7+(−3/7)=2/7 Multiplication and Division of Rational Numbers Just like we saw above that subtraction can be quite easily understood once addition is clear, similarly, division of two rational numbers is quite easy to comprehend once multiplication is clear. First, let us look at multiplication. When two rational numbers are to Practice Personal Hygiene protocols at all times. 57 be multiplied together, then the simple thing to do is to multiply both numerators together to get the new numerator, and then the two denominators to get the new denominator. So when we multiply 3/5 and 4/7, the answer is 3/5×4/7=(3×4)(5×7)=12/35. For division, we need to find the multiplicative inverse of the second rational number. Therefore (3/4)(5/7)=3/4×7/5=(3×7)(4×5)=21/20. Source: https://www.cuemath.com/maths/operations-on-rational-numbers/ Learning Competency with Code The learner performs operations on rational numbers. (M7NS-If-1) Directions: In doing the different given activities, remember that honesty is the best policy. Apply what you have learned about the operations of rational numbers. Hope you will enjoy! Activity 1: Reveal the Real Me! Perform the indicated operations and connect the dots in the order you created to reveal the image. Practice Personal Hygiene protocols at all times. 58 Activity 2: The colors of my life! Perform the indicated operations and color the shapes with corresponding answers. Practice Personal Hygiene protocols at all times. 59 Activity 3: Flower Fractions! Solve each problem. Color the picture using the answer key below. Practice Personal Hygiene protocols at all times. 60 Activity 4: Make It A Habit! Match the columns. Then write the letters on the space provided that match the numbers on the correct lines to solve the missing word. (Clue: We must do this always to prevent Covid – 19.) 1. _____ 3.5 ÷ 2 = 2. _____ 78 𝑥 0.4 = 3. _____ 9.6 𝑥 13 = 4. _____ 3.24 ÷ 0.5 = 5. _____ 1.248 ÷ 0.024 = 6. _____ 27.3 𝑥 2.5 = 7. _____ 9.7 𝑥 4.1 = 8. _____ 3.415 ÷ 2.5 = 9. _____ 53.61 𝑥 1.02 = 10. _____ 1948.324 ÷ 5.96 = 11. _____ 5.231 ÷ 0.1 = 12. _____ 70.1 𝑥 2.03 = 13. _____ 41.61 𝑥 0.02 = 14. _____0.345 ÷ 0.4 = 15. _____ 23.23 𝑥 2.1 = N B I C G E W F A J H L D P S 52.31 124.8 52 68.25 54.6822 326.9 1.75 48.783 6.48 1.366 39.77 0.8322 0.8625 142.303 31.2 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ 7 4 11 14 1 4 2 7 5 11 9 Practice Personal Hygiene protocols at all times. 61 Activity 5: My Real World Read the problem carefully and solve. Rubric for scoring is given below. 1 1 3 1. Maria brought 7 4 meters of silk, 4 2 meters of satin and 5 8 meters of velvet. How many meters of cloth did she buy? 1 1 2. After boiling, the 18 4 liters of water was reduced to 7 5 liters. How many water was evaporated? 3 3. Marjorie and Crisel are comparing their heights. If Marjorie’s height is 167 4 cm and Crisel’s 1 height is 155 2 cm. What is the difference in their heights? 1 1 4. A drum full of rice weight 43 2 kg. If the empty drum weights 14 4 kg. Find the weight of rice in the drum. 87 23 48 5. A basket contains three types of fruits weighing 4 kg in all. If 4 of these are oranges, 7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket? 1 2 6. Marjorie spent 3 2 hours doing her assignment. Crisel did his assignment for 1 3 times as many hours as Marjorie did. How many hours did Crisel spend doing his assignment? 7. How many thirds are there in six-fifths? 2 8. Marjorie donated of her monthly allowance to the Santiago City frontliners. If her monthly 5 allowance is P3500, how much did she donate? 1 1 9. The enrolment for this school year is 2340. If 6 are sophomores and 4 are seniors, how many are freshmen or juniors? 2 10. At the end of the day, a store had 5 of a cake leftover. The four employees each took home the same amount of leftover cake. How much of the cake did each employee take home? Rubric for Scoring CRITERIA Understands the problem Accuracy OUTSTANDING (4) Identifies special factors that influences the approach before starting the problem. The computations are accurate. A wise use of key concepts of operations on rational numbers. SATISFACTORY (3) Understands the problem. The computations are accurate. Use of key concepts of operations on rational numbers. DEVELOPING (2) Understands enough to solve part of the problem or to get part of the solution. The computations are erroneous and show some use of key concepts of operations on rational numbers. BEGINNING (1) Doesn't understand enough to get started or make progress. The computations are erroneous and do not show some use of key concepts of operations on rational numbers. Reflection Practice Personal Hygiene protocols at all times. 62 I have learned that ____________________________________________ References K to 12 Curriculum Guide in Mathematics. Available at:https://lrmds. deped.gov.ph/detail/5455 Mathematics 7 Teaching Guide, p. 78 – 79 https://www.cuemath.com/maths/operations-on-rational-numbers/ Answer Key Activity 1: Reveal the Real Me! Practice Personal Hygiene protocols at all times. 63 Activity 2: The colors of my life! Activity 3: Flower Fractions! Practice Personal Hygiene protocols at all times. 64 Activity 4: Make It A Habit! 1. ___W__ 3.5 ÷ 2 = 2. ___S__ 78 𝑥 0.4 = 3. ___B__ 9.6 𝑥 13 = 4. ___A__ 3.24 ÷ 0.5 = 5. __I___ 1.248 ÷ 0.024 = 6. ___C__ 27.3 𝑥 2.5 = 7. __H___ 9.7 𝑥 4.1 = 8. ___J__ 3.415 ÷ 2.5 = 9. ___G__ 53.61 𝑥 1.02 = 10. ___E__ 1948.324 ÷ 5.96 = 11. ___N__ 5.231 ÷ 0.1 = 12. ___P__ 70.1 𝑥 2.03 = 13. ___L__ 41.61 𝑥 0.02 = 14. ___D__0.345 ÷ 0.4 = 15. ____F_ 23.23 𝑥 2.1 = 52.31 124.8 52 68.25 54.6822 326.9 1.75 48.783 6.48 1.366 39.77 0.8322 0.8625 142.303 31.2 N B I C G E W F A J H L D P S _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ 7 4 11 14 1 4 2 7 5 11 9 HANDWASHING Activity 5: My Real World 1 1. 17 8 m 2. 11 3. 12 4. 29 5. 9 1 7 1 4 kg 6 18 5 or 5 6 hours 3 liters 7. cm 8. P1,400.00 kg 9. 1,365 students are freshmen or juniors 20 1 4 1 35 6. 5 10. or 3 5 1 10 of the cake Prepared by: CRISEL C. BISTANTE MARJORIE INGRARAN ROMMEL A. SIMON Practice Personal Hygiene protocols at all times. 65 MATHEMATICS 7 Name: ___________________________________________ Date: ____________________________________________ Grade Level: ____ Score: __________ LEARNING ACTIVITY SHEET Principal Roots and Irrational Numbers Background Information for Learners This learning activity sheet serves as a self-learning guide for the learners. It facilitates lesson comprehension as it specifically aims for students’ mastery on principal square root and describe whether rational or irrational numbers. Squaring a number is like multiplying a number by itself. The square of 4, written as 42, and read as “four squared”, is like (4)(4) = 16. The square of -4 is (-4)2 = (-4)(-4) = 16. Otherwise, 16 is the result of squaring a number, 16 is an example of a perfect square. Below are the listed perfect squares. Perfect Square 1 4 9 16 25 36 49 64 81 100 Factored Form 12 = (1)(1) 22 = (2)(2) 32 = (3)(3) 42 = (4)(4) 52 = (5)(5) 62 = (6)(6) 72 = (7)(7) 82 = (8)(8) 92 = (9)(9) 102 = (10)(10) Square Root 1 2 3 4 5 6 7 8 9 10 The square root of a number is one of the two equal factors of a perfect square. The square root of 16 is 4, since (4)(4) = 16. However, since (-4)(-4) = 16, therefore -4 is also a square root of 16. Every nonzero real number has two square roots, one positive and one negative. The square root of a number n is written in symbol as √𝑛. The symbol √ radical sign, and the numbers n under the radical sign is called radicand. is called Model: √144 = 12 since 122 = (12)(12) = 49 √0.25 = 0.5 since 0.52 = (0.5)(0.5) = 0.25 4 Rational numbers such as 0.16, 100, and 4.84 are also perfect square. The square roots of perfect squares are rational numbers while the square root of numbers that are not perfect squares are irrational numbers. Practice Personal Hygiene protocols at all times. 