mathsHeuristics™

Question posted by Parent

2012-02-24T14:52:00.000+08:00

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Parents Workshop March 2012

2012-02-16T15:13:00.005+08:00

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Question from Parent

2011-11-09T14:44:00.000+08:00

From: Mr Peter Cheng

Hi Sunny, tried applying UTM but can't solve this. Can you advise, tks

J and P had a sum of money. J gave P 0.4 of her money. P then gave J 1/2 of her money. In the end, J had three times the amt of money that P had. If J gave P $125 more than what P gave J , how much money did J have at first?

Ans: $1250.

Thank you

From desk of Sunny Tan……..

Heuristics: Effective Approach to A* in PSLE Maths & Science

2011-10-28T15:51:00.000+08:00

Primary 4 – Unit Transfer Method Publication, Chaper 2/ Q8 - From Madam Ser, Parent

2011-10-09T17:23:00.000+08:00

From: Madam Ser, Parent

Dear Sir

We refer to the UNIT TRANSFER METHOD Primary 4 book, Chap 2, Q8

Mrs Gan is changing the water in her fish tank.

If she uses a 4-litre pail to fill the tank, 4 litres of water will overflow.

If she uses a 2-litre pail to fill the tank, she will need another 3 more pails of water.

How many litres of water are needed to fill the fish tank.

The answer provided by the book indicates that the fish tank’s capacity is “16 litres”

However, when we work backwards :

Case 1: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 4 pails of 4 litres each to fill the tank. The amount of water available to Mrs Gan was 20 litres, so, 4 litres would overflow.

Case 2: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 8 pails of 2 litres each to fill the tank. If the amount of water available to Mrs Gan was 20 litres, so, there would still be an excess of 4 litres

Please clarify.

From desk of Sunny Tan……..

Case 1: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 4 pails of

4 litres each to fill the tank. The amount of water available to Mrs Gan was 20 litres, so, 4 litres would overflow.

Comment: Therefore the number of pails used is 5 pails.

Case 2: If fish tank’s capacity is 16 litres, that means that Mrs Gan used 8 pails of 2 litres each to fill the tank. If the amount of water available to Mrs Gan was 20 litres, so, there would still be an excess of 4 litres

Comment 1: If she use 8 pails of 2-litre each, she will fill up the tank completely, she

will not need another 3 pails, this assumption is invalid as it contradicts the question.

Comment 2: If the amount of water available to Mrs Gan was 20 litres, so, there

would still be an excess of 4 litres

This assumption is invalid. Case 1 and Case 2 scenarios are if..and if…, the two events never took place. Therefore we cannot assume that 20 litres of water, that is available in Case 1 is equal to that in Case 2.

Comment 3: Number of pails = 5 pails.

Total volume = 5x2 =10 litres

The capacity is 16 litres

Therefore she need extra 6 litres, which is 3 additional pails.

-----------------------------------------------------------------------------------------------------------------

From: Madam Ser, Parent

Dear Sir

Thank you for your explanation.

The model that we created as below:

U : No. of 4-litre pails

P : No. of 2-litre pails

Capacity of tank = 4U

4 litres that overflowed = 1 pail = 1U

Therefore, 4U = 16 litres

Check :

2P + 6 litres = 4U = 16 litres

Therefore, P = 5 pails of 2-litre each, resulting in shortage of 6 litres (3 pails of 2-litre each)

Please advise if the above interpretation is correct. Else, please help provide working.

Thank you.

From desk of Sunny Tan……..

I noticed from your model, the U and P is the same.

In fact, this fact can be established in the beginning, that is the number of pails used in both scenarios Case 1 and Case 2 are the same.

Thus, it is unnecessary to introduce P, too many unknown variables may confuse the child.

Let define: 1u = represents the number of pails

2 u = 10

1u = 5 (5 pails)

Either use

case 1: 4u – 4 = 4x5 – 4 =16

case 2: 2u + 6 = 2x5 + 6 =16

Hope this helps.

Question from Raymond

2011-10-04T12:29:00.002+08:00

Hi Mr Tan

Please help me with the following problem using UTM and model.

45 pupils in a class. 1/4 of boys and 2/3 of girls wear spectacles. 25 pupils wear spectacles. How many girls wear spectacles/ (answer 22)

Thanks
Raymond

From the Desk of Sunny Tan........

