Mathematics 8,6 and5 - WEEK8- d5_q2.docx
- 1. GRADES 1 to 12 DAILY LESSON LOG School: STO. NIO INTEGRATED SCHOOL Grade Level: 5,6, 8 Teacher: CHARLOTTE O. CORALDE Learning Area: MATHEMATICS Teaching Dates and Time: NOVEMBER 22, 2024 (DAY 5) Quarter: 2ND QUARTER MATHEMATICS 5 MATHEMATICS 6 MATHEMATICS 8 I. OBJECTIVES A. Content Standards The learner demonstrates understanding of the four fundamental operations involving decimals and ratio and proportion The learner demonstrates understanding of order of operations, ratio and proportion, percent, exponents, and integers. The learner demonstrates understanding of key concepts of logic and reasoning. B. Performance Standards The learner is able to apply the four fundamental operations involving decimals and ratio and proportion in mathematical problems and real-life situations The learner is able to apply knowledge of order of operations, ratio and proportion, percent, exponents, and integers in mathematical problems and real-life situations. The learner is able to communicate mathematical thinking with coherence and clarity in formulating and analyzing arguments. C. Learning Competencies and Objectives Expresses ratios in their simplest forms. M5NS-IIi-125 describes and interprets the basic operations on integers using materials such as algebra tiles, counters, chips, and cards. M6NS-IIh-155 illustrates the equivalences of: (a) the statement and its contrapositive; and (b) the converse and inverse of a statement. M8GE- IIg-2 D. Content Expresses ratios in their simplest forms. Numbers and Number Sense Illustrating Equivalences II. LEARNING RESOURCES Mathematics Grade 5 Alternative Delivery Mode Quarter 2 Module 10: Solving Problems Involving Multiplication First Edition, 2020 Lumbre, Angelina P. and Alvin C. Ursua. (2016). 21St Century Mathematics 5 Textbook. Quezon City: Vibal Group, Inc. Northcutt, Ellen (Ed.). (2000). Pre-GED Mathematics. USA: Steck-Vaughn Most Essential Learning Competencies 6, M6NS-IIh-155 Abuzo,E.P., Bryant,M.L., Cabrella,J.B., Caldez,B.P., Callanta,M.M., Castro,A.I., Halabaso,A.R., et.al (2013). Mathematics 8 Learners Module. Department of Education, Pasig City, Philippines, pp. 317-327. Manalo,C.B, Suzara J.L., Mercado J.P.,EsparragaM.S.,Jr.ReyesN.V.,New Century Mathematics.Phoenix Publishing House,pp. 405-409
- 2. Company III. PROCEDURE A. Reviewing previous lesson or presenting the new lesson Let us refresh your memory and try to answer the following exercises below by giving at least two equivalent ratios. 1) 5 : 10 ___________ , __________ 2) 7 : 11 ___________ , __________ 3) 4 : 8 ___________ , __________ 4) 12 : 14 ___________ , __________ 5) 3 : 15 ___________ , __________ Add the following integers. Write your answers on your answer sheet. 1) 8 + 9 = 2) +10 + 15 = 3) +45 + +6 = 4) +10 + 15 = 5) 50 + +15 = Directions: Transform the following statements into its converse, inverse and contrapositive and answer the guide questions. Write your answers on a separate sheet of paper. Guide Questions: a. How did you transform the statements into its converse? b. How did you transform the statements into its inverse? c. How did you transform the statements into its contrapositive?
