Q2 Lesson Exemplar for Mathematics Grade 4 (Philippines) PDF

4 Quarter 2 1 Lesson Exemplar Lesson for Mathematics 8 IMPLEMENTATION OF THE MATATAG K TO 10 CURRICULUM Lesson E...

4 Quarter 2 1 Lesson Exemplar Lesson for Mathematics 8 IMPLEMENTATION OF THE MATATAG K TO 10 CURRICULUM Lesson Exemplar for Mathematics Grade 4 Quarter 2: Lesson 8 (Week 8) SY 2024-2025 This material is intended exclusively for the use of teachers in the implementation of the MATATAG K to 10 Curriculum during the School Year 2024- 2025. It aims to assist in delivering the curriculum content, standards, and lesson competencies. Any unauthorized reproduction, distribution, modification, or utilization of this material beyond the designated scope is strictly prohibited and may result in appropriate legal actions and disciplinary measures. Borrowed content included in this material are owned by their respective copyright holders. Every effort has been made to locate and obtain permission to use these materials from their respective copyright owners. The publisher and development team do not represent nor claim ownership over them. Development Team Writers: Rosalie P. Cayabyab, EdD. (City College of San Fernando Pampanga) Kimberly G. Mallari, Ph.D. (City College of San Fernando Pampanga) Validator: Aurora B. Gonzales, Ph.D. (Philippine Normal University – Manila) Management Team Philippine Normal University Research Institute for Teacher Quality SiMERR National Research Centre Every care has been taken to ensure the accuracy of the information provided in this material. For inquiries or feedback, please write or call the Office of the Director of the Bureau of Learning Resources via telephone numbers (02) 8634-1072 and 8631-6922 or by email at [email protected]. MATHEMATICS / QUARTER 2 / GRADE 4 I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES A. Content Addition and subtraction of similar fractions, including mixed numbers. Standards B. Performance Perform addition and subtraction of similar fractions, including mixed numbers. Standards C. Learning Learning Competency Competencies 1. Determine similar and dissimilar fractions and Objectives 2. Add and subtract similar fractions two proper fractions, two mixed numbers, a mixed number and a proper fraction, a whole number and a proper fraction, and a whole number and a mixed number. C. Content Addition and Subtraction of Similar Fractions a. Addition and Subtraction of two proper fractions b. Addition and Subtraction of two mixed numbers c. Addition and Subtraction of a mixed number and a proper fraction d. Addition and Subtraction of a whole number and a proper fraction e. Addition and Subtraction of a whole number and a mixed number D. Integration Values of sharing, fairness and building friendship. II. LEARNING RESOURCES Jalon, H. F. et. al. (2019). Phoenix Math for the 21st Century Learners. Phoenix Publishing House, Inc., Quezon City Misa, E. L. (2019). The World of Mathematics and Beyond. Brilliant Creations Publishing, Inc., Quezon City Yn, G. U. (2017). Our World of Math. Vibal Group, Inc., Quezon City 1 III. TEACHING AND LEARNING PROCEDURE NOTES TO TEACHERS A. Activating Prior DAY 1 Knowledge 1. Short Review The learners will write their Write the fraction for the shaded part of each figure. answers on the board. The teacher may ask the Set A Set B following: a) What have you observed on the fractions on Set A and Set B? (Learners noticed that the sets of fractions on Sets A and B have the same denominator) b) How about on the fractions on Set C and Set D? Set C (Learners noticed that the sets of fractions on Sets C and D have different Set D denominators) 2. Feedback (Optional) B. Establishing 1. Lesson Purpose Lesson Purpose Fractions on Sets A and B have the same denominator. In Set A the common Teacher may ask questions denominator is 5, while in Set B the common denominator is 7. Fractions on about valuing similarities and Sets C and D contain different denominators. It is important to know how to differences in characteristics determine sets of fractions with the same denominator and different among friends. denominators. Lead the learners to the lesson topic, 2  2. Unlocking Content Area Vocabulary Similar fractions