PSLE 2011 Question

2011-10-01T17:24:00.004+08:00

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Parents’ Seminar: Cracking the code to PSLE Maths and Science

2011-09-13T14:35:00.000+08:00

Many primary school students struggle with Maths and Science despite attending tuition classes and spending many hours practicing tons of worksheets. Help your child to achieve breakthroughs in PSLE Maths and Science with the Heuristics approach.

In this Parents’ workshop organized by Home Team NS, the author of Mastering Heuristics Series, Mr Sunny Tan and Mr Cedric Chai will share with parents:

▪ the missing link that keeps your child underperforming.
• the latest trend in PSLE Maths and Science questions
• how Unit Transfer Method (UTM) took a CHIJ girl from 52% to 99% within 20 weeks
• how to apply heuristics approach in recent PSLE maths and top school maths exam questions
• common misconceptions on preparing for PSLE exams
• how thinking frameworks help with exam performance

For Parents
Date: 22 Oct 2011(Sat)
Time: 10am-1pm
Venue: HomeTeamNS@Bukit Batok Cell Room (Level 2)
Fees: Member ($3) / Guest ($5)
For registration, please contact Jianhong at 6665-4608 or e-mail jianhong@hometeamns.sg

Singapore's Child: Tips to getting the 'hard' Math / May 2011

2011-06-03T13:45:00.000+08:00

Sg Child

Today's Parent: Training Your Child's Mind / Apr-May 2011

2011-04-13T14:37:00.000+08:00

Today's Parent

The Business Times: Cracking the code to PSLE Mathematics / 22 March 2011

2011-03-22T13:57:00.000+08:00

The Business Times

Home Team NS: Excel Method / March-April 2011

2011-03-19T13:58:00.006+08:00

Home Team

Singapore's Child: See it clearly, Solve it fast! / March 2011

2011-03-01T17:43:00.000+08:00

March Singapore's Child

Singapore's Child: Gear up for PSLE/Feb 2011

2011-02-10T15:00:00.002+08:00

Feb 2011 Singapore's Child

mathsHeuristics Centre Holiday Break

2010-12-11T13:16:00.000+08:00

The centre will be closed from 13th Dec 2010 to 3rd Jan 2011 for our annual short break. Do email us at enquiry@mathsheuristics.com and we will get back to you a.s.a.p. Thank you for the wonderful 2010 and have a great holiday!

ST Forum: Why all that drilling may not count for much

2010-12-08T14:02:00.000+08:00

Why all that drilling may not count for much

I REFER to the letter by Mr Wong Tuck Yin on Tuesday ("Express stream entry rate"). He said that despite the extensive exam preparations, the 63.5 per cent rate for Express stream entry was low and therefore it must be because the Primary School Leaving Examination (PSLE) was too difficult.
He failed to consider the possibility that the preparation method was flawed. Intensive worksheet practice only helps students to be exposed to different types of exam questions, but it does not teach them how to tackle a question that they have never encountered before.
Based on our study of exam performance of Primary 6 pupils for science and maths, study skills, conceptual understanding and question practice are heavily emphasised in the preparation for exams. Yet one very essential skill set is usually left out - a thinking framework for answering exam questions. Pupils need a thinking framework to approach questions in a systematic manner that will lead them to the right answer expressed correctly on paper. Without such a framework, practice does not necessarily make perfect.
When pupils are explicitly taught a thinking framework to tackle maths and science questions, they experience a marked improvement in their ability to answer different types of questions without the need for drilling. It's no surprise that their grades also improve dramatically.
It is time for parents to stop and think of a different way to prepare their children for PSLE.
Sunny Tan
Principle Trainer, Author
Maths Heuristics Pte Ltd

Source: http://www.straitstimes.com/STForum/OnlineStory/STIStory_610167.html

Sunny Tan's Interview by 93.8 LIVE!

2010-11-09T17:46:00.004+08:00

The better way to study for exams

Exams are important, but according to expert educator, Sunny Tan, parents have it wrong when it comes to helping their children prepare.

There's just too much worksheet drilling, especially in tuition centres when it comes to exams such as PSLE.

He has devised a novel approach known as the Unit Transfer Method that simplifies the learning of math.