66 Examples: Determine whether the following is rational or irrational. a. √169 b. √41 Answer a. Since 169 is a perfect square, √169 is rational. √169 = 13 b. Since 41 is not a perfect square, √41 is irrational. Learning Competency Describes principal roots and tells whether they are rational or irrational (M7NS-Ig-1) Activity 1: Directions: Find each square root. 1. 2. 3. 4. √25 √225 √196 √576 9 5. √25 6. 7. 8. 9. √961 √529 √361 √77.44 1 10. √81 Activity 2: Directions: Write two integers between which the given square root lies. 1. 2. 3. 4. 5. √70 √134 √215 √406 √700 6. √92 7. √189 8. √334 9. √509 10. √1001 Activity 3: Direction: Tell whether the following is a rational or irrational. Practice Personal Hygiene protocols at all times. 67 1. 2. 3. 4. 5. √121 √84 √105 √289 √600 6. √441 7. √0.09 8. √2601 9. √503 10. √104.04 Activity 4: Multiple Choice: 1. Which set below includes only irrational numbers? a. {-√12, −3.7666 … , √36, 4.3858 …} c. {-5.6, √14, 6.3245, √256} b. {-7.23222…, √5, √15, 8.27451…} d. {-√8, 3.77…,3.265165065…, √900} 2. Which list contains only rational numbers? 1 9 a. -4, 0, 4, √4 1 b. 0, 2, 1.5, √8 3 c. -2, 1, 2.6…, 2 d. 0, 0.3636…, 4, √24 3. What type of number is √26? a. Whole number b. Integer c. Rational number d. number 4. Which element below is an element in the set of irrational number? Irrational √4, 3.45, -8.7, √8 a. √4 b. 3.45 c. -8.7 5. Which irrational number is between 4 and 5? a. √12 b. √20 c. √34 d. √8 d. √80 Activity 5: Solve each problem and write whether the answer is rational or irrational. 1. A standard classroom measures 7 meters by 9 meters. Its diagonal is √140 meters. Find the value of √140. 2. The length of a rope is √1369 centimeters. Find its length. 3. The area of a square is determined by squaring the length of its side. If the area is 361 square meters, what is the length of its side? 4. Mr. Cruz is buying a square piece of land which is 506.25 square meters in area. What is the length of each side of the land? Reflection I have learned that… Practice Personal Hygiene protocols at all times. 68 _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _______________ References Next Century Mathematics 7, Elementary Algebra I, E-MATH 7 Revised Edition Year Answer Key Activity 1: Activity 2: Activity 3: 1. 5 2. 15 3. 14 4. 24 3 5. 5 6. 31 7. 23 8. 19 9. 8.8 3 10. 1. 8 & 9 2. 11 & 12 3. 14 & 15 4. 20 &21 5. 26 & 27 6. 9 & 10 7. 13 & 14 8. 18 & 19 9. 22 & 23 10. 31 & 32 1. rational 2. irrational 3. irrational 4. rational 5. irrational 6. irrational 7. rational 8. rational 9. irrational 10. rational 5 Activity 4: 1. b 2. a 3. d 4. d 5. b Activity 5: 1. 11.8321 – irrational 2. 37 – rational 3. 19 – rational 4. 22.5 - rational . Triangle Prepared by: RANDY B. TOLENTINO T-I Practice Personal Hygiene protocols at all times. 69 MATHEMATICS 7 Name: ______________________________________ Grade & Section: ______________________________ Score: __________ Date: ___________ LEARNING ACTIVITY SHEET 1 Perfect Match! Background Information For Learners Taking the square root of a number is like doing the reverse operation of squaring a number. For example, both 5 and –5 are square roots of 25, since 52 = 25, and (–5)2 = 25. Meaning, the product of multiplying a number to itself is perfect square. In both 5 and –5, 5 is the positive square root or it is called as principal square root, and the other one is negative square root.The square roots of perfect squares are rational numbers while the square roots of numbers that are not perfect squares are irrational numbers. You will learn in this learning activity sheet on how to classify perfect squares and principal roots. Learning Competency and Code The learner determines between what two integers the square root of a number is. Code: M7NS-Ig-2 Practice Application and Activity 1.Encircle the perfect squares found in the box. 45169 16 200 1 754 36 49 3 16 8 64 90 9 7121 214 20 225 24 265 30 289 326 17 101 19 81 164 2 6 100 42 99 196 68 Activity 2.Match column A to column B. Write the letter of your choice on the space provided before the number. Column A (Principal Roots) _____ 1. 5 _____ 2. 8 _____ 3. 2 Column B (Perfect Squares) A. 49 B. 16 C. 144 Practice Personal Hygiene protocols at all times. 70 _____ 4. 10 _____ 5. 4 _____ 6. 12 _____ 7. 7 _____ 8. 15 _____ 9. 19 _____10. 23 D. 25 E. 529 F. 225 G. 4 H. 100 I. 64 J. 361 Reflection. What I have learned in this activity? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ References: Learners Manual in Mathematics 7, pp. 63 – 68. Answer key: Activity 1 (in any order) 1. 169 2. 16 3. 49 4. 81 5. 16 6. 1 7. 64 8. 9 9. 121 10. 4 Activity 2 1. 2. 3. 4. 5. 6. C 7. A 8. F 9. J 10. E D I G H B 11. 12. 13. 14. 15. 225 36 289 196 100 Prepared by: JUN – JUN P. DARIANO Teacher III Practice Personal Hygiene protocols at all times. 71 MATHEMATICS 7 Name: ______________________________________ Grade & Section: ______________________________ Score: __________ Date: ___________ LEARNING ACTIVITY SHEET Thorn Between Two Perfect Squares! Background Information For Learners Perfect squares are numbers that have rational numbers as square roots. If a principal root is irrational, the best you can do is to give an estimate of its value. Estimating is very important for all principal roots that are not roots of perfect n th powers. For example, between which two integers does √20 lie? In this question, you have to determine the closest perfect squares between √20. The closest perfect squares are √16 and √25 or you can expressed as √16<√20<√25, then by getting the principal root, you can write in integers as 4 <√20< 5. Therefore, the two consecutive integers between √20 are 4 and 5. You will learn in this learning activity sheet on how to write the perfect squares or principal rootsand determining what two consecutive integers each square root is between. Learning Competency and Code The learner determines between what two integers the square root of a number is. Code: M7NS-Ig-2 Practice and Application Activity 1.Write the perfect square into its equivalent principal root and vice versa. Principal Roots 1. 9 2. 7 3. ____ 4. 6 5. ____ Perfect Squares 1. ____ 2. ____ 3. 169 4. ____ 5. 