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.

 

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)

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

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

Recommended Maths Olympiad Books for Self Learning / Domain Test

Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain.

A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series)

The Art of Problem Solving, Vol. 1: The Basics

The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions.

GEP Math Olympiad Books

If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid!

A suitable book would be The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.

Other Suitable Math Olympiad Books for GEP

These are some books that are very popular and highly rated on Amazon.


Challenging Problems in Algebra (Dover Books on Mathematics)

Challenging Problems in Geometry (Dover Books on Mathematics)
Math Circles for Elementary School Students: Berkeley 2009 and Manhattan 2011 (MSRI Mathematical Circles Library)

My Best Mathematical and Logic Puzzles (Dover Recreational Math)
The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics)

The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)

Secondary 4 O Level E Maths and A Maths @ 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

 

O Level E Maths & A 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 Maths Tuition @ Bishan starting in 2014.

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

Maths Tuition @ Bishan starting in 2014.

O Level E Maths and A Maths.

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

Past students have gone from fail to top in class! Mr Wu is a good mentor, and elder brother to two medical students (one studying in Monash University, Australia, another studying in NUS)

Email: mathtuition88@gmail.com

O Level E Maths and A Maths Tuition starting next year at 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.

Time needed for each O Level E Maths / A Maths Question

E Maths / A Maths: Maximum time per question

Paper 1: 2 hours (120 min) — 80 marks

Max. Time taken per mark: 1.5 min per mark

Paper 2: 2 hours 30 minutes (150 min) — 100 marks

Max. Time taken per mark: 1.5 min per mark

In O Levels Maths, speed and accuracy is very important indeed!

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

Maths Group Tuition starting in 2014!

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

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

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

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.)

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

Email: mathtuition88@gmail.com

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).

O Level Maths Tuition Flyer

O Level Group Tuition Flyer
O Level E Maths & A Maths
Tuition at Bishan
碧山数学补习
Location: Block 230 Bishan Street 23 #B1-35 S(570230)
Schedule:
• Monday 7pm-9pm (E Maths)
• Thursday 7pm-9pm (A Maths)
Website: https://mathtuition88.com/group-tuition/
Tutor: Mr Wu
(from RI GEP, NUS Maths 1st Class Honours, Dean’s List)
Class size is limited to 8 students only! (Small Group Tuition)

O Level E Maths and A Maths Tuition @ Bishan by Patient Tutor, NUS 1st Class Honours, Ex-RI (GEP)

Maths Tuition @ Bishan by Patient Tutor, NUS 1st Class Honours, Ex-RI (GEP)
——————————————————————————–
https://mathtuition88.com/group-tuition/

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

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

*Small Group Maths Tuition available in 2014 — Registration/enquiries open now*

Website: https://mathtuition88.com/

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

Subjects for tuition:
•O level (Secondary): E Maths, A Maths

Tutor is patient, experienced and qualified. (from Raffles Institution (GEP), NUS Mathematics Dean’s List)

Please email us at mathtuition88@gmail.com for more details.

Website: https://mathtuition88.com/

About Tutor: https://mathtuition88.com/singapore-math-tutor/
Fees & Schedule: https://mathtuition88.com/singapore-math-tuition-fees-schedule/
Contact Us: https://mathtuition88.com/singapore-math-tuition-contact-us/
https://mathtuition88.com/2013/05/21/free-exam-papers/
https://mathtuition88.com/2013/07/19/maths-tuition-centre/
https://mathtuition88.com/category/maths-tuition/
https://mathtuition88.com/tag/maths-tuition/

Secondary 4 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

Study Tips for Mathematics

Here are some useful study tips for Mathematics. The key to acing Maths is to understand that practice is key for Mathematics!

Sincerely hope these tips help.

Please do not study Maths like studying History, Literature or Geography, the study method for Maths is totally different and opposite from studying Humanities. Reading a Maths textbook without practicing is not very helpful at all.

Once a student understands the basic theory of a certain topic (usually just one or two pages of information), he or she can move on to practicing actual questions immediately. While practicing, the student will then learn more and more knowledge and question-answering strategies for that Maths topic.

