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## Welcome to CISM Math Department Blog

For most people who enjoy math, solving a math problem is an enjoyable and rewarding activity than answering a math exercise. What’s the difference? Math problems require the critical and creative use of math concepts and strategies whereas math exercises apply acquired math knowledge and techniques to achieve mastery. Mastery is necessary and valuable but students also need to experience solving challenging math problems.

CISM Middle School Math (Grades 6 – 8)

The CISM Middle School Math curriculum is designed to prepare CISM students for high school mathematics. Following the concepts and skills prescribed by the Common Core and the MYP-DP Math Continuum, this course commits itself to continue students’ development of mathematical fluency and reasoning as they progress to more complex Math topics. Computational skills with whole numbers, integers, decimals and fractions will be further developed and reinforced in this course through the various learning strategies, which includes drills, board work, and activities. Problem-solving analysis and critical thinking skills are stressed through cooperative learning and inquiry-based learning. A solid foundation of the math fundamentals are designed to prepare students for explorations in Elementary Algebra, Geometry, Statistics and Probability.

CISM High School Mathematics (Grades 9 – 10)

The curriculum empowers students with mathematical tool techniques and analytical skills while providing them with a strong foundation on fundamental algebraic skills and mastery of various mathematical concepts. Problem-solving skills are further enhanced in this curriculum through the use of drills with the application of technology. Critical and analytical thinking skills are used in a problem-solving context.

Aligned with the standards set by the Common Core and the MYP-DP Continuum, topics in the course focus in the development of logical, critical, creative thinking and perseverance in problem solving with the use of appropriate technology. Specifically, the Grade 9 Math covers Intermediate Algebra, Analytic Geometry, Trigonometry, Basic Probability and Statistics. Grade 10 Math integrates Advanced Algebra, Trigonometry, Discrete Math and Data Analysis. These topics prepare the students for the required learnings and requirements of IB Math. The introduction of TOK questions in these grade levels is also an effective method to prepare students to the expectations of IB Math.

GRUOP 5 in CISM

The IB Math syllabus aims to develop the mathematical knowledge as well as logical and critical thinking skills of the DP student using previous learned Math concepts and their skills in abstraction and generalization. The program also intends to encourage students to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

IB Math SL

The IB Math SL curriculum introduces important math concepts through the development of mathematical techniques. Students are introduced to the concepts in a comprehensive and coherent way. The mastery of the concepts in this course involves the application of mathematical knowledge through solving real-life problems in an appropriate context.

The math exploration, which is internally assessed, offers the students the opportunity to develop independent learning in math through the use of various mathematical activities and the investigation of different mathematical ideas.

IB Math HL

Math HL is for students who have a strong background in math and a wide range of analytical and technical skills. The curriculum allows students to apply their mathematical knowledge to solve problems in a variety of meaningful contexts and to justify and prove results.  It also offers the opportunity for students to develop insights on mathematical form and structure and become intellectually equipped to link between concepts in various topic areas.

The student’s math exploration shows independence in mathematical learning by using various mathematical approaches in the examination of mathematical ideas. This internally- assessed requirements also develop the student’s skills for communicating mathematical ideas in written form.

IB Math Studies SL

The Math Studies SL caters to student with varied backgrounds and abilities, and is designed to build confidence and encourage an appreciation of mathematics. This two-year course focuses on the application of mathematics to common real-world occurrences. This allows students to gain an understanding of a variety mathematical topics that can be applied in various settings, and develop sophisticated mathematical reasoning and critical thinking.

The internally-assessed written math exploration allows students to ask their own questions about a mathematical phenomenon and independently go through the process of applying learned mathematical concepts and skills, and utilizing mathematical tools of analysis relevant to the collected data in order to come to a final conclusion regarding their topic.

In alignment with the IB curriculum, the math department is dedicated to development of these traits in our students.

Inquirers. Our math classes encourage students to be naturally curious and encourage the love of learning throughout their lives.

Knowledgeable. In our classes, students learn math concepts and strategies that they could use across a broad and balanced range of disciplines.

Thinkers. Each math activity gives students the opportunity to apply critical and creative thinking skills in approaching challenging math problems.