16 Principal Roots 6. 11 7. ____ 8. ____ 9. 14 10. ____ Perfect Squares 6. ____ 7. 400 8. 529 9. ____ 10. 324 Activity 2.Determine what two consecutive integers each square root is between. Square Root Between of Perfect Square Between of integers 1. √40 1. ___ <√40<___ 1. ___ <√40<___ 2. √54 2. ___ <√54<___ 2. ___ <√54<___ 3. √75 3. ___ <√75<___ 3. ___ <√75<___ 4. √112 4. ___ <√112<___ 4. ___ <√112<___ 5. √147 5. ___ <√147<___ 5. ___ <√147<___ 6. √205 6. ___ <√205<___ 6. ___ <√205<___ 7. √238 7. ___ <√238<___ 7. ___ <√238<___ 8. √462 8. ___ <√462<___ 8. ___ <√462<___ 9. √717 9. ___ <√717<___ 9. ___ <√717<___ Practice Personal Hygiene protocols at all times. Consecutive Integers 1. ___ and ___ 2. ___ and ___ 3. ___ and ___ 4. ___ and ___ 5. ___ and ___ 6. ___ and ___ 7. ___ and ___ 8. ___ and ___ 9. ___ and ___ 72 10. √947 10. ___ <√947<___ 10. ___ <√947<___ 10. ___ and ___ Reflection What I have learned in this activity? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ References Learners Manual in Mathematics 7, pp. 63 – 68. Answer key Activity 1 1. 2. 3. 4. 5. Activity 2 Square Root 1. √40 2. √54 3. √75 4. √112 5. √147 6. √205 7. √238 8. √462 9. √717 10. √947 81 49 13 36 4 6. 121 7. 20 8. 23 9. 196 10. 18 Between Perfect Square 1. √36<√40<√49 2. √49<√54<√64 3. √64<√75<√81 4. √100<√112<√121 5. √144<√147<√169 6. √196<√205<√225 7. √225<√238<√256 8. √441<√462<√484 9. √676<√717<√729 10. √900<√947<√961 Between integers 1. 6 <√40<7 2. 7<√54<8 3. 8 <√75<9 4. 10<√112<11 5. 12<√147<13 6. 14<√205<15 7. 15<√238<16 8. 21<√462<22 9. 26<√717<27 10. 30<√947<31 Consecutive Integers 1. 6 and 7 2. 7 and 8 3. 8 and 9 4. 10 and 11 5. 12 and 13 6. 14 and 15 7. 15 and 16 8. 21 and 22 9. 26 and 27 10. 30 and 31 Prepared by: JUN – JUN P. DARIANO Teacher III Practice Personal Hygiene protocols at all times. 73 MATHEMATICS 7 Name: ______________________________________ Grade & Section: ______________________________ Score: __________ Date: ___________ LEARNING ACTIVITY SHEET Perfect Combination! Background Information For Learners Combining two closest perfect squares between the square root of an irrational number is the key in determining two consecutive integers. These two perfect squares are rational numbers. You will learn in this learning activity sheet the concepts of square roots of rational and irrational numbers. Learning Competency. The learner determines between what two integers the square root of a number is. Code: M7NS-Ig-2 Practice and Application Activity 1. True or False. Write true if the statement is correct and false if it’s not. Write your answer on the space provided before the number. _____1. Rational numbers are numbers that can be expressed as a ratio of two numbers, where a non zero for denominator. _____2. The product of multiplying a number to itself is a perfect square. _____3. The principal root of √784 is –28. _____4. 22 and 23 are two consecutive integers of √508. _____5. If 17 is the first consecutive integer, then the second integer of √275 is 18. Activity 2. Multiple Choice. Write the letter of your choice on the space provided before the number. _____1. What is the √441? A. ±20 C. ±22 B. ±21 D. ±23 _____2. Which of the following is an example of rational number? A. non-terminating decimal C. pi (Π) B. non –repeating decimal D. principal root ____3. Between what two consecutive integers does √128 lie? A. 10 and 11 C. 12 and 13 Practice Personal Hygiene protocols at all times. 74 B. 11 and 12 D. 13 and 14 _____4. What is the sum of the principal roots of √324 and √626? A. 22 C. 44 B. 34 D. 52 _____5. Which of the following is correct? I. √81 II. √144 III. √225 A. I < II C. II > III B. III < I D. I > III _____6. What are the two consecutive integers of this notation: √4<√6<√9? A. 2 and 3 C. 4 and 9 B. 4 and 6 D. 6 and 9 _____7. If x is the first consecutive number, then which of the following illustrates the second number? A. x – 1 C. x + 1 B. x + 2 D. x – 2 _____8. Between what two consecutive integers does √1198 lie? A. 31 and 32 C. 33 and 34 B. 32 and 33 D. 34 and 35 _____9. Does the product of the root of √81 and √144 a perfect square? A. Yes C. Cannot be determined B. No D. None of the above _____10. Which of the following is correct notation between two consecutive integers of the square root of irrational number? A. √121<√132<√144 C. √169<√157<√196 B. √256<√290<√324 D. √49<√71<√64 Reflection What I have learned in this activity? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ References Learners Manual in Mathematics 7, pp. 63 – 68. Answer key Practice Personal Hygiene protocols at all times. 75 Activity 1 1. 2. 3. 4. 5. True True False True False Activity 2 6. B 7. D 8. B 9. C 10. A 11. A 12. C 13. D 14. C 15. A Prepared by: JUN – JUN P. DARIANO Teacher III Practice Personal Hygiene protocols at all times. 76 MATHEMATICS 7 Name of Learner: ________________________________ Section: _________________________________________ Grade Level: _____ Date: ____________ LEARNING ACTIVITY SHEET Estimates the Square Root of a Whole Number to the Nearest Hundredth Background Information For Learners In Mathematics, a square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Exponent can be used to show that the number has been multiplied by itself one or more times. A perfect square is the square of a whole number. The number 9 is a perfect square because 9= 32 . The number 7 is not a perfect square because there is no whole number that can be squared to get 7. However, to estimate square root, numbers to be illustrated must not be perfect square. In this module, learners will be learning how to estimate the square root of a whole number to the nearest hundredth. It has an important concept of standard deviation that is used in probability theory and statistics. As part of the learning activity the learners will be able to accomplish exercises to practice skills in solving square root. It is also strengthen and stimulate the learners creative thinking skills to be ready for the activity. Having this kind of activity will help the learners solve the drill at ease. To give you an idea on to how estimate the square root of a whole number to the nearest hundredth, divide and average method will be used to illustrate. Practice Personal Hygiene protocols at all times. 77 Illustration 1. How to get Non- Perfect Square Root Approximating Square Roots Practice Personal Hygiene protocols at all times. 78 Illustration 1.1 How to get square root? Illustration 2 Approximate √112 to the nearest hundredths. Step 1: Find the value of the whole number. 100 < 112 < 121 Find the perfect squares nearest to 112. √100 < √112 < √121 Find the square roots of the perfect squares. 10 < √112 < 11 The number will be between 10 and 11. The whole number part of the answer is 10. Step 2: Find the value of the decimal. 112 – 100 = 12 Find the difference between the given number, 112, and the lower perfect square. 121 – 100 = 21 Find the difference between the greater perfect square and the lower perfect square. 