S4_SD_HOTS-in-Practice-Math.pptx........

S4_SD_HOTS-in-Practice-Math.pptx........

1. TRAINING ON HIGHER - ORDER THINKING SKILLS PROFESSIONAL LEARNING PACKAGE (HOTS-PLP) FOR MATHEMATICS TEACHERS January 24 – 26, 2024 Julita NHS

2. SESSION 4 HOTS in Practice Worksheets 4A, 4B, 4C and 4D in Mathematics 2 Learning Facilitators

3. 3 Session 1: HOTS-PLP Walk-through Session 6: Facing the Forces Session 5: Workplace Application Plan Session 2: SOLO and HOTS in the Classroom Session 7: Professional Learning Community in Schools Session 3: Supporting HOTS in the Classroom through Learning Approaches Session 4: HOTS in Practice Training on Higher-Order Thinking Skills Professional Learning Package (HOTS-PLPs) for English, Science, & Math Teachers

4. Session Objectives At the end of the session, participants will be able to… 4 identify the components of the HOTS learning package; analyze how SOLO-based item is crafted; and practice writing sample items and rationalization based on the SOLO framework. PPST Strand 1.5. (P & HP) S trategies for developing critical and creative thinking, as well as other higher-order thinking skills PPSSH Strand 3.2 – (P) Teaching performance feedback PPSS Strand 3.1. (P) Support for Instructional Leadership

5. Presentation Outline 5 Presentation of the HOTS learning package Run through the parts of the learning package. Examine how each item in the package is crafted. Practice answering question based on SOLO-based item framework. Give rationalization for a SOLO-based item Craft SOLO-based items and justify its level

6. HOUSE RULES 6 Punctuality: Arrive on time to each workshop session. No Disturbances: Cell phones should be turned off at the beginning of the workshop and should remain off until the end except during breaks. Respect Others: Respect each other, yourselves, and the trainer. Participation: You are your own best resource.

7. HOUSE RULES 7 5. Agree to Disagree: During this workshop everyone must feel free to express opinions and concerns. 6. Ask Questions: There are no stupid questions. 7. Give your honest feedback: Constructive criticism is appreciated and is the only way that we can improve.

8. REVIEW What do you mean by unistructural level of SOLO Model? Unistructural Level At this stage, the learner gets to know just a single relevant aspect of a task or subject; the student gets a basic understanding of a concept or task. Therefore, a student is able to make easy and apparent connections, but he or she does not have any idea how significant that information be or not. In addition, the students’ response indicates a concrete understanding of the task, but it focuses on only one relevant aspect. 8

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10. REVIEW What about multistructural level of SOLO Model? Multistructural Level At this stage, students gain an understanding of numerous relevant independent aspects. Despite understanding the relationship between different aspects, its relationship to the whole remains unclear. Suppose the teacher is teaching about several topics and ideas, the students can make varied connections, but they fail to understand the significance of the whole. The students’ responses are based on relevant aspects, but their responses are handled independently. 10

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12. REVIEW What about relational level of SOLO Model? Relational Level This stage relates to aspects of knowledge combining to form a structure. By this stage, the student is able to understand the importance of different parts in relation to the whole. They are able to connect concepts and ideas, so it provides a coherent knowledge of the whole thing. Moreover, the students' response indicates an understanding of the task by combining all the parts, and they can demonstrate how each part contributes to the whole. 12

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14. MAGSOLO KA MUNA! 14 Direction: Write U if the SOLO level is Unistructural, M for Multistructural, R for Relational, and E for Extended Abstract.  Identify a prime number between 20 and 30. List three different ways to represent the number 1/2. Compare and contrast the properties of squares and rectangles. Explain the relationship between the radius and diameter of a circle. Create an original real-life problem involving solving a linear equation system.

15. MAGSOLO KA MUNA! 15 Identify a prime number between 20 and 30. List three different ways to represent the number 1/2. Compare and contrast the properties of squares and rectangles. Explain the relationship between the radius and diameter of a circle. Create an original real-life problem involving solving a linear equation system. Answer: U M R R E

16. Supporting HOTS in the Classroom: Worksheet 4A 16

17. Session Objectives At the end of the session, participants will be able to… 17 identify the components of the HOTS learning package ; analyze how SOLO-based item is crafted; and practice writing sample items and rationalization based on the SOLO framework.

