Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

CoC_titlescreen_2013

We can learn some mathematics from the popular game, Clash of Clans!

Lets look at the Building Cost and Production Rate of the Gold Mine.

Source: http://clashofclans.wikia.com/wiki/Gold_Mine

Gold Mine11clash of clans gold mine ap gp

We see that the Build cost actually follows a geometric progression(approximately) as each time, the build cost approximately doubles.

The formula for the n-th term of a geometric progression is \boxed{ar^{n-1}}, where a is the first term, and r is the common ratio.

The above formula works well for the first 2 terms, for example the second term is 300=150(2^{2-1}).

However, the Production Rate follows an arithmetic progression, as per level, the production rate increases by 200/hr.

The formula for the n-th term of an arithmetic progression is \boxed{a+(n-1)d}, where a is the first term, and d is the common difference. The formula works for all the 5 levels: for instance at level 5 the production rate is 1000=200+(5-1)(200).

Thanks for reading, and do “like” this post if you enjoy reading it! Hope you learnt some mathematics along the way.

JC School Posting Results 2014

Source: http://www.moe.gov.sg/media/press/2014/01/posting-results-2014-jae-and-jpsae.php

Posting Results For The 2014 Joint Admissions Exercise (JAE) and Joint Polytechnic Special Admissions Exercise (JPSAE)

1The Ministry of Education (MOE) will release the posting results for the 2014 Joint Admissions Exercise (JAE) and the Joint Polytechnic Special Admissions Exercise (JPSAE) on Wednesday, 5 February 2014, at 8.00 am.Applicants can obtain their posting results via the following channels:

2JAE

  • The JAE-Internet System (JAE-IS) is accessible through the JAE website at http://www.moe.gov.sg/education/admissions/jae; and
  • Short Messaging System (SMS) text messages sent to the mobile phone number provided by the applicant during registration.

3JPSAE

4Applicants posted to a Junior College (JC) or the Millennia Institute (MI) should report to these institutions on Thursday, 6 February 2014, at 7.30 am. Applicants posted to a Polytechnic or Institute of Technical Education (ITE) course will receive further instructions via an enrolment package from the respective institutions by mail.

Read more at: http://www.moe.gov.sg/media/press/2014/01/posting-results-2014-jae-and-jpsae.php

Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

Is there a mathematical reason why chocolate chip cookies have 37% (1/e) chocolate in them?

Source: http://math.stackexchange.com/questions/651823/is-there-a-mathematical-reason-why-chocolate-chip-cookies-have-37-1-e-chocola?newsletter=1&nlcode=97485%7cd140
Someone once briefly explained to me why it is that chocolate chip cookies have 37% chocolate in them. To the best of my memory it has to do with the way trying to place dots in a circle in a random and scattered way behave, which turns out to be 1/e or ≈37.
Chocolate Chip Cookie 37% 1/e

Interesting article for chocolate lovers!

Source: http://math.stackexchange.com/questions/651823/is-there-a-mathematical-reason-why-chocolate-chip-cookies-have-37-1-e-chocola?newsletter=1&nlcode=97485%7cd140

Math Fun Facts

Source: http://www.math.hmc.edu/funfacts/

Check out this website by Professor Francis Su!

Math Fun Facts are ideas and puzzles that will change the way you think.

This archive is designed as a resource for enriching your math courses and nurturing your interest and talent in mathematics! Each Math Fun Fact is a math puzzle or short article that contains a cool mathematics idea.  You’ll can learn about the mathematics of things like card shuffling to poker to computer  vision to fractals to music, just to name a few.  This makes great enrichment material for gifted math students or problem-solving groups.

http://www.math.hmc.edu/funfacts/

The Lesson of Grace in Teaching

Source: http://mathyawp.blogspot.sg/2013/01/the-lesson-of-grace-in-teaching.html

Excerpt:

The Lesson of Grace in Teaching           

From weakness to wholeness, the struggle and the hope

Francis Edward Su MAA Haimo Teaching Award Lecture Joint Math Meetings, January 11, 2013 An audio file is available: bit.ly/W4gyD0.