- 3. B. Establishing Lesson Purpose Think and understand. Dana has a bar of chocolate. It was divided equally into 30 smaller pieces. When her friends came, 15 smaller pieces were eaten. What is the ratio of the remaining smaller pieces to the total pieces of the whole bar? Express the ratio in its simplest form. Look at the problem situation below. Solution: To find the difference of the water level, we are going to subtract +3 from +5. Whats My Truth Value? Directions: Consider the given conditional (if- then) statement: If the last digit is zero, then it is divisible by 5. Identify whether the following implications are TRUE or FALSE. 1. If the last digit of a number is 0, then it is divisible by 5. 2. If the last digit of a number is 0, then it is not divisible by 5. 3. If the last digit of a number is not 0, then it is divisible by 5. 4. If the last digit of a number is not 0, then it is not divisible by 5. C. Presenting examples/ instances of the lesson lets discuss expressing ratio in its simplest form. Did you know that we can express the ratio in the simplest form in different ways? To illustrate these different ways, we refer to the situation about a chocolate bar given in the previous part of this module, while following through the lesson. The ratio of the shaded smaller pieces to the whole figure is 15 to 30, that is; 15:30 or /0. Thus, the lowest term of the ratio 15/30 is 1/2 since 1 and 2 are relatively prime. Also, we have shown that 15/30 = 1/2. Recall that we used 3, 5, and 15 as our divisors of the given numbers to get 1/2 and 15 is the largest among them and is the greatest common factor (GCF) of 15 and 30. Find: +5 +3 = SUBTRACTING POSITIVE NUMBERS To fully understand the concepts in basic operations on integers, you can use counters and number lines. Subtraction of Positive Integers Using Counters To perform the subtraction operation using counters, follow the suggested steps below: Step 1: Get the exact number of counters as your minuend. Get the 5 positive counters. Place them on your table. Step 2: Look at the operation and decide what to do. The operation is subtraction. Subtraction means to take away, to get, to deduct, or to The truth table required to answer Question B in the previous activity will look like the one presented below. As reflected in the table, the hypotheses of implications 1, 2, 3 and 4 are validated as True, True, False, and False, respectively. Furthermore, the conclusions of implications 1, 2, 3 and 4 are validated True, False, True, and False, respectively. Given that the hypothesis and conclusion of the implications are already validated as either true or false, the following rules have to be followed to futher validate the truthfulness of the implication as a
- 4. minus from the first quantity. Take away 1 positive counter from 10 positive counters on the table as indicated in your subtrahend. Can you get 1 positive counter from what is shown on the table? (Yes) Step 3: Perform the operation and write your answer. In this number sentence, you need to take away 3 positive counters from the set of 5 positive counters. Answer: How many counters do you have left on the table? (2 counters) whole: The rules above can be applied in validating the truthfulness or falsehood of the implications used in the previous activity. The table that follow is shown to illustrate. D. Discussing new concepts and practicing new skills #1 To get the GCF, we may follow the methods given below. These methods were discussed in the previous lessons. Method 1: Enumeration of Factors Factors of 15: {1, 3, 5 and 15} Factors of 30: {1, 2, 3, 5, 6, 10, 15, 30} Common factors of 15 and 30: {1, 3, 5, 15} Greatest Common Factor (GCF): {15} Method 2: Prime Factorization So, in order to reduce a ratio to its simplest form, it is necessary to find the greatest common factor (GCF) for both terms in the SUBTRACTING NEGATIVE INTEGERS Subtraction of Negative Integers Using Counters Find: 5 3 = N To perform the subtraction operation using counters, follow the suggested steps below: Step 1: Get the exact number of counters as your minuend. Get 5 the negative counters. Place them on your table. A. Truth Values of an If-Then Statement Consider the if-then statement: If the last digit of a number is 0, then it is divisible by 5. Follow the steps to determine its truth values. Step 1: Identify the hypothesis (p) and conclusion (q) of the given if-then statement. Step 2: State the implications following the formats illustrated.
- 5. ratio or fraction. This is the shortcut to finding the simplest form of a ratio. Let us have an example. Example 1: The ratio of boys to girls is 6 to 24. Express the given ratio in its lowest term. To do this, we will first find the GCF of 6 and 24, as shown below: Clearly the GCF is 6. So, the largest number that can divide both the terms of the given ratio is 6. Thus, we have: Step 2: Look at the operation and decide what to do. The operation is subtraction. Subtraction means to take away, to get, to deduct, or to minus from the first quantity. Take away 3 negative counters from 5 negative counters on the table as indicated in your subtrahend. Can you get 3 negative counters from what is shown on the table? (Yes) Step 3: Perform the operation and write your answer. In this number sentence, you need to take away the 3 negative counters from the set of 15 negative counters on the table. How many counters are left on the table? (2 counters) Do these counters have the same sign? (Yes) What is the sign? (Negative) Therefore, if you subtract -3 from -5 you will get the difference of -2. -5 -3 = -2 Note that the formats of writing the implications can be rearranged. This means that format not p, not q may come first before fomat p,q and so on and forth. Step 3: Compare the hypothesis and conclusion of the implication with the hypothesis and conclusion of the original if-then statement. If a part has the same thought or words as the original part, then its truth value is true. If a part has a thought opposite of the original, then the truth value is false. Determine truth value of each implication and rule used.