are fractions with similar or the same denominators. Dissimilar fractions are fractions with dissimilar or different denominators. C. Developing and SUB-TOPIC 1: Addition and Subtraction of two proper/improper fractions that Deepening are similar Understanding 1. Explicitation Opener: Angel, a Grade 4 student, completed of her assigned tasks on a long For Sub-Topic 1: 2 5 1 The teacher may give more weekend. She continued the following day and completed 5 of the tasks. How examples when needed. much of the assigned tasks did Angel accomplish? How much of the assigned tasks were not accomplished? The concept of addition and subtraction (Sub-Topic 1) can The teacher may I ask the learner on how the problem may be solved? Then lead also be develop using a number the learners to the lesson topic: Addition/subtraction of similar fractions line. 2. Worked Example 2 1 Example 1: Find the sum of + 5 5 Ask the learners to use discs to represent the completed tasks of Angel. Ask the learners to construct the diagram (disc) representing the total completed tasks by Angel. 2 1 3 5 + 5 = 5 3 So, 5 of the assigned tasks was accomplished by Angel. Rule: To add proper fractions that similar, add the numerators then use the common denominator. 3  Then, to find how much of the assigned tasks were not accomplished by Angel, we will use subtraction. 5 3 Example 2: Subtract 5 − 5 5 3 The whole task can be represented by the fraction. Since was the total 5 5 3 5 accomplished tasks by Angel, we subtract from This can be explained by the 5 5. diagram below. To develop the concept involve here, the “take away” concept of subtraction may be used thru number line. 5 5 3 5 𝟐 𝟓 𝟓 𝟑 𝟐 − = 𝟓 𝟓 𝟓 3 5 “take away 5 from 5 “ 2 So, 5 of the assigned tasks were NOT accomplished by Angel. Ask the learners to make conclusion on getting the difference of the given fractions. Bring the learners to the rule below. Rule: To subtract proper/improper fractions that are similar, subtract the numerators and use the same denominator. 3. Lesson Activity A. Use a diagram to represent the sum or difference of the following fractions 1 4 7 4 1. + 2. − 8 8 10 10 Lesson Activity (Sub-Topic 1) B. Perform the indicated operation. B. Answers: 1 6 75 42 1. 7/10 6. 117/200 1. 10 + 10 6. 200 + 200 11 6 56 12 2. 17/21 7. 44/85 2. 21 + 21 7. 85 − 85 3. 2/19 8. 9/10 4 2 4 1 5 1 4. 6/13 9. 2/45 3. − 19 8. (10 + 10) + (10 − 10) 19 5. 3/100 10. 0 4  9 3 5 2 4 1 4. 13 − 13 9. (45 + 45) − (45 + 45) 47 44 8 3 9 4 5. − 10. ( − ) −( − ) 100 100 19 19 19 19 DAY 2 SUB-TOPIC 2: Addition and Subtraction of two mixed numbers that Similar 1. Explicitation 3 1 1 Opener: Rosell bought 5 4 kg of grapes. He gave 1 4 kg to his cousin Nat and 2 4 For Sub-Topic 2: Number line may also be used as kg to his grandmother. How much kg of grapes did he give to his cousin and models in adding similar mixed grandmother? How much grapes were left to Rosell? numbers. Ask the learners to identify the type of fractions involve in the problem. Then The teacher may give other lead the learner to the lesson topic. examples when needed. 2. Worked Example Example 1: How much kg of grapes did he give to his cousin and grandmother? 1 1 Learners are actually asked to find the sum of 1 4 and 2 4. Guide the learners in solving the problem using models then to the use of symbols. 1 1 2 1 1 4 + 2 4 = 3 4 or 3 2 2 1 So, 3 4 or 3 2 kilograms of grapes were given to her cousin and grandparent. Rule: To add mixed numbers that are similar, add the whole numbers then add the numerators and use the common denominator. Example 2: How much grapes were left to Rosell? 3 2 Learners are asked to find the difference between 5 and 3. Guide the learners 4 4 in solving the problem using a number line then to symbols. 5  3 2 1 5 4 − 3 4 = 2 4 1 So, 2 kilograms of grapes were left to Rossel. 4 Rule: To add mixed numbers that are similar, add the whole numbers then add the numerators and use the common denominator. 8 3 Example 3: 5 15 + 4 15 =? 8 3 8 3 11 Solution: 5 +4 = (5 + 4) ( + ) =9 15 15 15 15 15 Example 4 involves regrouping; 1 3 modeling may be used if learners Example 4: 7 8 − 5 8 =? find it difficult to understand the Solution: 9 68 −5 3 = 𝟑 𝟏𝟒 process. 