“We know truth, not only by reason, but also by the heart.” —Blaise Pascal

I’m honored but I’m also really humbled to be giving this talk to a room full of great teachers, because I know that each of you have a rich and unique perspective on teaching.  I had to ask myself: could I really tell YOU anything significant about teaching? So I decided instead to talk about something else, that at first may appear to have nothing to do with teaching, and yet it has everything to do with teaching. I want to talk about the biggest life lesson that I have learned, and that I continue to learn over and over again.  It is deep and profound.  It has changed the way I relate with people.  It has reshaped my academic life.  And it continually renovates the way I approach my students. And perhaps it will help you frame your own thoughts about teaching.  The beginning of that lesson is this:

Your accomplishments are NOT what make you a worthy human being.

It sounds easy for me to say, especially after having some measure of academic ‘success’ and winning this teaching award. But twenty years ago, I was a struggling grad student, seeking validation for my mathematical talent but flailing in my research, seeking my identity in my work but discouraged enough to quit.  My advisor had even said to me:

“You don’t have what it takes to be a successful mathematician.”

It was my lowest point.  Weak and weary, with my identity and my pride stripped away and my PhD nearly out of reach, I realized then that my identity and self-worth could NOT rest on whether I succeeded or failed to get my PhD.  So *IF* I were to continue in mathematics, I could not do it for any acclaim that I might receive or for the trappings of what the academic world would call success.  I should only do it because math is beautiful, and I feel drawn to it.  In my quiet moments, with no one watching, I still found math fun to think about.  So I was convinced it was my calling, despite the hurtful thing my advisor had said. So did I quit?  No.  I just changed advisors. This time, I chose differently.  Persi Diaconis was an inspiring teacher.  More than that, he had shown me a great kindness a couple of years before.  The semester I took a class from him, my mother died and I needed an extension on my work.  I’ll never forget his response: “I’m really sorry about your mother.  Let me take you to coffee.” I remember thinking: “I’m just some random student and he’s taking me to coffee?” But I really needed that talk.  We pondered life and its burdens, and he shared some of his own journey.  For me, in a challenging academic environment, with enormous family struggles, to connect with my professor on a deeper level was a great comfort.  Yes, Persi was an inspiring teacher, but this simple act of kindness—of authentic humanness—gave me a greater capacity and motivation to learn from him, because we had entered into authentic community with each other, as teacher and student, who were real people to each other.

Continue reading this inspirational article at: http://mathyawp.blogspot.sg/2013/01/the-lesson-of-grace-in-teaching.html

Recommended Maths Tuition Singapore

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Maths Tuition @ Bishan starting in 2014

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

O Level Tuition

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Cost of education in Singapore

Source: http://www.epigami.sg/blog/cost-of-education-in-singapore/

How much does it cost to educate a child in Singapore?

Answer: $80,940 or approximately 3 Round-the-World Trips!

Read more at: http://www.epigami.sg/blog/cost-of-education-in-singapore/

Release of O Level Results 2014

Sincerely wishing every student all the best for their O Level Results!

Meanwhile, all Secondary 3 to 4 students should start studying hard for their O Levels. 🙂

It has been many years since the release of my O Level Results. Sincerely wish my students to do well and even surpass me in their O Level Results.

maths-tutor-o-level-cert
Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.

O Level Maths Group Tuition at Bishan

Secondary 3 Students who want to learn Secondary 4 Maths in Advance

Calling all Secondary 3 Students who wish to study Secondary 4 E Maths and A Maths in advance, while revising Secondary 3 topics at the same time!

Join our group tuition at Bishan (https://mathtuition88.com/group-tuition/) !

Highly recommended for Secondary 3 students who are fast learners and wish to learn and get familiarised with Secondary 4 topics as soon as possible.

A typical lesson in our group tuition comprises of revising Secondary 3 topics (which is still important as it takes up almost 40% of the O Level questions), while learning Secondary 4 advanced topics. We will finish the school syllabus by June to start practising Ten Year Series and past year papers.

The best tip to not procrastinate (Maths Tuition at Bishan)

Source: http://www.thedutchphdcoach.com/time-management/the-best-tip-to-not-procrastinate/

The best tip to not procrastinate

It is incredibly easy, but as with anything, it takes a little practice. Try it now: Identify the most important thing you have to do today. Decide to do just the first little part of it — just the first minute, or even 30 seconds of it. Getting started is the only thing in the world that matters.

Get started, and the rest will flow.

– See more at: http://www.thedutchphdcoach.com/time-management/the-best-tip-to-not-procrastinate/#sthash.EqJDWUrJ.dpuf

Start Maths Revision Early for the Best Results!