Communicators. Students in our math classes collaborate with each other and are able to express their ideas in various modes of communication.

Principled. Math encourages students to perform their best at all times, however they are also taught to act with integrity and honesty on all occasions.

Open-minded. As math students collaborate with each other, they learn to see and evaluate a range of views and are willing to grow from the experience.

Caring. Math classes teach our students to show empathy and respect towards others and commit themselves to make a positive difference on their lives.

Risk-takers. Challenging math problems in class allow students to explore possible solutions with the use of acquired skills and techniques.

Balanced. Although focus is on the mastery of the acquisition of math concepts and strategies, various teaching and learning strategies are employed in every math class.

Reflective. Students in our math classes learn to assess and understand their strengths and limitations to support their learning and development in the course.

Once again, welcome to our blog! Let’s work together to make this the best year ever.

Charlston D. Chavez
Mathematics

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## IB Math SL1 – Statistics

HG Wells, famous English author of The Time Machine, once wrote, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read.” That time has come. We now need statistical thinking or the ability to weigh the merits of different options based on whatever available data we have.

When you hear the word statistics, you most probably think of graphs, batting averages, percentages of employed and unemployed persons and in general, tedious and boring descriptions of society and nature by means of a set of numbers. True, statistics involves organizing and representing numbers, however, it does much more than this.

Next month, we will be studying statistics and its applications to the different disciplines.  You will need Statistics when doing your Math IAs and other IB subjects. In IB Psychology, both descriptive and inferential statistics are required in your IAs to get the significant difference of the independent variables. In IB Business Management and Economics, your knowledge in interpreting graphs is an essential tool to fully understand the data

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## Geometry in Nature

Geometric shapes and figures abound in nature. The honeycomb of bees is one such example; individual cells have hexagonal openings. The spider web is constructed with a series of polygons anchored in radial thread lines. The orbits of planes and stars are elliptical with some nearly circular. Th cross sections of many fruits and trees are circular. A stone thrown on still water causes the formation of a series of circular waves with increasing circumferences as the ripples move outward. Arc shapes can be found in petals of many flowers. The beautiful rainbow is in the form of arc.

Symmetry is one of the most geometric characteristics in nature. Symmetry brings balance and enhances appearance. The symmetrical and almost perfect cone of Mount Mayon and Mount Fuji make it world famous. We find symmetry abounding in leaves, flowers and fruits.

Artists and builders of all cultures were and are influenced by the geometric shapes and figures observe in nature and have since time immemorial incorporating their observations in their works. This, the pyramids of Egypt and the temples, palaces and churches around the world are wondrously decorated with geometric figures and combinations of them.

Engineers apply triangles in building structures because it is the most stable construction. (You will discover why when you study triangles.) Towers and bridges shape are often constructed with a series of triangles. For rotating  motions, the circular shape is a must. The circular shape is applied in innumerable machine parts – wheels, camshafts to name but a few.

Indeed, everybody once in a while applies geometric knowledge in his/her various activities like estimating lengths, areas and/or surface areas and volumes and perhaps the cost of materials.

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## IB Learner Profile: Balanced

One of the IB Learner Profile states that an IB student is someone who exemplifies honesty, integrity, justice, and respect. Collectively these traits describe a principled learner. How is this learner profile evident in a Math class?

An IB student knows when to persevere until a solution to a problem has been reached but they also recognize the need for guidance or assistance from the teacher or a classmate. This allows them to not only find the solution to the problem but learn the process of how the solution has been reached. Principled learners know when to seek help from others and at the same time offer help to those who may be struggling.

Principled learners are healthy competitors. They exert effort in everything that they do but their mindset is always to bring everyone up with them. They are not threatened with competition rather they use it to inspire and motivate themselves to become better.

—-Mr. Chavez—-

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## Ring-gle bells! Ring-gle bells! Ring-gle all the way!

Identify the number of ring-gle bells you hear before Yuletide season and New Year’s Eve.

Infinite?

Possibly!