8 3 1 8 You cannot subtract 8 from 8. Regroup 1 from 7 and express it as 8 Teacher may give more example as needed. The teacher may use 3. Lesson Activity board work or group work in A. Find the missing fractions. answering problems in lesson 7 1. 6 12 + = 8 12 8 3. 12 11 - 6 = 9 11 2 activity. Lesson Activity A (Sub-Topic 2) 2. - 3 95 = 1 25 4. + 8 7 = 10 15 13 Answers: 13 1. 2 1/12 2. 11 4/5 B. Solve the following. 3. 3 4/11 2 3 3 2 4. 7 3/13 1. Subtract 3 5 from 5 5. 2. Find the sum of 8 9 and 7 9. Lesson activity B Answers: 1. 2 1/5 2. 15 5/9 6 DAY 3 SUB-TOPIC 3: Addition and Subtraction of a mixed number and a proper fraction that are similar 1. Explicitation For Sub-Topic 3: To make the learners engaged, the teacher will use “Math Storytelling” in The teacher may choose any of introducing the lesson. the following options: In a faraway land, there lived a beautiful and intelligent lady named Cinderell- Ask a learner to read the X. She loved doing puzzles and math problems since she was young. While growing story with clarity and up, she hid this exceptional ability from her stepmother and stepsisters. One day, a emphasis. man from the palace came to bring an invitation to the Grand Fraction Ball organized The teacher will read the by the Crown Prince, Decimalus, also known for being a math wizard. For Cinderell- story imitating the voice X to participate in the ball, her fairy godmother transformed her into a beautiful lady. behind Disney movies Hence, during the ball, she made a grand entrance. While walking in the hallway, she encountered a fraction word problem on the The teacher will play a wall: "If 3 1/4 yards and 2/4 yards of cloths are used to make a cape, how many simple video regarding the yards are needed to make a cape?" With confidence, Cinderell-X answered the story problem with ease. Use of AI voice over as a Decimalus saw her and was impressed. She walked again and saw the 2nd narrator word problem, If you owned 9 7/8 hectares of land and decided to donate 6/8 hectares, how many hectares were left?" Again, she solved the problem quickly. As Through this questioning she continued to solve word problems, Decimalus could not help but fall in love with technique, the learners will have her. So, they danced, laughed, and solved word problems together while enjoying an idea of what their lesson is their magical moment. about. However, Cinderell-X had to leave before midnight, so she dashed and left her glass shoe. The next day, Decimalus used his math skills to find the perfect glass Kind – mixed and proper shoe fit. The shoe fit perfectly with Cinderell-X’s foot. Similar fractions ….and they live happily ever after while solving fraction word problems Operations – addition and together. subtraction THE END Virtual manipulatives may also The teacher will process this story by asking these questions: be utilized. See the link below for 1. What was the 1st word problem solved by Cinderell-X? reference: 2. What kind of fractions were given in the problem? https://toytheater.com/fraction- 3. What have you noticed with their denominators? strips/ 4. If you were Cinderell-X, what operation are you going to use? 5. What do you think was Cinderell-X’s answer to the 1st problem? Who would like to be Cinderell-X and show the solution on the board? The teacher will guide the learners model the answer using fraction strips. 7 2. Worked Example From the story: "If 3 1/4 yards and 2/4 yards of cloths are used to make a cape, how many yards are needed to make a cape? 1 2 Example 1: 3 4 + 4 = Solution: 3 So, 3 yards of cloth are needed to 4 make a cape. For the 2nd problem. A learner may be guide to work on it on the board. The teacher will use the same questioning technique as the 1st word problem. 7 6 1 Example 2: 9 − = 9 8 8 8 (use number line in demonstrating the answer to the problem) Based on these examples, how do you add or subtract a mixed number and a proper fraction with the same denominators? (Without regrouping) 1. Copy the whole number. 2. Add or subtract the numerators of both fractions. 3. Copy the common denominator. Examples here involve regrouping. 