- 6. E. Discussing new concepts and practicing new skills #2 F. Developing mastery (Leads to Formative Assessment 3) Using your positive and negative counters, give the difference of the following integers. Write your answers on your answer sheet. 1) +9 +7 = N 2) 12 8 = N 3) 20 25 = N Directions: Consider the if-then statement: If a figure is a square, then it is a quadrilateral; and its implications. Complete the table of truth values that is shown below. G. Finding practical applications of concepts and skills in daily living Joshuas basketball team won 9 games out of 15 games played. What is the ratio of games won to games played? Jane lost 5 kilograms after a month of doing her exercise and healthy diet. If Jane was 75 kilograms last month, how heavy is she now? Situation: You received a call from your two friends who reported that your neighbor had a dry cough. Along the conversation, one of your one friends said that , "If your neighbor
- 7. had a dry cough, then your neighbor is positive of Corona Virus Disease 2019 (CoVID-19)". That friend of yours even warned you to keep away from your neighbor. Questions: 1. Will you directly believe in the statement given by your friend? 2. Give real-life reasons to support your belief. You may write your reasons in a paragraph form. H. Making generalizations and abstractions about the lesson A ratio is said to be in (1) ___________ form if both the quantities are relatively (2 )__________ with each other. The only factor common to both the terms is 1. The (3)_____________ is the greatest number that can divide both terms of the ratio. To express ratio to its simplest form, we (4) ___________ both the terms by their GCF. The resulting ratio in its simplest form is (5) ____________ with the given ratio. In subtracting positive integers: First, change the sign of the number to be subtracted or the subtrahend. Second, change the subtraction operation to addition. Follow the rule in adding integers with unlike signs. Then, copy the sign of the number with larger value in the answer. In subtracting negative integers: First, change the sign of the number to be subtracted or the subtrahend. Second, change the subtraction operation to addition. Then, proceed to addition of integers with unlike signs. Lastly, copy the sign of the number with the larger absolute value in the answer. I know that two if-then statements are equivalent _____________. I also know that an if-then statement and its _____________are equivalent. So to fill in the blank of the first column, I need to look for its _____________ truth value in the contrapositive column. From the table, it can be seen that in the contrapositive column the third row has a truth value of _____________, therefore the missing truth value of the first column should be _____________ also. And then, I also know that the converse and _____________ of an if-then statement are equivalent. Thus, to find the missing truth values of the converse and inverse, I just have to _____________columns. Following this concept, I finally found out that the missing truth values for the converse column are _____________and_____________, while on the inverse column the missing truth values are _____________andT. I. Evaluating learning Directions: Carefully read each statement Read and analyze the situations Directions: Choose the letter of the
- 8. below. Choose the letter that corresponds to the best answer. Write the chosen letter on a separate sheet of paper. 1. In a Math Club, there are 30 girls and 20 boys. The ratio of boys to girls in simplest form is ________. (A) 2 : 3 (B) 3 : 2 (C) 3 : 5 (D) 5 : 3 2. Which ratio is expressed in the simplest form? (A) 6 : 9 (B) 10 : 24 (C) 4 : 36 (D) 8 : 15 3. At XYZ factory, 18 employees work in the office and while others work in the warehouse. If there are a total of 48 employees in the factory. What is the simplest form ratio of employees who work in the office to the employees who work in the warehouse? (A) 3 : 5 (B) 5 : 3 (C) 3 : 8 (D) 8 : 3 4. If both numbers in a ratio are relatively prime, then the ratio is said to be _______________. (A) equivalent (C) in simplest form (B) even (D) odd 5. What is the greatest common factor of 36 and 54? (A) 6 (B) 12 (C) 18 (D) 2 below. Write the letter of the correct answer on your answer sheet. 1) You took away 5 negative counters from a group of 6 negative counters. How many negative counters were left? A. -1 B. 0 C. 11 D. -11 2) Xav placed 10 positive counters on the table. Ella, her friend, took away 4 positive counters. How many positive counters were left on the table? A. 8 B. 6 C. 14 D. 40 3) Using your counters, what is 15 4? A. 16 B. 19 C. +19 D. 11 4) On the number line, you moved 8 units to the right from zero. From there, you moved again 10 units to the left. In what integer are you now? A. +8 B. 2 C. +2 D. +18 5) Nine negative counters were taken from a group of 15 negative counters. How will you write the number sentence for this? A. 15 +9 = N B. 15 9 = N C. +9 15 = N D. 9 +15 = N correct answer. Write your answer on a separate sheet of paper. 1. Which of the following pairs of statements are equivalent? A. conditional and inverse C. converse and contrapositive B. conditional and converse D. conditional and contrapositive 2. Which of the following is equivalent to a converse? A. conclusion B. contrapositive C. inverse D. hypothesis 3. Which of the following best describes equivalent statements? A. If one statement is false and the other is true. B.If one statement is true and the other is false. C.If both statements have undefined truth values. D.If statements have the same corresponding truth values. 4. Which of the following statement is NOT true? A. Letters T and F , respectively are assigned for truth values True and False. B. Letters T and F , respectively are assigned for truth values False and True. C.The if-then statement and the corresponding contrapositive are logically equivalent. D.The converse and inverse of an if-then statement are logically equivalent 5. What is the implication of the converse if both hypothesis and conclusion are true? A. Your score improved, so you did study. B. Your score improved, but you did not