O Level Group Tuition @ Bishan starting in 2014!

Maths is a subject that requires students to start revision / practice early!

It needs consistent practice and last minute studying is not going to work well!

Many students have the wrong concept that they can start practising questions one or two months before the O Levels. The problem is, without constant practice, the questions from the Ten Year Series would be too difficult for students to even begin attempting the questions! This is especially true for Additional Mathematics. This leads to panic and is not the desired study strategy. This is the main reason why it is possible to score very low (less than 20 marks out of 100) in Maths, if the student does not have solid foundation or has lack of practice. To avoid this scenario, start practicing and revising Maths now! Many students already start studying / learning in advance during the December holidays. January is still a good time to start! As the Chinese proverb states: “一年之计在于春一日之计在于晨”, the best time to begin planning for a task is in Spring.

Also, the current O Level Maths is not like the O Level of the past! Due to higher education standards nowadays, and competition from foreigners (especially China students whose pet subjects are Maths and Chinese), the bell curve for E Maths has shifted very very high. Rumours have it that 90 marks is necessary for a guaranteed A1 in E Maths.

On the bright side, it is very possible to improve in Maths with practice. Look at the Mathematics questions in O Levels, one long question is around 10 marks. Answering that one question correctly will already boost your score by 10 marks. (2 grades). Answering two long questions correctly will boost score by a whopping 20 marks!

Hesitate no longer! Start revising for your Maths now!

O Level Group Tuition @ Bishan starting in 2014!

Bishan-Ang Mo Kio area to get new JC in 2017

Source: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Bishan-Ang Mo Kio area to get new JC in 2017

The site for the new JC at the junction of Sin Ming Avenue and Marymount Road.
Lee Jian Xuan

Saturday, Jan 04, 2014

SINGAPORE – A new junior college that will open in 2017 for students from three Integrated Programme (IP) schools will likely be built on the site of the Asian Golf Academy near Bishan.

A statement on the Ministry of Education (MOE) website says the new campus will be at the junction of Sin Ming Avenue and Marymount Road, where the driving range is located.

The area is also zoned for an educational institution, according to the Urban Redevelopment Authority’s Draft Master Plan 2013.

Singapore’s 20th school to offer a JC programme will take in IP students from Catholic High School, CHIJ St Nicholas Girls’ School and the Singapore Chinese Girls’ School. It will also admit more than 100 students from other secondary schools who have completed their O levels.

It will be the newest JC since Innova JC in Woodlands was completed in 2005.

Read more at: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Maths Group Tuition starting in 2014!

https://mathtuition88.com/

Maths Group Tuition starting in 2014!

https://mathtuition88.com/group-tuition/

O Level Maths Tuition (E Maths & A Maths Tuition) at Bishan starting in 2014!

Location: Block 230 Bishan Street 23 #B1-35 S(570230)

Google Maps: http://goo.gl/maps/chjWB

Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.

Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.

Directions to Bishan Tuition Centre:

A) Via BISHAN MRT (NS17/CC15)

(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.

Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)

It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).

Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary).
Schedule
•Monday 7pm-9pm
•Thursday 7pm-9pm

(Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.)

Secondary 4 O Level E Maths and A Maths Group Tuition, Bishan

https://mathtuition88.com/group-tuition/
https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

maths challenge

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to mathtuition88@gmail.com .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

4) Ionut-Zaharia Chirila (Ex Lower Danube University, Romania)

The ideal Singapore JC subject combination for applying to Medicine

Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine

Source: http://sgforums.com/forums/2297/topics/439605

Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics

Source: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=40&t=12228

Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

Singapore O Level Group Tuition Bishan

O Level E Maths and A Maths Tuition starting next year at Bishan ————————– View Mr Wu’s GEP Testimonial at https://mathtuition88.com/group-tuition/

Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.

He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes.

Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for tuition by themselves! (not the parents) His students also look forward to tuition, instead of dreading tuition.

O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore.

Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.

Register with us now by email (mathtuition88@gmail.com). Vacancies will be allocated on a first-come-first-serve basis.

Thanks and wishing all a nice day.