8  5 2 7 Method 1: Using the mixed number form 2 6 + 6 = 2 6 7 1 𝑠𝑖𝑛𝑐𝑒 6 𝑐𝑎𝑛 𝑏𝑒 𝑐ℎ𝑎𝑛𝑔𝑒𝑑 𝑖𝑛𝑡𝑜 1 6 , 𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 1 1 2 + 16 = 3 6 Method 2: Changing mixed number into improper fraction 5 2 29 2 31 1 2 + = + = or 3 6 6 6 6 6 6 For method 2, to add a mixed number and a proper fraction with regrouping, 1. Convert the given mixed number into an improper fraction. 2. Add the numerators. 3. Copy the common denominator. 1 2 Example 5: 5 3 − 3 = (Use number line to model this problem. Refer to subtopic 1 for your guide) Method 1: Using the mixed number form 2 1 3 𝑠𝑖𝑛𝑐𝑒 𝑐𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑟𝑖𝑔ℎ𝑡 𝑎𝑤𝑎𝑦 𝑓𝑟𝑜𝑚 , 5 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑐ℎ𝑎𝑛𝑔𝑒𝑑 𝑖𝑛𝑡𝑜 4 , ℎ𝑒𝑛𝑐𝑒, 3 3 3 1 𝟑 1 4 53 = 𝟒𝟑 + 3 = 4 3 1 2 4 2 𝟐 53 − 3 =4 3 − 3 = 𝟒𝟑 Method 2: Changing mixed number into improper fraction 1 2 16 2 14 2 5 − = − = 𝑜𝑟 4 3 3 3 3 3 3 How do you subtract a proper fraction from a mixed number with regrouping? 1. Convert the given mixed number into either an improper fraction or a mixed number whose fractional part is an improper fraction. 2. Subtract the numerators. 3. Copy the common denominator. 9 3. Lesson Activity The Lesson Activity can either be Perform the indicated operation. Show the necessary solutions. individual activity or group 14 3 1) 17 + 11 17 = 2 6 6) 7 + 2 7 = 2 7 activity. 1 4 7 5 2) 6 + 2 6 = 7) 9 − = Answers to the Lesson Activity 9 9 3) 15 3 5 18 − 18 = 5 7 8) 3 8 − 8 = (Sub-Topic 3): 6 13 12 9 1) 12 6)4 4) 1 25 + 25 = 1 25 9) 4 18 − 18 = 5 2 2) 2 6 7) 9 9 1 7 7 10 5) 7 + = 10) + 2 = 2 12 22 6 8 8 20 20 20 3) 5 18 8) 8 𝑜𝑟 28 3 4) 7 9) 4 DAY 4 18 SUB-TOPIC4: Addition and Subtraction of a whole number and a proper 5) 8. 10) 3 fraction 1. Explicitation The teacher will ask some Recall the topic discussed on the previous days. Ask students what are the volunteers to show the solutions different methods in adding and subtracting fractions. on board. 2. Worked Example 5 Example 1: 1 + 8 = In this part, the teacher may consider the following options: Use of actual fraction discs or fraction strips Use of pictures showing fractional parts Use of virtual manipulatives/games 5 Example 2: 3 - =7 Below are the suggested links for (Use number to demonstrate or model the problem ) reference: https://www.abcya.com/ga Example 3: 3 + 3 = mes/virtual-manipulatives 3 7 3 24 https://toytheater.com/fract Solution: 3 + =3 𝑜𝑟 ion-bars/ 7 7 7 https://toytheater.com/fract 3 Example 4: 3- ion-circles/ 7 3 7 3 4 Solution: 3 - 7 = 2 7 – 7 = 2 7 10 3. Lesson Activity For the MATHatag Quiz Bee, the To make the activity more engaging, the teacher will hold the “MATHatag Quiz learners will be grouped into five Bee”. groups to make the activity more 1 3 4 engaging. Their seats will be 1) 5 − = 6) ____ − = 4 arranged in circular formation. 4 7 7 4 4 2 Each group will have a whiteboard 2) + ___ = 6 7) 2 − = 13 13 5 and a marker where they can write 8 3 3) + 20 = 8) ____ + 17 = 17 their answers. If learners do not 14 9 4 5 have whiteboards and markers, they 4) +2 = 2 9) 1 − = 8 8 30 can use bond papers and pens. 4 13 5) 8 − = 10) 10 − = The teacher will use a timer. The 6 15 group who got the most correct DAY 5 answers will be the winner. SUB-TOPIC 5: Addition and Subtraction of a whole number and a mixed number Answers for the Lesson 1. Explicitation Activity (Sub-Topic 4): 3 1 “Draw Me” 1) 4 4 6) 4 7 Ask the learners to draw diagram (maybe discs, strip, or number line) 2) 6 3 7) 1 5 1 representing the fraction: 3 4 8 3 1 3) 20 14 8) 9 Then ask the learners to add 2 whole discs (if disc was used) to 3 4. 25 4) 4 9) 30 Finally, ask the learner to draw a separate diagram representing all the diagrams 2 2 used. Then bring the learners to the new lesson topic. 5) 7 6 10) 9 15 2. Worked Example Volunteers will be called to show The teacher will guide the learners in getting the correct answers from the given their illustrations on the board. illustrations. Each correct answer will be placed in a table showing methods 1 The teacher will use these and 2. illustrations in processing the Method 1 Method 2 worked examples. Given (Use of Improper Fraction form) (Use of Mixed Number form) 1 2 3 5 1 1 1 The teacher may use a table to 1) 1 + 1 = + = 𝑜𝑟 2 1+1 =2 organize the possible solutions 2 2 2 2 2 2 2 1 5 8 13 1 1 1 for each example. 