18. Think-Pair-Share 18 Directions: Think Participants are given Worksheet 4A to think about individually. They take some time to study the worksheet and write their own comment or feedback b. Pair Participants look for a partner to discuss their thoughts. They take turns sharing their ideas and listening to their partner’s perspectives c. Share Once the pair discussion is complete,  RP asks for volunteers to share their insights and findings with the whole class

19. EXPLORATION 19 - Worksheet 4A Item 1 (Unistructural) Item 2 (Multistructural) Item 3 (Relational) Competency, Stem, Question, Acceptable Answer, Rationalization

20. 20 Competency Stem Question Acceptable Answer Rationalization Solves problems involving algebraic equations Traveling by Car Car A starts from Davao City Terminal and heads for Butuan City at 50 kph. Two hours later Car B leaves the same terminal with the same route with Car A traveling at 70 kph. Unistructural   Which car is faster? A car with the highest speed is the fastest car. Since Car B has a speed of 70 kph which is higher than the speed of Car A which is 50 kph, then Car B is the fastest. This question falls under the unistructural SOLO level. It requires basic understanding of comparing two values (speeds) to determine which one is greater. The question does not involve any complex analysis or relationship between variables. It solely focuses on comparing the speeds of two cars to determine which one is faster.  

21. 21 Competency Stem Question Acceptable Answer Rationalization Solves problems involving algebraic equations Traveling by Car Car A starts from Davao City Terminal and heads for Butuan City at 50 kph. Two hours later Car B leaves the same terminal with the same route with Car A traveling at 70 kph. Multistructural   How long before Car B overtakes Car A? This item is at the multistructural level because it requires several procedures and undertaking several sequential steps. In this case, an equation was formulated and solved. The question requires integrating these different components and calculations to arrive at the final answer, demonstrating a multistructural understanding.

22. 22 Competency Stem Question Acceptable Answer Rationalization Solves problems involving algebraic equations Traveling by Car Car A starts from Davao City Terminal and heads for Butuan City at 50 kph. Two hours later Car B leaves the same terminal with the same route with Car A traveling at 70 kph. Relational   If Car C started from the same terminal one hour after Car B leaves the terminal traveling in opposite direction at 60 kph.   At what distance will Car C and Car B be apart during the time Car B overtakes Car A? This question falls under the relational SOLO level. It involves analyzing the relationship between the distances traveled by Car B and Car C during the time Car B overtakes Car A. The question requires considering the speeds, times, and distances covered by the cars. This analysis demonstrates a relational understanding, as it requires examining the relationship between the distances of Car C and Car B during the specific event of Car B overtaking Car A.

23. 23 You have 30 minutes for the exploration including the writing of your findings, observation, comments, and suggestions. SOLO Based Assessment Items

24. Question Acceptable Answer Rationalization Presentation of findings and observations

25. Question Acceptable Answer Rationalization Abstraction

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27. Health Break 30 minutes

28. Supporting HOTS in the Classroom: Worksheet 4B 29

29. Session Objectives At the end of the session, participants will be able to… 30 identify the components of the HOTS learning package; analyze how SOLO-based item is crafted; and practice writing sample items and rationalization based on the SOLO framework. PPST Strand 1.5. (P & HP) S trategies for developing critical and creative thinking, as well as other higher-order thinking skills PPSSH Strand 3.2 – (P) Teaching performance feedback PPSS Strand 3.1. (P) Support for Instructional Leadership

30. - Worksheet 4B Item 1 (Unistructural) Item 2 (Multistructural) Item 3 (Relational) Competency, Stem, Question, Acceptable Answer , Rationalization Exploration

31. Directions: Read item numbers 1-3 in the given worksheets and give acceptable for unistructural, multistructural and relational levels of SOLO model. The worksheet is composed and provided with competency, stem, question, and rationalization. The column in the acceptable answer will be your task. Do it honestly and religiously. 32 Group Activity

32. 33 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4B Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 1 Competency Stem Unistructural Question Acceptable Answers Rationalization Solving problems involving linear inequalities Firefighter Exam   Justin is taking an exam to become a volunteer firefighter. The exam has 10 essay questions and 50 short questions. Justin has 90 minutes to take the exam and knows he is not expected to answer every question. An essay question takes 10 minutes to answer and a short question takes 2 minutes. How many items will Justin finish to answer if he chooses only essay questions? The question does not require Justin to make connections or analyze the information in a complex manner. It focuses on a single aspect (the number of items answered) based on the given information.

33. 34 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4B Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 2 Competency Stem Multistructural Question Acceptable Answers Rationalization Solving problems involving linear inequalities Firefighter Exam   Justin is taking an exam to become a volunteer firefighter. The exam has 10 essay questions and 50 short questions. Justin has 90 minutes to take the exam and knows he is not expected to answer every question. An essay question takes 10 minutes to answer and a short question takes 2 minutes. What linear inequalities describes the constraints on Justin’s time given above? The question involves understanding and integrating multiple aspects, such as the time taken for different question types and the total available time, to formulate the appropriate linear inequalities.