Learn more here

Listen to [ 1 ] | [ 2 ]

The Straits Times - Heuristics: The ladder to A*/A in PSLE Maths and Science

2010-11-02T17:20:00.002+08:00

Heuristics

Parents Preview @ SMU

2010-10-21T15:19:00.003+08:00

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Expert Opinions - Singapore's Child (Oct 2010)

2010-10-10T23:37:00.001+08:00

Sunny Tan, mathsheuristics innovator shares his insights with Singapore's Child magazine - Exam Tips on the run

Unit Transfer Method Book Sold Out!

2010-09-03T15:39:00.000+08:00

The Unit Transfer Method has sold over a thousand copy and it is currently out of stock. Thank you one and all for your support.

Mastering Heuristics Series Authors Exclusive Interview in TODAY

2010-08-22T12:19:00.004+08:00

"Mastering Heuristics Series Authors Exclusive Interview in TODAY"

TODAY speaks to Sunny Tan, author of the Mastering Heuristics Series and Principle Trainer at mathsHeuristics™, and discovers firsthand how Unit Transfer Method (UTM) helps children and parents solve challenging Maths problems with ease.

(Click on the Picture below to view pdf version)

PSLE Higher Order Thinking Skills (for high achievers)

2010-07-24T12:59:00.003+08:00

PSLE Maths Explained!

2010-07-18T11:57:00.000+08:00

Heuristics of the Week

2010-07-16T14:34:00.002+08:00

Every week, we will post a Maths question with step-by-step easy to follow animation, guiding you and your child through the problem-solving process using heuristics approach. You are welcome to contribute questions to the blog by emailing us at utm@mathsheuristics.com. We will post the answers on this blog as soon as time permits.

Featured heuristics: Stack Model

Conventional Model vs Stack Model, Excerpt from Model Approach to Problem Solving

2010-07-15T13:42:00.002+08:00

Conventional Model

Stack Model

Excerpt from Unit Transfer Method In Solving Challenging Upper Primary Maths Problems

2010-07-15T13:37:00.001+08:00

(Before and After concept: Single unchanged quantities)

Coming Soon....

Readers of the UTM book will soon be able to access to our exclusive easy to follow step-by-step interactive flash explanation online.

UTM- Before and After Concept

2010-07-10T18:36:00.000+08:00

Dear Mr Sunny Tan,

May I enquire if unit transfer method can be applied to solve the following problem. If yes, please show me.
Tan X, Y and Z each contained some water. Tank X contains 3 times as much water as Tank Y. After 15% of the water in Tank X and 15% of Tank Y was poured in Tank Z, Tank Z had 30% more than before. If Tank Z had 104 litres of water, how many litres of water had Tank X at first ?

Thank you

Yours sincerely,

Danielle Teo
(your student)

From the Desk of Sunny Tan........

Case1 - Case 2 (work backwards)

2010-07-06T18:12:00.000+08:00

C1 C2-workbacks

Case 1 - Case 2 (Total unchanged quantities)

2010-06-29T18:34:00.000+08:00

Case 1 - Case 2

Maths Heuristics featured in Absolutely Parents PSLE Guide 2010

2010-05-12T15:25:00.001+08:00

Alternate Approach in solving Challenging Mathematical Problems

Unit Transfer Method offers a simple, logical and yet systematic way for understanding and solving higher-order thinking questions.

Solving mathematical questions using the heuristic of model method requires students to conceptualize a visual model in their mind before translating it onto their worksheet. However, interestingly, not all students are apt in this skill of visualizing. For many such students, UTM appeals more since it uses the prevalent knowledge of ratio and tabulation in analyzing problems. More importantly, complementing UTM with model method, allows students to solve questions in nearly all topics ranging from whole number, fraction, decimal, percentage up to ratio. ... Click Here to continue reading

UTM Question on Repeated Identity

2010-05-07T15:46:00.001+08:00

Dear Mr Sunny Tan

I have bought your UTM handbk but unable to solve this question. Hope you will help.

Andy, Betty, Candy and Danny each has some money. The amount of money Andy has is 1/3 of the total amount of money Betty, Candy and Danny have. The amount of money Betty has is 1/4 of the total amount of money Andy, Candy and Danny have. The amount of money Candy has is 1/5 of the total amount of money Andy, Betty and Danny have. If Danny has $1725, how much do they have altogether?

Mr Teo

From the Desk of Sunny Tan........