2) 1 + 2 = + = 𝑜𝑟 3 1 +2=3 4 4 4 4 4 4 4 1 7 3 4 1 1 1 Since the pupils can already add 3) 2 − 1 = − = 𝑜𝑟 1 2 −1=1 3 3 3 3 3 3 3 and subtract fractions with 3 3 12 11 1 3 4 3 1 regrouping, as discussed in the 4) 3 − 2 = 3−2 = − = 3−2 =2 −2 = 4 4 4 4 4 4 4 4 4 previous lesson, the teacher may 11 3. Lesson Activity do some review/recall. This will To make this activity more engaging, the learners will play the “Fraction Relay”. help the pupils better Set A Set B comprehend the next lesson. 5 3 1) 15 15 − 15 = 1) 1 − 16 = The learners will be grouped into 7 5 11 five groups. Members of each 2) 6 − 4 10 = 2) __ − 3 16 = 4 16 group will be seated in a single 3 2 2 line. Each learner will be 3) 8 11 + 5 = 3) 4 5 + __ = 6 5 provided a sheet of paper 1 7 4) ___ + 3 = 7 7 containing the math problem 4) 17 +3= 12 9 9 he/she needs to answer. The 1st 5) 6 − 5 21 = 12 5) 6 12 − 8 24 = in the line will begin answering the 1st question. Subsequently, this learner will pass his/her paper to the one seated behind him/her. This process will continue until the last learner per group receives the papers, including his/her answer. The group with the greatest number of correct items will be the winner. In the event of a tie, the fastest group among the highest pointers will be the winner. For Sub Topic 5: Worked Example Examples 1 - 4: (Method 1) - Change both the whole number and the mixed number to improper fractions - Subtract the numerators. - Copy the common denominator 12  Examples 1 – 3: (Method 2) Simply add or subtract the whole numbers and copy the proper fraction. Example 4: (Method 2) - Change the whole number to a mixed number whose fractional part is an improper fraction. - Subtract the whole numbers. - Subtract the numerators - Copy the common denominators Answers for the Lesson Activity (Sub Topic 5): SET A SET B 5 13 1) 15 6) 16 13 3 2) 𝑜𝑟 1 7) 8 10 15 3 3) 13 11 8) 2 1 4) 20 12 9) 4 9 18 5) 21 10) 324 D. Making 1. Learners’ Takeaways Generalizations The teacher will guide the learners in accomplishing this table. What I’ve Concepts that are Concepts I Key Ideas/Concepts Learned from the Somewhat Totally Don’t Discussion Confusing Understand Addition and Subtraction of two proper fractions Addition and Subtraction of two mixed numbers Addition and Subtraction of a mixed number and a proper fraction 13  Addition and Subtraction of a whole number and a proper fraction Addition and Subtraction of a whole number and a mixed number 2. Reflection on Learning The learners will complete the following statements: “I realized that adding and subtracting fractions of different kinds offers a lot of opportunities to ____________________________________”. “My most favorite part of the lesson is _______________________ because ________________________”. IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER’S REFLECTION NOTES TO TEACHERS A. Evaluating 1. Formative Assessment Learning Perform the indicated operation. 18 4 10 1. − 6. 12 − 7 21 21 22 8 5 3 2. 14 + 14 7. + 16 9 6 1 3 2 3. 3 −1 8. 2 − 7 7 7 7 3 2 12 2 4. 35+ 45 9. 6 14 + 14 4 3 1 1 1 5. 3 17 + 4 10. (2 5 + 5 5) − (2 5 + 2 5) 2. Homework (Optional) B. Teacher’s Note observations on any of The teacher may take note of Effective Practices Problems Encountered Remarks the following areas: some observations related to the effective practices and problems strategies explored encountered after utilizing the different strategies, materials materials used 14  learner engagement/ used, learner engagement, and interaction other related stuff. others Teachers may also suggest ways to improve the different activities explored/lesson exemplar. C. Teacher’s Reflection guide or prompt can be on: Teacher’s reflection in every Reflection ▪ principles behind the teaching lesson conducted/facilitated is What principles and beliefs informed my lesson? essential and necessary to Why did I teach the lesson the way I did? improve practice. You may also consider this as an input for the ▪ students LAC/Collab sessions. What roles did my students play in my lesson? What did my students learn? How did they learn? ▪ ways forward What could I have done differently? What can I explore in the next lesson? 15