Exercises in Counting Techniques - Part I

Exercises in Counting Techniques - Part II

Exercises in Counting Techniques - Part III

Sample Test in Calculus I - Part I

Sample Test in Calculus I - Part II

Sample Test in Calculus I - Part III

Figure 1 for Problem 3 in College Algebra

Violent Crime in the Philippines

Continuation of Math 1 - College Algebra

Activity in Mathematics 1 - BSCrim College Algebra

After downloading, please share the activity to your classmates.

Activity in Mathematics 0 - BSBA Basic Mathematics

These exercises should be done in two meetings during your scheduled time in Math 0.

Solve the following non-routine problems and submit to your class Mayor.

Figure 1: Problem 4

1. Samuel went to the circus during the town fiesta. He saw 7 clowns. Some were riding on bicycles while others were on tricycles. He counted 16 wheels. How many bicycles were there? How many tricycles?
2. A farmer makes a wire fence on a square lot of which each side is 6 meters long. If there will be a post every 2 meters, how many posts were used by the farmer? How long was the wire used in fencing the area?
3. The teacher said to the 3 students, “I will blindfold you and place a mark on each of your foreheads. Each of you will either have a black or white mark. When I tell you to take your blindfolds off, you are to raise your hand if you see a black mark on the foreheads of either of the other applicants. Then the first one who correctly tells the color of your own mark wins the game.” All three students raised their hands at the same time. One of them however came up with the correct color of her own mark. What color is her mark, and how did she figure it out?
4. In Figure 1, place the digits 1 to 9 in each square so that each of the diagonals adds to 26 and also the four corners add to 26. You can not repeat any digit.

Activity in Mathematics 2 - BSBA Basic Statistics

1. The following are the numbers of customers a restaurant served for lunch on 120 week-days:

50 64 55 51 60 41 71 53 63 64 46 59
66 45 61 57 65 62 58 65 55 61 50 55
53 57 58 66 53 56 64 46 59 49 64 42
47 59 62 58 63 58 59 64 45 42 53 48
78 76 48 75 72 48 59 58 65 64 57 71
45 78 74 72 64 58 48 42 47 49 53 64
66 48 44 55 77 65 67 72 42 48 65 68
64 58 59 64 57 58 66 48 42 64 58 62
47 65 49 62 55 54 53 69 58 49 57 61
59 64 55 43 44 48 64 62 60 70 75 41

Group these figures into a distribution having the classes

40 – 44, 45 – 49, 50 – 54, 55 – 59, ... , 75 – 79

2. Convert the distribution obtained in Exercise 1 into a

• percentage distribution
• “less than” cumulative frequency
• “more than” cumulative percentage distribution
• “or more” cumulative distribution beginning with “40 or more”

3. Using the distribution Exercise 1, draw a

• Histogram
• Bar chart
• Frequency polygon
• Ogive of the cumulative distribution

Syllabus for Probability

2010 Mass Training of First Year Teachers in Mathematics

The Division of Aurora conducted the Division Mass Training of all First Year High School teachers on the implementation of 2010 Secondary Education Curriculum. Thirty Five (35) first year mathematics teachers participated the training.The following teachers attended the training:

1.  Armando Picart
2. Luningning Abel
3. Liwanang Gutierrez
4. Peter Dela Cruz
5. Milagros Gutierrez
6. Antonino Bernabe
7. Reynaldo Dayson
8. Evangeline Dela Cruz
9. Daisery Felizardo
10. Josefina Galope
11. Cesar Agno
12. Lourdes Villaros
13. Vincent Crosby
14. Ethelbert Bagapuro
15. Fanny Magdaleno
16. Brenda de Guzman
17. Erwin Carasco
18. Guillermo Emilio
19. Annabelle Zabat
20. Meredel Viaje
21. Julita Rivera
22. Dennis Valdez
23. Ronald Dela Torre
24. Felicidad Rodriguez
25. Joel Duaso
26. Nova Resueno
27. Rita Pumihic
28. Julita Hokam
29. Jean Mora
30. Isabelito Trucilla
31. Rodolfo Leti Jr.
32. Ronald Canopin
33. Lily Pacio
34. Rizalina Soriano

Understanding by Design

INTRODUCTION

The Context

As a matter of practice, the curriculum in the Philippines is revised every ten years, but the rapid rate of change in education and the fast obsolescence of knowledge necessitate a continual revisiting and updating of the curriculum to make it responsive to emerging changes in the needs of the learner and the society. Thus, the refinement of the curriculum remains to be a work in progress.

Aside from the issue of relevance, the refinement of the secondary education curriculum was guided by the need, as articulated in the Education for All Plan 2015, to streamline its content in order to improve student mastery and contribute to the attainment of functional literacy. This became a primary consideration in the design of the curriculum and the formulation of standards and the essential understandings from which the content of the curriculum was derived. 