Singapore math

Source: http://en.wikipedia.org/wiki/Singapore_math

Singapore math (or Singapore maths in British English[1]) is a teaching method based on the national math curriculum used for kindergarten through sixth grade in Singapore.[2][3] It involves teaching students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process.[2][3] The three steps are concrete, pictorial, and abstract. In the concrete step, students engage in hands-on learning experiences using concrete objects such as chips, dice, or paper clips.[4] This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.[5]

The development of Singapore math began in the 1980s when the country’s Ministry of Education developed its own mathematics textbooks that focused on problem solving and heuristic model drawing.[3][6] Outside Singapore, these textbooks were adopted by several schools in the the United States (U.S.) and in other countries such as Canada, Israel, and the United Kingdom.[7][1][8] Early adopters of these textbooks in the U.S. included parents interested in homeschooling as well as a limited number of schools.[3] These textbooks became more popular since the release of scores from the Trends in International Mathematics and Science Study (TIMSS), which showed Singapore at the top of the world three times in fourth and eighth grade mathematics.[9] U.S. editions of these textbooks have since been adopted by a large number of school districts as well as charter and private schools.[3]

Read more at: http://en.wikipedia.org/wiki/Singapore_math

The bar model can be drawn as a comparison model to compare two bars of unequal lengths, which can then be used to solve a subtraction problem.

 

On the road to make math fun: An army major who quit to become a mathematics teacher

Source: http://www.telegraphindia.com/1120625/jsp/calcutta/story_15629755.jsp#.Uq7JOJVDGDk

On the road to make math fun

MITA MUKHERJEE
Madanlal Baldevraj Ghai during the city leg of his tour. Picture by Sayantan Ghosh

An army major who quit to become a mathematics teacher has embarked on a self-funded tour of the country to promote the subject.

Madanlal Baldevraj Ghai, 70, stayed in a dormitory at Howrah station to keep costs down during the three days he spent in Calcutta recently, meeting officials of the primary and secondary board and the school education department to offer suggestions on how to make the study of mathematics more interesting.

“India has produced brilliant mathematicians not just in the Vedic and medieval ages but also in modern times. Unfortunately, for quite a few years, not many students have been pursuing the subject at the higher level, which has resulted in a decline in the number of top-quality mathematicians,” the former teacher at PMN College in Rajpura, Punjab, told Metro.

“We, the elderly mathematics teachers, need to reach out to students and guardians in every corner of the country to dispel the misconception that mathematics is dry and boring,” added Ghai, who has an MPhil in the subject and is pursuing his PhD at Punjabi University, Patiala.

His 50-day tour was also prompted by the Prime Minister declaring 2012 as the year of mathematics as a tribute to Srinivasa Ramanujan, the autodidact mathematician who died in 1920 at the age of 32.

Read more at: http://www.telegraphindia.com/1120625/jsp/calcutta/story_15629755.jsp#.Uq7JOJVDGDk

Maths tutoring adds up for students: OECD study (Singapore PISA tuition effect)

Source: http://www.smh.com.au/data-point/maths-tutoring-adds-up-for-students-oecd-study-20131206-2ywop.html

Many of the world’s most mathematically gifted teenagers come from countries with the most lucrative tutoring industries.

Figures released this week show tutoring in Asia’s powerhouses is widespread, with participation rates more than double those  in Australia, though the extent to which their success is a result of a punishing study schedule is unclear.

In test results released by the OECD, 15-year-olds from Shanghai  topped the mathematics rankings, performing at a level equivalent to three years ahead of students in Australia.
Read more: http://www.smh.com.au/data-point/maths-tutoring-adds-up-for-students-oecd-study-20131206-2ywop.html#ixzz2nXVdY3h0

Math is at the heart of physics. (O Level Maths and Physics Tips)

Source: http://www.academictips.org/acad/physic/physics_study_skills.html

Studying and practising Mathematics is one of the most useful things an O level student can do.

Not only are the two Maths (E Maths and A Maths) highly intertwined, studying Maths can actually help the students’ Physics too. There are some topics like Vectors and Kinematics in Physics that are also present in Mathematics.

Math is at the heart of physics. So the better your math, the better you’ll do in physics.

A good working knowledge of algebra and trigonometry is needed for Physics.

Mnemosyne with a mathematical formula.
Mnemosyne with a mathematical formula. (Photo credit: Wikipedia)

Mathematics is not a spectator sport (How to study Maths for Humanities students)

Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.

I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.

One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)

Mathematics is not a spectator sport

Source: http://www.math.umn.edu/~rogness/math1001/syllabus/node20.html

Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics.  Sometimes this means doing even more than the assigned problems.  (See “time committment” above.)  This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.

I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself.  But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.