𝟏𝟐 𝟐𝟏 12 ÷ 21 ≈ 0.571 Write the difference as a ratio. Divide to find the approximate decimal value. The decimal part of the answer is approximately 0.571. Practice Personal Hygiene protocols at all times. 79 Step 3: Find the approximate value. 10 + 0.571 = 10.571 Combine the whole number and decimal. 10.571 ≈ 10.57 Round to the nearest hundredth. The approximate value of √112 to the nearest hundredth is 10.57. Learning Competency with code The learner estimates the square root of a whole number to the nearest hundredth (M7NS-lg-3) EXERCISE 1: UNCOVER THE SQUARE ROOT Directions: Estimate the square root to the nearest hundredths. Use the number line illustrated below. Solve the mark number. 1. 2. 3. 4. 5. EXERCISE 2: NUMBERED LETTER EXERCISE Direction: Step 1. Unlock the numbers using the Alphabets. Step 2. Write your answer from the box provided. Step 3. Add all the number to get the exact whole number. Step 4. Solve the added number by estimating the square root to the nearest hundredths. Practice Personal Hygiene protocols at all times. 80 A R T Q B U P C S V O D N W M E L X F K Y G Z H I J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Practice Personal Hygiene protocols at all times. 81 EXERCISE 3: COMPLETING THE BOX EXERCISE 1. . 2. Practice Personal Hygiene protocols at all times. 82 3. 4. Practice Personal Hygiene protocols at all times. 83 Processing Activity Answer the following question: 1. How do you find the activity? _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________. 2. How to estimate the square root of non perfect square? _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________. Reflection: Complete the statement: I have learned that ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _________________________________________________. References: Pictures and Illustration by Cristobal A. Felipe http://images.pcmac.org/SiSFiles/Schools/GA/MaconCounty/MaconMiddle/Uploads/Docum entsSubCategories/Documents/Estimating%20Square%20Roots_1.pdf Practice Personal Hygiene protocols at all times. 84 Answer Key: EXERCISE 1. UNCOVER THE SQUARE ROOT 1 2.40 2 3.43 3 3.86 4 3.14 5 4.22 EXERCISE 2. NUMBERED LETTER EXERCISE EXERCISE 3: COMPLETING THE BOX EXERCISE 1. 9.11 2. 6.86 3. 12.04 4. 8.49 Prepared by: CRISTOBAL A. FELIPE Teacher Practice Personal Hygiene protocols at all times. 85 MATHEMATICS 7 Name : _____________________ Grade & Section:_______________ Score: ____________________ Date: _______________________ Learning Activity Sheet LOCATE ME IF YOU CAN Background information for Learners This activity sheet serves as a supplement learning material guide for learners. It will direct the students familiarize in plotting the points of irrational numbers in a number line. 𝑛 Irrational numbers are numbers that can NOT be written in the form of 𝑑, where n and d are integers and d is not equal to zero. For example: √2 , √8 , √11 , ∏. Plotting the points of irrational numbers are like plotting points of rational numbers, however it is much complicated without further knowledge in Pythagorean Theorem. Furthermore, knowing how to locate points of irrational numbers will help us understand how Global Positioning System (GPS) works. Illustrative example. Plot the points of √𝟐 𝒂𝒏𝒅 √𝟑 So this is how we plot the points of irrational numbers. Use ruler and compass. 1. From the point of origin or zero draw a right triangle having 1 unit in its base and 1unit on its height, mark zero as point O, mark 1 as point A and point B on the height of a triangle. For √𝟑 we will draw another line start at point B which measures 1 unit perpendicular to OB and mark that as point C. Connect point O to C, then we have triangle OBC as shown in the figure at the top. Applying again the Pythagorean Theorem then we will have OC equal to√𝟑 . Finally use the compass to locate or plot the point of √𝟑 to the number line. For us to plot the point of the negative irrational numbers like -√𝟑, we just draw an arc intersecting the number line on its negative side. See figure above. Practice Personal Hygiene protocols at all times. 2. Since we have now a right triangle OAB then we can now apply the Pythagorean Theorem to plot the point of irrational numbers. 𝑂𝐵2 = 𝑂𝐴2 + 𝐴𝐵2 = 12 + 12 𝑂𝐵2 = 2 𝑶𝑩 = √𝟐 3. So we have now the value of OB, use a compass to finally plot the point of √2 point the tip of the compass on zero and at point B then slide it to create an arc until it intersects the number 86 line since all radii of a circle are congruent then mark the point of intersection as √𝟐 . Learning Competency with Code Plots irrational numbers (up to the square roots) on a number line.***(M7NS-lg-4) Activity 1: Hunting time! Instruction: Encircle all words related and terminologies use in plotting irrational numbers. Words can be spelled downward, upward, diagonal and sideward. P E R P E N D I C U L A R E M B a V L G C O P Y T H O P P Y T H A G O R E A N T Y N D V B A N U M B E R L I N E T R Y E I O P M A I O P L N P R O T R A C T O R A A E C I R C L E S T O F R D R Q L O V E R S S R A D I U S A N O N T E R M I N A T I N G M I N I R R A T I O N A L R R A T I O N A L A B Activity 2: Identify me? List down all irrational numbers found in the box below. 1 2 1.25 2.44948974…. 1.333.. -√5 ∏ -√37 √25 √17 √11 √4 -√9 √10 √8 √26 √50 Activity 3: Put me in a right track! Be a GPS. Create your number line and plot the following irrational numbers on a number line you have created. Use compass and protractor or computer to illustrate how points of irrational numbers is being plotted. a. √𝟓 , −√𝟓, b. √𝟔 , −√𝟔 c. √𝟕 , −√𝟕, d. √𝟏𝟎 , −√𝟏𝟎 e. √𝟏𝟏 , −√𝟏𝟏 CRITERIA Point plotting OUTSTANDING (4) Plot the points of irrational numbers SATISFACTORY (3) Plot the points of irrational numbers Practice Personal Hygiene protocols at all times. DEVELOPING (2) Plot some of the given irrational BEGINNING (1) Doesn’t know how to plot 87 accurately and illustrations on how to locate points are well done. but the illustrations on how plot the points are not well done. numbers but the illustration on how to plot points are not well done. points of irrational numbers on a number line. Reflection: What have you learned today? _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _______________________________________ Answer Key Activity 1. Hunting time! P M P D T N C L N M E B Y V R P I O O I R T B Y R R V N N P V H A E O C E T I E L A N I T L R E R N G G U O R E S R R D C O M P A S S M A I O R B M C T R I T C P E E A T O A N I U Y A R I O F D A O L T N L R R I T N A H T I O A D U I A R O Y N P A R S N L E P N E L E Q A G R R A T I O N A L A B Activity 2: Identify me? 2.44948974…. √26 -√37 √17 √11 -√5 √8 √50 ∏ √10 Activity 3. Put me in a right track! Be a GPS. -√𝟓 √7 √𝟓 √6 √𝟓 Practice Personal Hygiene protocols at all times. 88 √5 -√𝟔 √𝟔 C1 2 -3 -2 -1 0 1 2 3 -√𝟕 √𝟕 -√𝟏𝟎 √11 1 √10 √𝟏𝟎 1 3 -3 -2 -1 0 1 2 3 √𝟏𝟏 -√𝟏𝟏 References: www.topperlearning.com Prepared by: Rex C. Isla Mathematics Teacher Practice Personal Hygiene protocols at all times. 