34. 35 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4B Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 3 Competency Stem Relational Question Acceptable Answers Rationalization Solving problems involving linear inequalities Firefighter Exam   Justin is taking an exam to become a volunteer firefighter. The exam has 10 essay questions and 50 short questions. Justin has 90 minutes to take the exam and knows he is not expected to answer every question. An essay question takes 10 minutes to answer and a short question takes 2 minutes. Will Justin have enough time if he will answer only half of the essay and short questions? This question prompts the learner to analyze the relationship between the time required for essay questions (10 minutes each) and short questions (2 minutes each) in relation to the total available time of 90 minutes. It encourages the learner to consider the relative time commitments of each question type and their impact on the overall time management during the exam. By answering this question, the learner demonstrates an understanding of the time distribution and allocation between essay and short questions within the given time constraint..

35. Acceptable Answer (for Items 1, 2, and 3) You have 1 hour to work and provide an Acceptable Answer for all three (3) items. Workshop: 4B

36. Acceptable Answer (for Items 1, 2, and 3) Presentation of Output

37. Guide Question 1. Based on your consolidated answers, when can we say that the acceptable answers are unistructural, multistructural and relational levels of SOLO model? 38

38. Guide Question 2. Why is it important to have a good stem? 39

39. 3. Do you think you can make questions based on the stem the three (3) different levels of SOLO model namely the unistructural, multistructural and relational? 40 Guide Question

40. 4. As classroom teachers, how are you going to help students from unistructural to become multistructural and relational? 41 Guide Question

41. 5. What do you think is your impact or contribution in helping learners develop their higher order thinking skill? 42 Guide Questions

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44. Supporting HOTS in the Classroom: Worksheet 4C 46

45. Session Objectives At the end of the session, participants will be able to… 47 identify the components of the HOTS learning package; analyze how SOLO-based item is crafted ; and practice writing sample items and rationalization based on the SOLO framework.

46. MAGSOLO KA MUNA! 48 Identify a prime number between 20 and 30. List three different ways to represent the number 1/2. Compare and contrast the properties of squares and rectangles. Explain the relationship between the radius and diameter of a circle. Create an original real-life problem involving solving a linear equation system. Answer: U M R R E

47. - Worksheet 4C Item 1 (Unistructural) Item 2 (Multistructural) Item 3 (Relational) Competency, Stem, Question, Acceptable Answer , Rationalization Exploration

48. Worksheet 4C

49. Worksheet 4C

50. Worksheet 4C

51. Directions: Read item number 1-3 in the given worksheets and give rationalization for unistructural, multistructural and relational levels of SOLO model. The worksheet is composed and provided with competency, stem, question, and acceptable answer. The column in the rationalization will be your task. Do it honestly and religiously. 53 Group Activity

52. Rationalization (for Items 1, 2, and 3) You have 1 hour to work and provide Rationalization for all three (3) items. Workshop: 4C

53. 55 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4C Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 1 Competency Stem Unistructural Question Acceptable Answers Rationalization Solves problems involving linear functions JHS Enrolment   Gabi National High School had 1200 students enrolled in 2017 and 1500 students in 2020. If the student population P; grows as a linear function of time t, where t is the number of years after 2017. What is the total number of students added from 2017 to 2020? The total enrolment of students in 2017 is 1200 The total enrolment of students in 2020 is 1500 The total increase is given by the difference between the enrolment of 2020 and 2017   1500-1200 = 300  There is a total of 300 students enrolment added in 2020 from 2017.

54. 56 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4C Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 2 Competency Stem Multistructural Question Acceptable Answers Rationalization Solves problems involving linear functions JHS Enrolment   Gabi National High School had 1200 students enrolled in 2017 and 1500 students in 2020. If the student population P; grows as a linear function of time t, where t is the number of years after 2017. . How many students will be enrolled in the school in 2024? The given information may be written as ordered pairs (t , P).  The year 2017 correspond to t = 0 and the year 2020 corresponds to t = 3, hence the 2 ordered pairs (0, 1200) and (3, 1500) Since the population grows linearly with the time t, we use the two ordered pairs to find the slope m of the graph of P as follows m = (1500 - 1200) / (3-0) = 100 students / year The slope m = 100 means that the student’s population grows by 100 students every year. From 2017 to 2024 there are 7 years and the student’s population in 2024 will be P(2024) = P(2017) + 7 * 100 = 1200 + 700 = 1900 students.