- 9. study. C. Your score did not improve, that is why you study. D. Your score did not improve, because you did not study. J. Additional activities for application or remediation Directions: Express the following as ratios in the simplest form. Example: 46 apples to 4 boxes : 歎 = : 1) 35 cupcakes to 15 brownies 2) 14 children to 40 adults 3) 45 fried eggs to 20 boiled eggs 4) 20 cups of juice to 35 glasses of coconut water 5) 20 males to 18 females Subtract the given integers. Write your answers on your answer sheet. 1) 7 13 = ______. 2) What is the difference when 12 is subtracted from 24? 3) +15 when subtracted from +9 is equal to ______. 4) +40 +15 = ______. 5) +20 +8 = ______. Directions: Write a free-verse poem related to if-then statements, truth values, and equivalence. You may also include in the poem details of your experiences in going through this module. Your work will be judged according to the rubric below. IV. REMARKS V. REFLECTION A..No. of learners who earned 80% in the evaluation ___ of Learners who earned 80% above ___ of Learners who earned 80% above ___ of Learners who earned 80% above B.No. of learners who require additional activities for remediation who scored below 80% ___ of Learners who require additional activities for remediation ___ of Learners who require additional activities for remediation ___ of Learners who require additional activities for remediation C. Did the remedial lessons work? No. of learners who have caught up with the lesson ___Yes ___No ____ of Learners who caught up the lesson ___Yes ___No ____ of Learners who caught up the lesson ___Yes ___No ____ of Learners who caught up the lesson
- 10. D. No. of learners who continue to require remediation ___ of Learners who continue to require remediation ___ of Learners who continue to require remediation ___ of Learners who continue to require remediation E. Which of my teaching strategies worked well? Why did these work? Strategies used that work well: ___ Group collaboration ___ Games ___ Solving Puzzles/Jigsaw ___ Answering preliminary activities/exercises ___ Carousel ___ Diads ___ Think-Pair-Share (TPS) ___ Rereading of Paragraphs/ Poems/Stories ___ Differentiated Instruction ___ Role Playing/Drama ___ Discovery Method ___ Lecture Method Why? ___ Complete IMs ___ Availability of Materials ___ Pupils eagerness to learn ___ Group members Cooperation in doing their tasks Strategies used that work well: ___ Group collaboration ___ Games ___ Solving Puzzles/Jigsaw ___ Answering preliminary activities/exercises ___ Carousel ___ Diads ___ Think-Pair-Share (TPS) ___ Rereading of Paragraphs/ Poems/Stories ___ Differentiated Instruction ___ Role Playing/Drama ___ Discovery Method ___ Lecture Method Why? ___ Complete IMs ___ Availability of Materials ___ Pupils eagerness to learn ___ Group members Cooperation in Doing their tasks Strategies used that work well: ___ Group collaboration ___ Games ___ Solving Puzzles/Jigsaw ___ Answering preliminary activities/exercises ___ Carousel ___ Diads ___ Think-Pair-Share (TPS) ___ Rereading of Paragraphs/ Poems/Stories ___ Differentiated Instruction ___ Role Playing/Drama ___ Discovery Method ___ Lecture Method Why? ___ Complete IMs ___ Availability of Materials ___ Pupils eagerness to learn ___ Group members Cooperation in doing their tasks F. What difficulties did I encounter which my principal or supervisor can help me solve? __ Bullying among pupils __ Pupils behavior/attitude __ Colorful IMs __ Unavailable Technology Equipment (AVR/LCD) __ Science/ Computer/ Internet Lab __ Additional Clerical works __ Bullying among pupils __ Pupils behavior/attitude __ Colorful IMs __ Unavailable Technology Equipment (AVR/LCD) __ Science/ Computer/ Internet Lab __ Additional Clerical works __ Bullying among pupils __ Pupils behavior/attitude __ Colorful IMs __ Unavailable Technology Equipment (AVR/LCD) __ Science/ Computer/ Internet Lab __ Additional Clerical works G. What innovation or localized materials did I use/discover which I wish to share with other teachers? Planned Innovations: __ Localized Videos __ Making big books from views of the locality __ Recycling of plastics to be used as Instructional Materials __ local poetical composition Planned Innovations: __ Localized Videos __ Making big books from views of the locality __ Recycling of plastics to be used as Instructional Materials __ local poetical composition Planned Innovations: __ Localized Videos __ Making big books from views of the locality __ Recycling of plastics to be used as Instructional Materials __ local poetical composition
- 11. Prepared by: Checked: CHARLOTTE O. CORALDE GINNER C. SALDAA SST-I1 Head Teacher III