SAN PABLO DIOCESAN CATHOLIC SCHOOLS SYSTEM Diocese of San Pablo Immaculate Conception Catholic School - Santa Cruz, Laguna Senior High School Department Learning Module – Week 2 (1st Sem-1st Qtr) September 6-10, 2021 Teacher: Ms. Edith E. Estremera Subject: Business Mathematics Grade Level: Gr. 11 Most Essential Learning Competencies LC1-ABM_BM11RP-If-4 - Solve problems involving direct, inverse and partitative proportion LT1.1- ABM_BM11RP-If-4 – I can define the important terms and the three types of proportion. LT1.2- ABM_BM11RP-If-4 - I can justify when to use direct, inverse and partitive proportion. LT1.3- ABM_BM11RP-If-4 - I can compute real life word problems involving direct, inverse and partitive proportion Lesson – Ratio and Proportion TIME FRAME 07:00 – 07:30am Synchronous 07:30 - 08:15 am ACTIVITIES Finalization of Project 1 and Reading of Learning Module INSTRUCTIONS 1. Online Class Decorum 2. Engage/Explore Activity (Map of Conceptual Change) 1. (Greetings, Prayers, Attendance) 2. It is amazing to note that the study of ratio and proportion leads to understanding other concepts. Learning ratio and proportion should be easy as it is a skill and not a complex concept. So lets turn the bulb on with different colors as you compute for ratio and proportion. Prepare coloring materials and paper. 3. Explain Activity (Attachment 1) 3. Using Slide Presentation, discuss briefly: Status of Project 1 Short Quiz – True or False (5 items) Proportion Color by Answer Add on Lesson on Percentage Ratio and Proportion Types of Proportion – Direct, Inverse and Partitive Solving simple exercises Project 2 Submission of : a. Proportion Color by Answer b. Worksheet 3.1 (Attachment c. Warhead 3.2 (Attachment) d. Project 2 – Real Life Problems applying direct, inverse, and partitive proportion involving you e. Competency Self Assessment Asynchronous 08:15 – 09:00am 4. Extend Activities 4.1 Answer Worksheet3.1 - The Three Types of Percentage Problems and Worksheet 3.2 - Solving Problems on Ratio and Proportion (Attachment 3) Submit answers via email (edithestremera0604@gmail.com), once received, to be checked and recorded and answer key will be given. 09:00 – 9:15am 09:15 – 09:30am (Map of Conceptual Change) At this point, let us look again at Proportion activity - Light Bulb (Engage Activity) and at the space provided, write your realization or new things that you have learned. 09:30 – 10:45am 5. Evaluation Activities 5.1. Making of Project 2 Formulate real life problems applying direct, inverse, and partitive proportion involving you To assist you in your project and to summarize today’s lesson, watch the following video: Clickable link: https://www.youtube.com/watch?v=f wWXN2eigSY 10:45 – 11:00am Self-Assessment: Using the Competency Self-Assessment, assess the learning you have acquired for this week. Ask for clarifications for gray areas in the lesson/s. (Attachment 5) Value Integration: The learners will be able to persevere and at the same time have fun while learning. They will be encouraged to be creative, resourceful and to use their intellectual competence as well as critical thinking skills and be able to apply these in solving real life problems. The true measure of the value of any business leader and manager is performance. Brian Tracy Resources: References: Business Mathematics Third Edition, pp. 112-123 and pp. 140-147 Learning Module Video link: https://www.youtube.com/watch?v=fwWXN2eigSY Link: https://ideagalaxyteacher.com/proportions-activities/ eee/1ST Sem-1ST Qtr-BusMath-WEEK 1 p 3 ATTACHMENTS Attachment 1 eee/1ST Sem-1ST Qtr-BusMath-WEEK 1 p 4 Attachment 2 WEEK 2( September 06-11, 2021) Add on Lesson about Percentage The Three (3) Types of Percentage Problems A. Finding percent (P) of a number Given the base (B) and the rate (R), to find the percentage (P) use the formula :P = B x R Example: Find 15% of 300 B = P300 R = 15% or .15 P = P300 x .15 Answer: P45.00 B. Finding what percent one C. Finding a number when a number is of another percent of that number is (find the Rate (R) ) known (find the Base (B) ) Given the base (B) and the Given the base (B) and the percentage (P), to find the percentage (P), to find the rate rate (R), use the formula :R = (R), use the formula :B = P / R P / B or R = 𝑷 or B = 𝑩 Example: 140 is what % of P280? P = 140 B = 280 R= 𝟏𝟒𝟎 𝟐𝟖𝟎 𝑷 𝑹 𝟏 Example. 8 is 2 % of what 𝟐 𝟏 R = 2 % or number ? P = 8 𝟏 𝟐 2.5% or .025 x 100 = 𝟐 x 100 B= Answer : 50% 𝟖 .