The results of national and international assessments were reviewed and analyzed for their implications for teaching and learning. The findings were used to further tighten the standards and improve the delivery of the curriculum and the teaching-learning process. The results of the evaluation of the implementation of the 2002 Basic Education Curriculum were likewise considered in the review of the curriculum. The findings and recommendations (see Annex A) guided the training of teachers and the capacity-building of school heads in managing the pilot test of the curriculum in 23 secondary schools nationwide. 

The Process

The refinement of the curriculum followed the Understanding by Design (UbD) model developed by Jay McTighe and Grant Wiggins. 

The curriculum design has the following elements:

Stage 1 

A. Results/Desired Outcomes, which define what students should be able to know and do at the end of the program, course, or unit of study; generally expressed in terms of overall goals, and specifically defined in terms of content and performance standards


A.1. Content standards, which specify the essential knowledge (includes the most important and enduring ideas, issues, principles and concepts from the disciplines), skills and habits of mind that should be taught and learned. They answer the question, “What should students know and be able to do?”


A.2. Performance standards, which express the degree or quality of proficiency that students are expected to demonstrate in relation to the content standards. They answer the question, “How well must students do their work?” or “At what level of performance would the student be appropriately qualified or certified?”


B. Essential Understandings, which are the big and enduring ideas at the heart of the discipline and which we want the children to remember even long after they leave school

C. Essential Questions, which are open-ended, provocative questions that spark thinking and further inquiry into the essential meanings and understandings 

D. Curriculum Objectives, which are expressed in terms of knowledge and skills that teachers can use as guide in formulating their own classroom objectives

Stage 2

A. Assessment, which defines acceptable evidence of student’s attainment of desired results; determines authentic performance tasks that the student is expected to do to demonstrate the desired understandings; and defines the criteria against which the student’s performances or products shall be judged.


B. Products and Performances, which are the evidence of students’ learning and a demonstration of their conceptual understanding, and content and skill acquisition 

Stage 3

A. Learning Plan, which details the instructional activities that students will go through to attain the standards

A.1. Instructional Activities, which are aligned with the standards and are designed to promote attainment of desired results. Questions to guide the review of Stages 1 to 3 are provided in Annex B.

A series of consultations with critical stakeholders: students, teachers, school heads, parents, supervisors, industry, local government officials, the religious, and experts from the academe, among others, were made to validate and further refine the formulation of standards, the essential understandings, the essential questions, and the assessment criteria and the tools to measure students’ products and performances. Workshops were conducted to draft the curriculum documents, write the instructional plan and develop lesson exemplars.

Teachers were trained and school heads from the 23 identified pilot schools underwent capacity-building to prepare them for the management of the try-out of the curriculum. The schools were identified based on their location (i.e., Luzon, Visayas, Mindanao) and the type of program (i.e., regular high school, specialist high school) they offer.

Meetings with school heads and classroom visits were made on a quarterly basis to monitor the try-out of the curriculum. Teachers’ feedback on the lesson guides became the basis for further refinement of the standards and the other elements of the curriculum.

Education supervisors were later trained on providing instructional support to teachers. A follow-through training was subsequently conducted to further equip them with the tools of supervision given the requirements of the program.

Results
 
Initial feedback from the teachers has been useful in further improving the design of the curriculum. What has evolved from the try-out is a core curriculum that builds on and retains the principles of the 2002 BEC (i.e., constructivism, integrative teaching) and integrates the richness of the special curricular programs (Arts, Sports, Engineering and Science Education Program, Journalism, Technical-Vocational Program, and Foreign Language). The latter shall be offered in schools as special interest areas which children can pursue among many other career options in livelihood education. The curriculum has the following features:

What is being envisaged is that the core curriculum shall be implemented with special curricular programs: special program in the arts (SPA), special program in sports (SPS), special program in journalism (SPJ), special program in foreign language, special science/math (S&T), technical-vocational program (tech-voc) being offered on the side, to develop the students’ multiple intelligences.

Mathematics Curriculum Framework

The goal of basic education is functional literacy for all. In line with this goal, the learner in Mathematics should demonstrate the following core competencies: problem solving, communicating mathematically, reasoning mathematically and making connections and representations.
The macro skills critical to these four competencies are computational skills and comprehension, application to real life, creative and critical thinking and visual imagery.

These competencies and skills are expected to be developed using approaches such as practical work/outdoor activities, mathematical investigations/games and puzzles, and the use of ICT and integration with other disciplines. The theories underpinning these approaches are Experiential Learning of David Kolb, Constructivism and Cooperative Learning.

Values inherent in Mathematics such as accuracy, patience, honesty, objectivity, creativity and hard work are developed integratively in the teaching-learning process.

Eureka

View my account daily so that you can be updated of the new trends and practices in Mathematics Education and the Learning Technologies in the classroom.

This  web is made for the Mathematics teachers and educators in Aurora.