89 MATHEMATICS 7 Name of Learner:_____________________________ Section:____________________________________ Grade Level:___________ Date:________________ LEARNING ACTIVITY SHEET Oh! It’s Real! Background Information for Learners The set of real numbers consists of all numbers on a number line. Subsets can include any collection of numbers, but the elements of an important subset should at least have several characteristics in common. Most of these subsets are only useful for specific calculations, but there are a few that have interesting properties and that help in understanding how real number system works. The set of real numbers consists of the rational and the irrational numbers. Rational numbers are integers and numbers that can be expressed as a fraction or decimal or even percentage. All other real numbers are irrational which include numbers such as the square root of 2 and the number pi. Since irrational numbers are defined as a subset of real numbers, all irrational numbers must be real numbers. Learning Competency with code Illustrates the different subsets of real numbers M7NS-Ih-1 Directions: Exercise 1. REFLECT: What is your opinion about the following questions on NUMBERS? Write your answer on the space provided for each number. 1. When did humans first grasp the basic concept of a number? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 2. Why do we use numbers in our daily life? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Practice Personal Hygiene protocols at all times. 90 Exercise 2. WORD ATTACK: Eight different words or partition of numbers are hidden in each row. Reveal the term or word by crossing out the excess letters. Put the excess letters in the box below to reveal a secret message. MZIERSO TFARAKCTIEONSS A D E R C I E M A L numbers P R O N O A T F U R A L numbers T H W H A O L T E numbers RAYTIOONUALS A R E I R R A T I O T N A L number RIYNTEGERINGS Secret Message: Answer the following questions: 1. Based on the activity, how many words are familiar to you? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 2. What word/s did you encounter during your younger days? Enumerate them and give examples of each. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3. Which word/s is/are not familiar to you? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Practice Personal Hygiene protocols at all times. 91 Exercise 3. TRASH IT RIGHT: Wastes have value and only need to be properly sorted. In this exercise, the following wastes have different situations written on it. These situations represent numbers/set of numbers. Sort them by drawing an arrow to which waste sorter they belong. Answer the following questions: 1. Did the different situations related to numbers help you in sorting wastes? How? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _________ 2. Did you experience numbers in your daily life? Cite a situation. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _________ Exercise 4. A. The set of numbers is called the real number system that consists of different partitions/subsets that can be represented graphically on a number line. Locate the following numbers on the number line by naming the correct point. Practice Personal Hygiene protocols at all times. 92 B. Determine the subset of real numbers to which each number belongs. Use a tick mark (√) to answer. Number 1. -21 2. 97.24 3. ¼ 4. √25 3 5. √27 6. -0.0028 7. -√100 8. e 9. -11.487 10. 0.1111… Whole number Integer Rational Irrational Carry out the task being asked by writing your response on the space provided for each number. 1. Are all real numbers rational numbers? Prove your answer. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _________ 2. Are all rational numbers whole numbers? Prove your answer. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _________ 1 3 3. Are − 5 and − 7 negative integers? Prove your answer. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 4. How is a rational number different from an irrational number? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 5. How do natural numbers differ from whole numbers? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Practice Personal Hygiene protocols at all times. 93 C. Complete the details in the Hierarchy Chart of the Set of Real Numbers. Exercise 5. In this activity, you are going to make a comic strip with dialogues on situations related to real numbers for your performance based output. Cell Total Relevance Elements Presentation Creativity RUBRIC Exceeds (3) Meets (2) At least 6 3-5 Clearly shows the Comic strip has little mathematics concept to do with the mathematical concept Has a title, student’s name The comic strip is is visible as the author of missing one element the comic strip as stated in column 2 Does not meet (1) 1-2 Comic strip has nothing to do with the mathematical concept Does not include any of the aforementioned elements The comic strip is neatly Overall appearance is Overall appearance is drawn in pencil. Overall average. poor. appearance is superior. The comic strip has unique, The comic strip has The comic strip does well drawn characters (not unique, well drawn not have unique, well stick figures) with some characters (not stick drawn characters (not humor or drama in the figures) with little stick figures) with wording. Cartoon should humor or drama in little to no humor or generate interest in the the wording. Cartoon drama in the subject. should generate little wording. Cartoon interest in the does not generate Practice Personal Hygiene protocols at all times. 94 subject. interest subject. in the Reflection Complete this statement: I have learned in this activity…. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ __________________________________________________________________________. References: Aseron, Elizabeth R.,et.al. (First Edition 2013), Mathematics 7 Teacher’s Guide. Pasig City, Philippines https://sciencing.com/what-are-subsets-of-real-numbers-13712247.htm This site provides short background for the topic. https://en.m.wikipedia.org This site provides some definitions used in this topic. https://believe.earth/en/13-tips-on-sorting-waste This site provides information on proper sorting of waste. https://www.universetoday.com This site provides examples of situations related to real numbers. https://www.rcampus.com/rubricshowc.cfm?code=G48C63&sp=yes& This site provides the rubric for the performance based output. https://www.google.com This site provides pictures that made the LAS more attractive. https://www.bitmoji.com This site provides pictures that made the LAS more attractive. ANSWER KEY Exercise 1. Answers may vary. Exercise 2. 1. ZERO 5. WHOLE numbers 2. FRACTIONS 6. RATIONALS 3. DECIMAL numbers 7. IRRATIONAL numbers 4. NATURAL numbers 8. INTEGERS Secret Message: “Mistakes are proof that you are trying.” Practice Personal Hygiene protocols at all times. 