And since the number of dates marked in our calendar nears coming into life,

I have here just a few reminders for you to keep on your memories:

1. Go and enjoy family and friendship get-togethers and party like you never did before! It’s good to spend some time having a blast after a period full of school work. Have a great time then!

2. The coming holidays are sure to bring fun full of laughs, don’t you think? If you would spend your time not letting go of what hurts you in the past, therefore, these holidays got no use for you. Remember that being happy and choosing to be happy with a dash of amusement is always a choice no matter what.

3. Don’t party and procrastinate without your brain. When you get back to school on January 2016, be sure that you have equipped your memories with something Mathematical and have completed the task I have assigned you.

And that’s it!

May you all have a great time, dear students!

MR. CHAVEZ

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## IB Learner Profile: Balanced

Final Examination for the first semester is coming up. It is expected that every student is ruffling through their notes and catching up with requirements. However, do not forget the other aspects of your student’s life. As a student, academics is not the only priority. You should be a well-rounded holistic learner.  A holistic learner is somebody who is able to balance the different facets of your life.

Time management is an important skill that you have to acquire in order to fulfill all your responsibilities  not only as a student but also an individual. Make sure that you allot certain times of the day to do different activities.

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## IB Learner Profile: Thinker

1. a, b, c and d are four distinct positive integers such that the product of any two of them is any multiple of 12. Find the least possible value of a + b + c +d.

2. My twelve-hour clock has four digits, two for the hours and two for the minutes. The minutes are shown with leading zeros but the hours are not. Upside down, the digits 0, 1, 2, 5, 6, 8 and 9 read 0, 2, 3, 5, 9, 8 and 6 respectively. One day, I made a phone call on the appointed time and learned that it was too early. Then, I realized that I had read the clock upside down. If you know by how much I was early, you will know the time when I made the call. The time I should have made the call was….

In order to solve these math problems,  you should be able to show you are a thinker. IB student should be able to use thinking skills critically  and creatively to understand problems in order to reach a solution/decision.

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## Huge Pyramids

Huge Pyramids

One of the strategies that can be used to engage students is cooperative learning. In Grade 7 math, we recently covered Combining Like Terms and instead of working individually through worksheets, the students collaborated with each other through an interactive activity.
The class made a large pyramid out of strips of coloured papers containing terms. They started from the bottom where all terms were aligned. Afterwards, they combined terms that are similar and wrote their answers on the strips of paper until they reach the top of the pyramid. This activity was adopted from https://mail.google.com/mail/u/0/#search/pyramid?projector=1 . The students enjoyed creating their group’s pyramid and it was interesting how different groups came up with different strategies on how they will divide their work so they can finish solving within the given time. This activity can also be used in other math concepts like integers, GCF, and LCM, among others.

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## All Aboard to Fifth Grade

I can’t believe it’s been two months already since we have welcomed school year 2018-2019. Time flies so fast! It feels like we have accomplished so much already in that span of time.

The kids have been busy working, learning and adapting to the routine of fifth grade. Since this is also a transition period from Elementary to Middle School, they are being trained to be socially responsible and to always show empathy and care to one another. Circle Time is also being done with the Guidance Counselor to help the kids cope with the challenges in fifth grade.

For the past seven weeks, kids have been spending a lot of time doing hands on activities and experiments in Science. They have been observing, exploring and note taking the changes in matter- whether it is a physical or a chemical change.

Math continues to be a challenging and fun class as they get to do Mental Sums and Speed Tests for 2 minutes, with 20 to 30 questions; solve problem sums and exit questions and do active and engaged activities. Power School (PS)  has also been introduced to the kids. They get to see their numerical grade (in real time) for both Maths and Science and how are their grades were generated in the Power School. Parents can also access their child’s grade in the Power School by logging in to their accounts.

Below are some photos from the past two months. I can’t wait to see more of their activities as the rest of the year goes.

Estimating the area and perimeter of the enclosed figure using yarn and pinky finger’s width of 1 centimetre.

Working in pairs, they are to tasked to inflate a balloon using baking soda and vinegar

Discussion time! Estimating the area and perimeter of the enclosed figure using yarn and pinky finger’s width of 1 centimetre.