Even if you already know how to do a question, it is useful to practice it to improve on speed and accuracy.

The study strategy for Maths and Physics are kind of similar, hence usually you will find that students who are good in Maths will also be good in Physics, and vice versa.

Students from China usually do very well in Maths exams because they understand the strategy for studying Maths (which works very well up till JC level), namely a lot of practice with understanding. The strategy is called “题海战术” in Chinese, which means “immersing oneself in a sea of questions”.

Source for diagram below: Email from JobsCentral BrightMinds

maths mindmap

Sec 4 Maths 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

O Level Maths Group Tuition

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

https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

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

Mathematics homework

O Level Formula List / Formula Sheet for E Maths and A Maths

E Maths Formula List / A Maths Formula Sheet

Attached below are the Formula Lists for E Maths and A Maths (O Level)

Do be familiar with all the formulas for Elementary Maths and Additional Maths inside, so that you know where to find it when needed!
Wishing everyone reading this all the best for their exams. 🙂

E Maths Formula List

A Maths Formula List

Click here to read about: How to prevent careless mistakes in math?


Maths Tuition

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Tutor profile: About Tutor


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Math Doesn’t Suck: How to Survive Middle-School Math Without Losing Your Mind or Breaking a Nail

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

数学补习 (碧山)

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

明年2014数学补习班将会在碧山开始。

教O Level E Maths 和 A Maths.

想报名的学生请联络mathtuition88@gmail.com.

谢谢。

Maths Tuition Singapore Keywords

Just for curiosity, I went to research on the top keywords for Maths Tuition for Google search engine.

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JC Junior College H2 Maths Tuition

If you or a friend are looking for Maths tuitionO level, A level H2 JC (Junior College) Maths Tuition, IB, IP, Olympiad, GEP and any other form of mathematics you can think of.

Experienced, qualified (Raffles GEP, NUS Maths 1st Class Honours, NUS Deans List) and most importantly patient even with the most mathematically challenged.

So if you are in need of the solution to your mathematical woes, drop me a message!

Tutor: Mr Wu

Email: mathtuition88@gmail.com

Website: Singapore Maths Tuition | Patient and Dedicated Maths Tutor in Singapore

O Level E Maths Tuition: Statistics Question

statistics-olevel-tuition-graph

Solution:

From the graph,

Median = 50th percentile = $22,000 (approximately)

The mean is lower than $22000 because from the graph, there is a large number of people with income less than $22000, and fewer with income more than $22000. (From the wording of the question, calculation does not seem necessary)

Hence, the median is higher.

The mean is a better measure of central tendency, as it is a better representative of the gross annual income of the people. This is because more people have an income closer to the mean, rather than the median.

Sec 3 Hwa Chong Institution Maths Test Papers and Resources

Site: http://anglc.wiki.hci.edu.sg/space/content

Description: Includes Sec 3 Hwa Chong Institution Maths Test Papers and Resources

 

Please visit our site https://mathtuition88.com/free-exam-papers for updates on more Free Exam Papers and Maths Tips.

Ten Year Series: How many questions or papers to practice for Maths O Levels / A Levels?

This is a question to ponder about, how many questions or papers to practice for Maths O Levels / A Levels for the Ten Year Series?

If you searched Google, you will find that there is no definitive answer of how many questions to practice for Maths O Levels/ A Levels anywhere on the web.

For O Level / A Level, practicing the Ten Year Series is really helpful, as it helps students to gain confidence in solving exam-type questions.

Here are some tips about how to practice the Ten Year Series (TYS):

1) Do a variety of questions from each topic. This will help you to gain familiarity with all the topics tested, and also revise the older topics.

2) Fully understand each question. If necessary, practice the same question again until you get it right. There is a sense of satisfaction when you finally master a tough question.

3) Quality is more important than quantity. It is better to do and understand 1 question completely than do many questions but not understanding them.

Back to the original query of how many questions or papers to practice for Maths O Levels / A Levels for the Ten Year Series, I will attempt to give a rough estimate here, based on personal experience.

5 Questions done (full questions worth more than 5 marks) will result in an improvement of roughly 1 mark in the final exam.