95 Exercise 3. Counting Numbers *Finding out how many days left before Christmas. *Asking your sister the available pairs of shoes are in her closet. *Determining the number of students enrolled in grade 7. Fraction/Decimal -Cardo shares his 2 pizzas among his 12 friends. -Junior paid Php 572.21 for his new bag. Integers *Pablo withdraws Php 2000 from his bank account. *Your dad told you that the height of Magat Dam is 114 meters. *Neptune has an average temperature around -214 degrees Celsius. Irrational -NASA regularly uses pi to calculate trajectories of spacecraft. Exercise 4. ¶ A. B. Number 1. -21 2. 97.24 3. ¼ 4. √11 3 5. √27 6. -0.0028 7. -√100 8. e 9. -11.487 10. 0.1111… C. Whole number Integ er / Rational Irrational / / / / / / / / / / / / / / Prepared by: LEONARD B. SAMBILE Rizal NHS Practice Personal Hygiene protocols at all times. 96 MATHEMATICS 7 Name of Learner: _______________________ Section: _______________________________ Grade Level: _____________ Date: ___________________ LEARNING ACTIVITY SHEET Sets and Real Number System Background Information for learners Do you still remember these numbers? Clipartkey.com Real numbers includes natural numbers, whole numbers, integers, rational numbers and irrational numbers. Lets have a closer look on the example below: A.Question : Which set of rational numbers is arranged from greatest to least? a. −6 −1 5 1 , 2 ,0,9,0.6,1.0 17 15 b. −3.25,8,5,0.5,3,6 c. d. 7 1 3 −1 ,0.9, , , ,0.7 6 2 8 10 9 7 −5 −10 , , 8 6 12 ,-1.1, 5 ,-3.6 Practice Personal Hygiene protocols at all times. 97 Learning Competency with Code Arranges real numbers in increasing or decreasing order and on a number line M7NS-Ih-2 Directions/Instructions In this activity you will be able to arrange real numbers, it is expected that you arrange real numbers in increasing or decreasing order. A prerequisite in the next activity is your knowledge in real numbers. Let us examine the illustrative example below. B. Can you guess the next set of numbers ? C. How about the missing three boxes below? D. Do you have the right guess for the two box below? Practice Personal Hygiene protocols at all times. 98 Are you ready for our activity? Activity 1 Identify which of the following set of numbers are arrange in increasing order. Encircle the whole set. 1. a. √23,5,6,43% b. 5,√23,6,43% c. 43%,5,√23, 6 d. 43%,√23, 5,6 Clipartkey.com 2. 1 −3 1 a. , , 4 7 2 1 1 −3 b. , , 24 7 −3 1 1 c. , , d. 7 24 −3 1 1 , , 7 42 3. 5 9 5 a. , , 8 16 12 9 5 5 b. 16,12, 8 9 5 5 c. 16, 8,12 5 9 5 d. 12,16,8 Activity 2 Identify which of the following set of numbers are arrange in decreasing Clipartkey.com order. Box the item that contains it. 1. a. 6,5, √23,43% b. 5,√23,6,43% c. 43%,5,√23, 6 d. 43%,√23, 5,6 2. 1 −3 1 a. 4, 7 ,2 1 1 −3 b. 2,4, 7 −3 1 1 c. , , d. 7 24 −3 1 1 , , 7 42 3. 5 9 5 a.8,16,12 b. 9 5 5 , , 16 12 8 9 5 5 c. 16, 8,12 Practice Personal Hygiene protocols at all times. 99 5 9 5 d. 12,16,8 Proceed to the next level? Activity 3 Identify and encircle the letter which of the following number lines shows decreasing order. A. 11 1 3 7 9 8 7 6 5 4 3 8 7 6 10 4 2 3 2 2 2 -3 -2.0 -1 0 1 √4 3 4 25 5 5 B. Clipartkey.com 11 √100 18 2 C. -5 -4 D. 1.4 1.5 2 2.1 1.0 2 √3 6 7 8 9 Activity 4 Identify and box the letter which of the following number lines shows increasing order. A. 11 1 3 7 9 8 7 6 5 4 3 8 7 6 10 4 2 3 2 2 2 -3 -2.0 -1 0 1 √4 3 4 25 5 2 2.1 1.0 2 √3 6 8 9 5 B. 11 √100 18 2 Clipartkey.com C. -5 -4 D. 1.4 1.5 Practice Personal Hygiene protocols at all times. 7 100 Final level? Activity 5 The final round will test you to locate the real numbers on the number line. You will show or graph in ascending and descending order. The real number line has points that represent fraction and decimals as well as integers. Drawing a point is called graphing or plotting the number. To plot a real number, draw and label a number line, find where the number is on the number line and place a dot on the number. Clipartkey.com 13 Given: (2,√16, 0 ,-1.5,2,2,-3,2.5, π) A. Ascending Order -4 -3 -2 -1 0 1 2 3 4 5 6 4 3 2 1 0 -1 -2 -3 -4 B. Descending Order 6 5 Rubric for scoring : Total Score Rating Activity 1( 1 point each) 3 pts 19-20 100% Activity 2( 1 point each) 3 pts 17-18 95% Activity 3( 3 points) 3 pts 15-16 90% Activity 4( 3 points) 3 pts 13-14 85% Activity 5 (4 points each) 8 pts 11-12 80% 9-10 75% 20 pts 8 and below Practice Personal Hygiene protocols at all times. 70% 101 Closure/Reflection Complete this statement I have learned about… ______________________________________________________ ___________________________________________________________ ___________________________________________________________ ___________________________________________________________ ___________________________________________________________ ___________________________________________________________ References for learners https://sciencing.com/what-are-subsets-of-real-numbers-13712247.html https://www.google.com/search?q=subsets+of+real+numbers+chart&sxsrf=ALeKk026VncBt ZzjmPGvBDxa8De3HqeNkg:1591363489062&tbm=isch&source=iu&ictx=1&fir=Tov4OKj GCgUVcM%253A%252CKIs9eoYRUxPB8M%252C_&vet=1&usg=AI4_-kRjON_I1I20HtlL-g_hf2TzW2FAQ&sa=X&ved=2ahUKEwiH-T74urpAhVHyYsBHQVRDrsQ9QEwBXoECAkQJg&cshid=1591363514771673&biw=102 4&bih=657#imgrc=Tov4OKjGCgUVcM: https://quizizz.com/admin/quiz/5c89bf62323742001ce31625/comparing-and-ordering-realnumbers https://saylordotorg.github.io/text_elementary-algebra/s04-01-real-numbers-and-the-numberli.html https://www.bbsd.com/cms/lib/PA01916419/Centricity/Domain/126/Compare%20and%20Or der%20Real%20Numbers%20Worksheet%20Notes.pdf Practice Personal Hygiene protocols at all times. 102 Answer Key A. d 4 B.85,90,95,100,105 1 C. 465,47,475 D. -5.75,-5.50 Activity 1 1.d 2.d 3.d Activity 2 1.a 2.b 3.a Activity 3 B Activity 4 C Activity 5 13 Given: (2,√16, 0 ,-1.5,2,2,-3,2.5, π) A.Ascending Order -3 -4 -3 1 0 2 -1.5 -2 -1 √16 6 5 4 1 0 B.Descending Order 32 √16 2 2.5 π 1 20 3 π 2.5 2 2 3 2 2 1 0 3 4 6 -3 -1.5 -1 5 -2 -3 -4 Prepared by: GEORGE M. VIBA Master Teacher I Rizal National High school Practice Personal Hygiene protocols at all times. 103 MATHEMATICS 7 Name: _________________________________ Date: __________________________________ Grade Level: ____________ Score: _________________ LEARNING ACTIVITY SHEET Expressing numbers in Scientific Notations and vice versa Background Information for Learners This activity sheet serves as a self-learning guide for the learners. It facilitates lesson comprehension as it specifically aims for students’ mastery on writing numbers in Scientific Notation and vice versa. Scientific notation is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits. It is the way to easily handle very large numbers or very small numbers. The process of writing numbers in a special way like this: • • • “A number” is equal to “Scientific Notation” 700 = 7 x102 4,900,000,000 = 4.9 x 109 The number is written in two parts: (1) Just the digits, with the decimal point placed after the first digit, followed by; (2) × 10 to a power that puts the decimal point where it should be. The following illustrates such: Credits: MathisFun.com To figure out the power of 10, think "how many places do I move the decimal point?" 