𝟎𝟐𝟓 = 320 Answer Ratio and Proportion A ratio is the relation between two similar quantities. It consists of two numbers, the antecedent which is the first number mentioned and the consequent, the second number. Just like a fraction, a ratio is written in fractional form like 𝟐 𝟑 or in this form, 2:3. Reduce ratios to their lowest terms in the same manner that fractions are reduced. Illustrative Problems: 1. What is the ratio of 16 ft. to 6 ft. ? Answer: 𝟏𝟔 𝒇𝒕. 𝟔 𝒇𝒕. = 2. What is the ratio of 2 lb. to 4 oz. ? 𝟖 𝟑 Answer: 𝟐 𝒍𝒃. 𝟒 𝒐𝒛. 𝟑𝟐 𝒐𝒛. 𝟒 𝒐𝒛. = = 𝟖 𝟏 Note: if the units are different, apply conversion A proportion is a statement that two ratios are equal. The ratios therefore constitute a proportion. A proportion is written as: 𝟑 𝟒 𝟑 𝟒 𝟗 𝟗 and 𝟏𝟐 are two equal ratios and = 𝟏𝟐 or 3 : 4 : : 9 : 12 Rule of Proportion : The product of the mean equals the product of the extremes: in 𝟑 𝟒 = 𝟗 𝟏𝟐 the means are the 4 and 9 while 3 and 12 are called extremes. the double : : is read as equals. Finding an unknown term in a proportion: 3. Assuming the second term is unknown, the proportion may be written as 6:n = 12:14. Using the rule, the product of means equals ST product of the extremes. eee/1the Sem-1STQtr-BusMath-WEEK 2 Solution: 6:n = 12:14 == > 6 x n = 12 x 14 12n = 84 n = 84 ÷ 12 n= 7 1. A motorist drove 140 miles in 5 hours, at the same rate of speed, how far can he drive in 7 hours? The ratio of the miles equals the ratio of the hours? Solution: N represents the missing distance 𝑵 𝟏𝟒𝟎 = ratio of the missing distance to the known time 𝟕 𝟓 = ratio of the missing distance to the length of the known time 𝑬𝒒𝒖𝒂𝒍 𝒓𝒂𝒕𝒊𝒐: 𝑵 = 𝟏𝟒𝟎 𝟕 𝟓 Cross product: 5 x N = 140 x 7 5N = 980 ; N = 𝟗𝟖𝟎 N 𝟓 = 196 miles 2. Cecil, Pam and Arlen are business partners who decided to divide their profit of P195,000 after a year of their operation. The women invested P15,000, P20,000 and P30,000, respectively. Find their share of profit? Solution: 1.5 + 2 + 3 = 6.5 parts 195,000 6.5 = P30,000 per share 1.5 x P30,000 = P45,000 (Cecil) 2 x P30,000 = P60,000 (Pam) 3 x P30,000 = P90,000 (Arlen) ATTACHMENT 3 Immaculate Conception Catholic School Sta. Cruz, Laguna WORKSHEET 3.1 – The Three Types of Percentage Problems Business Mathematics– Gr. 11 DATE: NAME: SECTION: TEACHER: 10 Ms. Edith E. Estremera I. Solve the percentage, rate and base of the following problems and encircle your final answer. I. Find the Percentage (P) 1. How much is 6% of P150? 4. II. Find the Rate (R) III. Find the Base (B) 2. P75 is what % of P350? 3. 22 is 40% of what amount? 3 % of P192 is what 5. What part of 180 is 140? 4 amount? 1 6. 42 % of what amount is P650? II. Solve completely the given real life problem on percentages. (4 pts) 7-10. Ragnar answered correctly 42 items of the 50-item Test A and 56 items of the 60-item test. In what test do you think Ragnar make a better rate? - Immaculate Conception Catholic School Sta. Cruz, Laguna WORKSHEET 3.2 – Solving Problems on Ratio and Proportion Business Mathematics– Gr. 11 DATE: TEACHER: NAME: SECTION: I. 10 Ms. Edith E. Estremera Solve the following problems: 1) N : 31 = 2 : 8 ___________________________ 3) N : 4 = 25 : 20 ___________________________ 2) 8 𝑁 = 40 45 _______________________________ 4) 6 : N = 8 : 20 ___________________________ A. The school enrollment in a computer school shows that there are 5 girls to 8 boys. The school enrollment this year was 5,200. how many are boys and how many are girls? (3 pts with solution) B. Mr. Santos and Mr. del Rosario are business partners. How much does each receive if a profit of P130,000 is divided in the ratio 7 to 3 in favor of Mr. Santos? (3 pts with solution) ATTACHMENT 4 THE ROMAN CATHOLIC BISHOP OF SAN PABLO FOR THE SAN PABLO DIOCESAN CATHOLIC SCHOOLS SYSTEM Diocese of San Pablo IMMACULATE CONCEPTION CATHOLIC SCHOOL- STA. CRUZ, INC. P. GUEVARRA AVE., BRGY. POBLACION, STA. CRUZ, LAGUNA BUSINESS MATHEMATICS - Gr. 11 edithestremera0604@gmail.com LEARNING COMPETENCIES Ratio and Proportion Week 2 BEFORE Sure IDNK Unsure AFTER Sure IK COMPETENCIES WITH CODE LC1- ABM_BM11RP-If-4 Solve problems involving direct, inverse and partitative proportion LT1.1- ABM_BM11RP-If-4 I can define the important terms and the three types of proportion. LT1.2- ABM_BM11RP-If-4 I can justify when to use direct, inverse and partitative proportion. LT1.3- ABM_BM11RP-If-4 I can compute real life word problems involving direct, inverse and partitative proportion. Sure IDNK Unsure Sure IK