Pei Hwa Pri/ P6 / 2009 SA1

2010-05-04T18:06:00.002+08:00

Alan, Ben, Calvin and Dean shared some postcards. Alan received 20% of the postcards. Ben received 16 fewer postcards than Alan. Calvin received twice as many postcards as Ben. Dean got the remaining 144 postcards.

(a) find the total number of postcards shared by Alan, Ben, Calvin and Dean
(b) how many per cent more postcards than Alan did Dean receive?

Maths Heuristics featured in Kaisu Parent's website

2010-04-28T16:38:00.003+08:00

We all know that times have changed, but who would have imagined that the foundational mathematical problem solving skills we were brought up on mean practically nothing for our next generation?

The mathematics questions found in primary schools these days can leave even the most academically inclined parents stumped! Regardless whether you’ve scored A* in your own PSLE maths paper decades ago, we’re sure you’ve had difficulty trying to guide your child with his/her homework using your old-school algebraic equations. Even the relatively newer model approach, involving drawing rectangular boxes/blocks, doesn’t always work.

Perhaps the alternative Heuristics approach will put those seemingly impossible-to-solve problem sums in a “less intimidating” light. Heuristics simply refers to rules, processes or methods that the student can discover... Click Here to continue reading

Using Equal Concept (UTM) to solve problem!

2010-04-21T15:08:00.001+08:00

Utilising Advancd UTM Techniques

2010-04-13T13:05:00.002+08:00

Mrs Lim said...

I have bought your Unit Transfer Method Book last month. I was trying to use Chapter 1.4 (All Changing Quanties) to solve the below question from my girl's P6 test paper but somehow just could not solve the question. Question: Jane had $108 more than Peggy at first. Jane used 2/9 of her money while Peggy used 2/5 of her money. After that, Jane had $340 more than Peggy. How many did Jane have at first?

April 11, 2010 9:16 AM

From the Desk of Sunny Tan........

Problems that involve “more than/less than” generally utilize Advanced UTM technique. This problem cannot be solved using “All changing quantities” – questions in “All changing” does not involve “more than/ less than”.

Advance technique involves modification of the basic UTM as follows:

I would advise to teach the child the basic UTM technique and ensure the child is proficient in applying the fundamental UTM framework before to expose them to the advanced UTM. Without the basic training in the UTM framework, the child will faces challenges in visualizing the above conversion and may end up confusing the child.

Below depicts an alternate method to the above problem using the stack model approach :

The Maths Challenge to Parent - UTM book Q5 Pg 20

2010-03-16T09:49:00.002+08:00

Hi Sunny

My daughter was trying out the Q5 on page 20 of your UTM book. I have download the answers and explanation, but I don't seem to understand what the "40" in the boxes that you have placed in the diagram. How did you derive the "40"?

Question: Three sisters, Angie, Bernice and Candice share some sweets. Angie's share is 40% of the total number of sweets the three sisters have. Bernice has 40 sweets more than Angie. Bernice's share is 4 times Candice’s. How much money did each of them have?

Thanks

Vijay

From the Desk of Sunny Tan........

The explanation in the book use conventional model. I will illustrate visualizing the model in another perspective - stack model:

Conventional Model VS Stack Model

2010-03-09T14:44:00.001+08:00

In my seminars, the following are the most common questions raised by many parents;

a) What are the differences between conventional and stack Model approach?
b) Which model is the more “superior” approach?
c) Will it be confusing for the child to “switch” from conventional to stack model?

Many parents have the misconception that stack Model is completely new approach, that is different from the conventional model. I would like to emphasis that Stack model and conventional Model uses the same fundamental concepts of units to solve problem. Basically, they are the same. The only MAIN difference is the orientation of drawing the model.

Stack model utilizes visual processing technique – enable the child to minimize the movement (rearrange) the models and to combine all the steps required in the conventional model into a single step by using a single model. Then objective is to enable the child to “see” the problems laterally!

I will use the below example to illustrate my point:

The total cost of 14 bags is equal to the total cost of 6 wallets. Each wallet costs $22 more than each bag. Find the cost of each wallet.

CONVENTIONAL MODEL:

STACK MODEL:

Stack Model in action

2010-02-25T14:07:00.001+08:00

Conventional Model

Stack Model

Mastering Heuristics Series II

2010-02-24T15:59:00.002+08:00

Releasing Soon

Model Approach to Problem-solving
Highly-visual, helps your child to see Maths – literally!