(The 5 Questions must be fully understood. )

So, if a student wants to improve from 40 marks to 70 marks, he/she should try to do 30×5=150 questions (around 7 years worth of past year papers). Repeated questions are counted too, so doing 75 questions (around 3 years worth of past year papers) twice will also count as doing 150 questions. In fact, that is better for students with weak foundation, as the repetition reinforces their understanding of the techniques used to solve the question.

If the student starts revision early, this may work out to just 1 question per day for 5 months. Of course, the 150 questions must be varied, and from different subject topics.

Marks improved by Long Questions to be done Approx. Number of years of TYS OR (even better)
10 50 2 1 year TYS practice twice
20 100 4 2 year TYS practice twice
30 150 6 3 year TYS practice twice
40 200 8 4 year TYS practice twice
50 250 10 5 year TYS practice twice

This estimate only works up to a certain limit (obviously we can’t exceed 100 marks). To get the highest grade (A1 or A), mastery of the subject is needed, and the ability to solve creative questions and think out of the box.

When a student practices TYS questions, it is essential that he/she fully understands the question. This is where a tutor is helpful, to go through the doubts that the student has. Doing a question without understanding it is essentially of little use, as it does not help the student to solve similar questions should they come out in the exam.

Hope this information will help your revision.

Challenging Geometry E Maths Question — St Andrew’s Sec 3 Maths Tuition Question

Question:

ABCD is a rectangle. M and N are points on AB and DC respectively. MC and BN meet at X. M is the midpoint of AB.

recommended maths tuition geometry

(a) Prove that \Delta CXN and \Delta MXB are similar.

(b) Given that area of \triangle CXN: area of \triangle MXB=9:4, find the ratio of,

(i) DN: NC

(ii) area of rectangle ABCD: area of \triangle XBC. (Challenging)

[Answer Key] (b) (i) 1:3

(ii) 20:3

Suggested Solutions:

(a)
\angle MXB=\angle NXC (vert. opp. angles)

\angle MBX = \angle XNC (alt. angles)

\angle BMX = \angle XCN (alt. angles)

Therefore, \Delta CXN and \Delta MXB are similar (AAA).

(b) (i) \displaystyle\frac{NC}{BM}=\sqrt{\frac{9}{4}}=\frac{3}{2}

Let BM=2u and NC=3u

Then DC=2\times 2u=4u

So DN=4u-3u=u

Thus, DN:NC=1u:3u=1:3

(ii)

We now have a shorter solution, thanks to a visitor to our site! (see comments below)

From part (a), since \Delta CXN and \Delta MXB are similar, we have MX:XC=2:3

This means  that MC:XC=5:3

Thus \triangle MBC:\triangle XBC=5:3 (the two triangles share a common height)

Now, note that \displaystyle\frac{\text{area of }ABCD}{\triangle MBC}=\frac{BC\times AB}{0.5 \times BC \times MB}=\frac{AB}{0.5MB}=\frac{2MB}{0.5MB}=4

Hence area of ABCD=4\times\triangle MBC

We conclude that area of rectangle ABCD: area of \triangle XBC=4(5):3=20:3

Here is a longer solution, for those who are interested:

Let area of \triangle XBC =S

Let area of \triangle MXB=4u

Let area of \triangle CXN=9u

We have \displaystyle\frac{S+9u}{S+4u}=\frac{3}{2} since \triangle NCB and \triangle CMB have the same base BC and their heights have ratio 3:2.

Cross-multiplying, we get 2S+18u=3S+12u

So \boxed{S=6u}

\displaystyle\frac{\triangle BCN}{\triangle BDC}=\frac{3}{4} since \triangle BCN and \triangle BDC have the same base BC and their heights have ratio 3:4.

Hence,

\begin{array}{rcl}    \triangle BDC &=& \frac{4}{3} \triangle BCN\\    &=& \frac{4}{3} (9u+6u)\\    &=& 20u    \end{array}

Thus, area of ABCD=2 \triangle BDC=40u

area of rectangle ABCD: area of \triangle XBC=40:6=20:3