Working in groups, they are tasked to inflate a balloon using baking soda and vinegar

Working in groups, they are tasked to inflate a balloon using baking soda and vinegar

Working in groups, they are tasked to inflate a balloon using baking soda and vinegar.

Working in pairs, they are tasked to inflate a balloon using baking soda and vinegar

Working in pairs, they are to find a way to control the amount of gas produced in a baking soda and vinegar reaction

Working in pairs, they are to list down the changes they have observed when one tablet of Berocca was dissolved in a cold water.

Jotting down their answers on the area and perimeter activity.

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## OneNote as my School Aid

Note taking… how do we organize it?

One of the problems I’d like to emphasize here is how we organize our notes. Over the years we have develop this practice of safeguarding our notes or documents, download files pictures and even clips that we feel are necessary or simply because they are good information. But alas, after all these gatherings and storing these “stuff” we literally end up with… stuff!

I have been searching the net and even have been into forums asking about what’s their best practice when it comes to organizing your notes. The best answer was OneNote.

OneNote is a Microsoft-based program that helps you with all your note taking… and more. It’s literally a digital notebook but better. If you have been using OneNote you’ll understand what I’m saying. So just to simplify things, here are some of the best benefits of OneNote that I truly am thankful for.

• Note taking by typing, handwriting, recording Audio or Video. Note taking has never been so flexible. If you’re fast in typing, or would rather write your notes by hand, OneNote allows you to do both. Say you can’t catch up with the lecturer’s speed or can remember a topic by seeing it, recording via audio and video is also possible with it.

• Automatic Saving. Have you ever experience typing something then the program closes? And worse when you open it up again it’s either it wasn’t saved or only part of it was saved. With OneNote you don’t have to save what ever you are doing since it saves it automatically

• Endless and Freedom of Space. When we use word we are limited to a size of a paper, but with OneNote we have an almost limitless space. When using our notebooks, we decide where to write, same is true with OneNote. Just click on anywhere and you can write, paste, post attach or link almost anything anywhere. It even gives you an option on resizing what you have written to make it bigger or smaller.

• Organization. Another thing that I truly love about it is the organization of the notes. Imagine having a notebook that is divided into sections and each section contains a page that is almost limitless in space. You can label your notebook, the Section and even the title of the page. And it even allows you to sort them out according to how you’d like them to be. Oh did I mention you can even assign color coding for these? How cool is that?

• Attachments. This is something that OneNote edges way above a regular notebook. You can attach almost anything to it such as (to name a few) word documents, excel sheets, PowerPoint, pictures, PDF files, audio, websites, articles from websites, Videos (that can be played in it) etc.

These are just a few of the things that you can do with OneNote and it’s free. You can even use OneNote over a pc, a Mac, Linux, Android, iOS… on your Phone, tablet, Laptop or desktop. And it synchronizes your notes in all your devices.

I know I may sound like I’m advertising OneNote, well probably your are right. But here’s the thing, I’m not getting paid for this. It has been such a great help in my work that I couldn’t help but share my best practices.

Lastly, as a math teacher this has been a great tool for me because of its math application included. So if you’re looking for a way of organizing your notes and doing something more, maybe you should try it. Who knows.

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## Math 101: Note-taking

In many math classes, there are times when the teacher lectures. Sometimes
the teacher writes key words, examples, and explanations on a whiteboard
or a projector. Sometimes the teacher uses presentation software like
PowerPoint. The examples may be the same or different than the examples in the
textbook.

As a student, you need to listen, understand, ask questions, and take notes. For
many learners, the very act of taking notes helps them retain the material. Notes
also are a record of what your instructor thinks is most important and a source of
help for doing homework.

When you are taking notes, you are writing, listening, and thinking about new
material at the same time. If you search the Internet for note taking in math, you will
find many different systems for organizing and using your notes. What you choose
to do depends on whether your teacher expects you to always take notes, how fast
you can write, how much you need to watch (not just listen) to learn, and how your
teacher presents the information. For most students, the system they use is not as
important as having a time as soon after class as possible in which they rewrite and
organize their notes, connecting the notes to the material in the textbook.