55. 57 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4C Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 3 Competency Stem Relational Question Acceptable Answers Rationalization Solves problems involving linear functions JHS Enrolment   Gabi National High School had 1200 students enrolled in 2017 and 1500 students in 2020. If the student population P; grows as a linear function of time t, where t is the number of years after 2017. When will the number of enrolments double? The enrolment in 2017 is 1200. The equation in solving for the population given time is P = 100 t + 1200. To double the population, P becomes 2400. Hence, 2400 = 100t + 1200 Solve for t, 100t = 2400 – 1200 100t = 1200 t = 1200/100 t = 12 Therefore, it will take 12 years to double the enrolment from 1200 in 2017 to 2400 in 2029.

56. Rationalization (for Items 1, 2, and 3) Presentation of Output

57. Guide Questions 1. How did you formulate the rationalization in unistructural, multistructural and relational levels of SOLO model? 59

58. 2. Can you discuss to the group which levels of SOLO model namely the unistructural,multistructural and relational did you find it difficult to formulate rationalization? Why? 60 Guide Questions

59. 3. What are your strategies in formulating rationalization based on the given stem? How did you do it? 61 Guide Questions

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61. Health Break 30 minutes

62. Supporting HOTS in the Classroom: Worksheet 4D 64

63. Session Objectives At the end of the session, participants will be able to… 65 identify the components of the HOTS learning package; analyze how SOLO-based item is crafted ; and practice writing sample items and rationalization based on the SOLO framework.

64. Worksheet 4D Item 1 (Unistructural) Item 2 (Multistructural) Item 3 (Relational) Competency, Stem, Question , Acceptable Answer , Rationalization Exploration: 4D

65. Question Acceptable Answer Rationalization for items 1, 2, and 3 You have 1 hour to work and provide the Question, Acceptable Answer, and Rationalization for all three (3) items. Workshop: 4D

66. Directions: Read item number 1-3 in the given worksheets and provide the question, acceptable answer, and rationalization for unistructural, multistructural and relational levels of SOLO model. The worksheet is composed and provided with competency and stem only. The column in the question, acceptable answer, and rationalization will be your task. Do it honestly and religiously. 68 Group Activity

67. 69 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4D Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 1 Competency Stem Unistructural Question Acceptable Answers Rationalization Solves problems involving sequences (Grade 10) A group of virologists studied a certain type of coronavirus and took a picture of the number of viruses in a circular dish every hour. The pictures below show what the virologist found out, with each dot representing 10 viruses.

68. 70 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4D Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 2 Competency Stem Multistructural Question Acceptable Answers Rationalization Solves problems involving sequences (Grade 10) A group of virologists studied a certain type of coronavirus and took a picture of the number of viruses in a circular dish every hour. The pictures below show what the virologist found out, with each dot representing 10 viruses.

69. 71 Capacity Building for Mentors on the Higher Order Thinking Skills Professional Learning Package (HOTS – PLPs) for Science, Mathematics and English/Reading Name: ________________________________ Division: _________________________ Worksheet No. 4D Position: __________________________ Region: __________________________ Plenary Session No. 7 Item 3 Competency Stem Relational Question Acceptable Answers Rationalization Solves problems involving sequences (Grade 10) A group of virologists studied a certain type of coronavirus and took a picture of the number of viruses in a circular dish every hour. The pictures below show what the virologist found out, with each dot representing 10 viruses.

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71. 74 Training on Higher-Order Thinking Skills - Professional Learning Package Program Management Team Research Center for Teacher Quality (RCTQ) National Educators Academy of the Philippines (NEAP) Professional Development Division Quality Assurance Division NEAP in the Regions Session Guide Writers and Presentation Deck Editors Alson Rae Luna Angelica B. Buaron Angelo D. Uy Analou O. Hermocilla Arnel Jr. M . Camba Eldefonso Jr. B. Natividad Elsie Jane M. Mantilla Fluellen L. Cos Hera Paz B. Yamson Jelly L. Sore Jojiemar M. Obligar Josephine P. Balasan Mae Laarni M. Saporna Marie Vic C. Velasco Maripaz T. Mendoza Mark Anthony A. Durana Melvin Willy II B. Roque Milaner R. Oyo-a Rejulios M. Villenes Renante Juanillo Renato N. Pacpakin Rosalyn C. Gadiano Sally A. Palomo Wilma S. Carrera NEAP Central Office Abdul Haiy A. Sali Guillermo Nikus Telan Dir. Leah B. Apao Jerson R. Capuyan Richie Carla A. Vesagas