1. When the number is 10 or greater, the decimal point has to move to the left, and the power of 10 is positive. 2. When the number is smaller than 1, the decimal point has to move to the right, so the power of 10 is negative Examples: • 0.0055 is written 5.5 x 10-3 • 0.000000078 is written 7.8 x 10-8 • 0.000000000000051491 is written to 5.1491 x 10-14 Practice Personal Hygiene protocols at all times. 104 Perform the following operations in scientific notation. Addition. The first step is to make sure the exponents are the same. We do this by changing the main number (making it bigger or smaller) so that the exponent can change (get bigger or smaller). Then we can add the main numbers and keep the exponents the same. Model: (2 x 102) + (7 x 102) = 9 x 102 (same exponent) = 900 (final answer) Model: (3 x 104) + (2 x 103) = (3 x 104) + (0.2 x 104) (divide 2 to 10 and add 1 exponent) = 3.2 x 104 (same exponent) = 32,000 (final answer) Subtraction. Just like addition, the first step is to make the exponents the same. Instead of adding the main numbers, they are subtracted. Try to convert so that you will not get a negative answer. Model: (4 x 107) – (2 x 107) = 2 x 107 (same exponent) = 20,000,000 (final answer) Model: (3 x 104) - (2 x 103) = (30 x 103) - (2 x 103) (multiply 3 to 10 and less 1 to its exponent) 3 = 28 x 10 (same exponent) = 2.8 x 104 (final answer) Multiplication. (the "easy" operation - remember that you just need to multiply the main numbers and add the exponents). Model: (8 x 105) x (3 x 105) = 24 x 1010 = 2.4 x 1011 Model: (2 x 102) x (6 x 103) = 12 x 105 = 1.2 x 106 Division. (a little harder - we basically solve the problem as we did above, using multiplication. But we need to "move" the bottom (denominator) to the top of the fraction. We do this by writing the negative value of the exponent. Next divide the first part of each number. Finally, add the exponents). (12 x 103) Model: ----------- = 2 x (103 x 10-2) = 2 x 101 = 20 (6 x 102) Learning Competency and Code Writes numbers in scientific notation and vice versa. (M7NS-Ii-1) Practice Personal Hygiene protocols at all times. 105 Activity 1: Transform Me! Direction: Express each in scientific notation. 11. 380 000 12. 7 000 000 13. 3 530 000 000 14. 348 000 15. 809 000 000 000 16. 507 000 000 000 17. 0.0000000456 18. 0.0000000005032 19. 457 20. 385.4 Activity 2:Make it larger! Direction: Express each in decimal form. 6. 7 x 106 7. 5 x 108 8. 8.4 x 107 9. 5.9 x 109 10. 7 x 10-6 11. 8.2 x 10-7 12. 8.13 x 107 13. 5.39 x 105 14. 6.49 x 10-9 15. 7.002 x 100 Activity 3: Make real life easy! Direction: Write the numbers in different Ways. (in Scientific Notations) 1. The population of the world is about 7,117,000,000. 2. The distance from Earth to the Sun is about 92,960,000 miles. 3. The human body contains approximately 60,000,000,000,000 to 90,000,000,000,000 cells. 4. The mass of a particle of dust is 0.000000000753 kg. 5. The length of the shortest wavelength of visible light (violet) is 0.0000004 meters. Practice Personal Hygiene protocols at all times. 106 Activity 4: Part 1. Operate me! Direction: First express the problem with the exponents in the same form, then solve the problem. 1. 2. 3. 4. (4 x 103) + (3 x 102) = (9 x 102) + (1 x 104) = (2 x 102) - (4 x 101) = (9 x 1012) - (8.1 x 109) = Activity 5: Part 2. Operate me! Direction: Write your answer as in the model above; first convert to a multiplication/Division problem, then solve the problem. 1. 2. 3. 4. (1 x 103) x (3 x 101) = (3 x 104) x (2 x 103) = (8 x 106) / (4 x 103) = (4 x 103) / (8 x 105) = Reflection (What is your reflections about the Activity?) _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ______________________________________________________. References • • • E-MATH 7 Revised Edition Math is Fun Scientific notation. Retrieved from https://www.mathsisfun.com/numbers/scientific-notation.html Dictionary-Scientific Notation. Retrieved from https://www.yourdictionary.com/scientific-notation Year Triangle Prepared by: MARK JOSEPH L. LEAL Teacher Practice Personal Hygiene protocols at all times. 107 MATHEMATICS 7 Name: ________________________________ Date: _________________________________ Grade Level: ____________ Score: _________________ LEARNING ACTIVITY SHEET The World of Real Numbers Background Information for Learners This learning activity sheet is an application of knowledge about real numbers. The knowledge in real numbers is not only applicable in mathematics but also in other learning areas like in MAPEH, TLE, Science and etc. There are problems in real life that can be simplified and solve using the concepts of real numbers. Real numbers is the set of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Natural numbers or counting numbers are 1,2, 3, 4, 5, 6, 7, …. Whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, …. Integers are the positive and negative numbers, example -5, -4, -3, -1, 0, 1, 2, 3, 4, and so on. Rational numbers are numbers that can be express as ratio of two quantities. Example 4 2 1 2 , 2, 3 , −3, 0.5 3, . Irrational numbers are numbers that cannot be written as ratio of two quantities. 3 Like for example √3 , √7 , √5 . Here are the examples of real life situations: 1. Maria’s weight decrease by 5 kg this can be expressed as – 5. 2. Juan Dela Cruz climbs 20 more steps uphill, this can be expressed as + 20. 3. Pedro weighed 110 kg when he enrolled in Maliksi Gym. After series of sessions he losses weight of 30 kg. Because of the pandemic covid-19 all gyms were closed he gain weight of 13 kg. What is weight of Pedro after a series of changes? Can be represented as 110 – 30 +13 -30 for losing weight and + 13 for gaining weight Solution: 110 – 30 +13 = 93 Therefore, Pedro”s weight is 93 kg Learning Competency: The learner represents real-life situations and solves problems involving real numbers.(M7NS-Ii-2 and M7NS-Ij-1 Practice Personal Hygiene protocols at all times. 108 Activity 1 Try this one! I. Directions: Read carefully the situations and write each representation on the right column. Situation 1. Cardo’s farm yield 30 cavans more than last cropping. 2. Amihan’s waist decrease by 3 cm 3. The speed of the habal-habal lessen into 2 km/hr. 4. Lam-ang gain 5 lbs after community quarantine. 5. During summer the electric consumption of Mario increases by 500. Representation Let’s have more! II. Directions: Solve the following. Show your solution 1. The Mac JB delivery boy delivered 8 egg sandwiches for Php 39 each, 5 large camote fries for Php55 each, 7 buko juice for Php 39 and 5 buko pie for Php 30 each. If you gave Php 1500.00, how much is your change? Representation: Solution: 2. Josefa has been raised to be an environmentalist. She advocates to plant trees every year. At the age of 8, she started planting 12 trees at Mt. Dariuk. How many trees would she have planted by the time she reach 35 years old, if she planted a constant number of trees each year? Representation: Solution: 3. Emilo wanted to buy a 500 square meter lot in Roque Subdivision. How much it cost if the lot cost Php 3500 per square meter? Practice Personal Hygiene protocols at all times. 109 Representation: Solution: Activity 2 I. Directions: Represent each of the following by real numbers. Then give the opposite of the quantity being described. Situation 1. Teodora gains 10 kg. 2. Rony’s grade in Mathematics is decrease by 2 points. 3. The humidity rose five degrees Celsius yesterday. 4. Angelei withdrawn Php 21 000 in her savings account. 5. A tarsier sits on a limb that is 30 ft above the ground Representation Opposite II. Directions: Write a situation using the given values. Values 1. increase 21 2. loss of 15 3. dropped 32 4. down 13 5. up 7 Situation III. Directions: Solve the given situation then match your answer to column B that corresponds to the correct chemical name of each chemical symbols. Write the letter of your answer before the number. Column A Column B Chemical Symbol Chemical Name _____1. ( Er ) It represent Juana’s debt of A. 10 Einsteinium Php 5,000.00 from a lending company. B.–5000.00 Erbium _____2. ( Cf ) A certain computer can perform 6.3 𝑥 106 . Calculation in a single second. C. 500 Europmium Practice Personal Hygiene protocols at all times. 110 How many calculations can it perform in 1 minute? _____3. ( Eu ) A room has a temperature of 350 , then the temperature dropped 200 , then rose 600 and finally dropped 250 . What is the temperature after the given changes? ______4. ( Ca ) The price of sugar increased Php 22.00. If the increase was spread equally over 4 days, how much did the price increase in one day? ______5. ( Es ) Diana is on the 6th floor of Manila hotel. She went an elevator up 7 floors, then down 3 floors. What floor is she now? D. 3.78𝑥108 Californium E. 5.5 Calcium F. 38.7𝑥107 Chromium Activity 3 History time. Who is that President? I. Directions: Identify the former Presidential candidate who is known with the given slogan. To determine the name of the former presidential candidate, answer the given problems then match your answer in the box below the problem. Write the name of the president on the space before the number. __________1. “Tama na! Sobra Na! Palitan na!” Rizal has a youtube channel to help her students in mathematics. Every month, Rizal receives a subscription fee of Php 20 from each subscribers to the channel. The channel had 15000 subscribers last month. This month 750 new members joined the channel and 10 members cancelled their subscription. How much money will Rizal’s online business earn this month. _________2. “Tapang at malasakit.” Maring lost her job because of lackdown.To have other source of income she sellschicken lumpia online. Her lumpia is Php 50 for 15 pcs. How much she earn if she spent Php 500 for 330 pcs? _________3. “Kung walang corrupt, walang mahirap.” Myrna wanted to donate washable facemask to barangay Batal. She sewed 10 pcs of facemask in 5 mins. How many facemask she can sew in 3 hours? _________4. “Ituloy ang daang matuwid.” In Baguio City the temperature varies. At 4 o’clock in the morning the temperature is 150 at 12 noon the temperature rose up to 100 , then at 2 pm the temperature was 300 , and finally at 7 pm the temperature dropped to 180 . What is the temperature after the given changes? ________5. “Sipag at Tiyaga.” Practice Personal Hygiene protocols at all times. 111 Albert drove his car at plane road with a speed of 100 kph, at the uphill part of the road he increased the speed 20kph, he reduced the speed of the car reaching the downhill part to 70kph. What is the speed of the car after the given changes? 360 – Benigno Aquino 50 – Manny Villar 14800 – Corazon Aquino 600 – Rodrigo Duterte 12 – Mar Roxas 18400 – Joseph Estrada I will solve my own problem. Directions: Create 3 word problems about real numbers. The situations must be related to your experiences during the pandemic. Solve each problem and then indicate the values you’ve learn from that experiences. 1. Problem: __________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Solution: Values:__________________________________________________________ ________________________________________________________________ ________________________________________________________________ 2. Problem: _______________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ Solution: Values:__________________________________________________________ Practice Personal Hygiene protocols at all times. 112 ________________________________________________________________ ________________________________________________________________ 3. Problem: ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ Solution: Values:__________________________________________________________ ________________________________________________________________ ________________________________________________________________ Reflection How did you find the lesson and activities? Why? _____________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ __________________ References Math Made Easy 7 by Michael B. Malvar, Queeny Joyce F. Sebastian and Jerson E. Sebastian. S 2017. Triangle Trigonometry, Module 2 (LM) BEAM Fourth Year, Practice Personal Hygiene protocols at all times. 113 Time to CHECK Answer Key Activity 1 I. 1. +30 2. -3 3.-2 4. +5 5. +500 II. 1. Representation:1500 – [(8x39) + (5x55) + (7x39) + (5 x30)] Solution: 1500 – [(8x39) + (5x55) + (7x39) + (5 x30)] = 1500 – (312 + 275 + 273 + 150) = 1500 – 1010 = 490 Therefore, his change is Php 490 2. Representation: 35 – 8 + 1 = number of years she’s planting trees 12 x number of years she’s planting trees = no of trees Solution: 12 x (35 – 8 + 1) = 12 x 28 = 336 Therefore, Josefa planted 336 trees in 28 years 3. Representation: 500 x 3500 Solution: 500 x 3500 = 1 750 000 Therefore, 500 square meter worth Php 1, 750, 000 .00 Activity 2 I. Representation Opposite 1.10 -10 2. -2 +2 3. +5 -5 4. -21000 +21,000 5. +30 -30 II. Example of expected answers. The answers of this activity varies. 1. The water level increase 21 cubic meters 2. The electric power plant experience power lost of 15 kw every day 3. The gross monthly income of Robinsons dropped to 32%. 4. Maria is in the 70th floor and she moves down 13 floors. 5. She moves up 7 steps. III. 1. B. Erbium - 5000.00 2. D. Californium 3.78 𝑥108 3. C. Europmium 500 Practice Personal Hygiene protocols at all times. 114 4. E.. Calcium 5.5 5. A.Einsteinium 10 Activity 3 I. 1. 14 800 – Corazon Aquino 2. 600 – Rodrigo Duterte 3. 360 – Benigno Aquino 4. 12 – Mar Roxas. 5. 50 – Manny Villar II. Rubrics 0 pt No attempt to create a problem or solve 1 pt Attempted to create or construct a word problem but did solve. 3pts Able to construct a word problem, show a solution of the problem but incorrect, and explain the value/s learned. 4pts Able to construct a word problem correctly, show a solution correctly, and explain the values learned. Module 13 (TG), EASE Module Fourth Year · Triangle Trigonometry, Mo, Module Prepared by: LEILANI T. SANTIAGO Teacher-III MYRNA GUIRING Teacher-III Practice Personal Hygiene protocols at all times. 115