The ability to visualise a problem goes a long way to solving it. The Model Approach to Problem-solving was borne out of this fact. Use drawings (models) in visualising a problem. Go beyond conventional models and solve challenging problems fast with highly-efficient techniques like Stack Model and Split Model.

by Sunny Tan
Releasing in June…

Maths Problem

2010-02-20T11:21:00.002+08:00

Hi Sunny,

Greetings!

My daughter, have attended your PR. 6 sesson.

I have one of her Pr. 6 problem that I know the answer but do not know how to present to her. Based on your method, how do you solve the following question:

Ai Tong School organized a 2-day camp. On the first day, the number of boys was 600 more than the girls. On the second day, the number of boys decreased by 10% but the number of girls increased by 10%. If there were 2540 children on the second day, how many children were there on the first day?

Appreciate your enlightening on the solution.

Thanks.

Mr Lee

From the Desk of Sunny Tan........

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Problems Involving Two Variables Concept

2010-01-20T13:45:00.001+08:00

Dear Sunny,

I have encountered a math's problem for primary 6, could you please advise me how to solve it?

There were a total of 820 boys and girls at a funfair. After 3/4 of the boys and 3/5 of the girls left the funfair, there were 120 more girls than boys remaining behind. How many boys were there at the funfair at first?

Thanks for your help

Yani

From the Desk of Sunny Tan........

Maths Question

2009-10-19T17:20:00.001+08:00

Dear Sunny,

Ms Tan gave some sweets to 6 boys and 11 girls. Each child was given the same number
of sweets. Each boy then gave 2/3 of his share of sweets to the girls. As a result, each
girl now received 12 more sweets than before.
a) How many sweets did each boy left?
b) Find the total number of sweets each girl had in the end.

From the Desk of Sunny Tan........

Math Question Enquiry

2009-07-24T13:43:00.001+08:00

Dear Sunny,

Can you advise me on the following math question?

Mary and Jason each has some money. If Mary spent $80 per day and Jason spent $40 per day. Mary wil had $500 left when Jason has spent all his money.

If Mary spent $40 per day and Jason spent $80 per day, Mary will have $1100 left when Jason has spend all his money.

What is the amount of money Jason has?

Regards,
Venus

From the Desk of Sunny Tan........

Parents Seminar @ The Kidz Academy 7th June 2009, Suntec Singapore Hall 602 & 603

2009-05-25T23:19:00.002+08:00

Parents Seminar @ The Kidz Academy
7th June 2009, Suntec Singapore Hall 602 & 603

Unit Transfer Method in Solving Challenging
Upper Primary Maths Problem

At the preview...

▪ Discover the latest trend of PSLE questions

▪ How UTM helped a CHIJ girl to BREAKTHROUGH her results from.52% to99% within 20 weeks!

▪ Apply UTM on.recent PSLE and top school exam problems

▪ Clarify common misconceptions like "Is model drawing or Guess and Check a waste of time?"

▪ How to help children who are not so adapt to the model approach.

Visit www.thekidzacademy.com.sg to register.

ParentsWorld, May 09 "Exclusive interview with Sunny Tan"

2009-05-25T23:08:00.002+08:00

Up coming Parents Seminar

2009-04-12T22:20:00.003+08:00

Unit Transfer Method Versus Model Drawing

2009-03-06T03:18:00.002+08:00

The question is the excerpt from the UTM publication, Chapter 1.1.
The following question is used to illustrate the Model Approach and Unit Transfer Method.

You will realise that the fundamental concept between UTM and MD is the same. While MD uses bar diagram and visual spatialisation, UTM uses tabulation and logical reasoning.

Question

5/6 of the buses were owned by Company C and the rest by Company S. Company S bought another 900 buses and now owns 2/3 of all the buses. How many buses does Company S have now?

Answer:

Try to solve the following using UTM:

Tom had a box of red beads and yellow beads. When he added in 30 red beads, 20% of the beads were yellow beads. He added another 100 yellow beads; as a result, 60% of the beads in the box were yellow. How many red beads were there in the box at first?

IMMEDIATE PRESS RELEASE

2009-03-02T02:27:00.002+08:00

Mastering Heuristics Series
Mathematical Strategies Made Simple

At last, a guidebook that delivers!

The Mastering Heuristics Series is the brainchild of Sunny Tan, Principle Trainer at Maths Heuristics.

The Mastering Heuristics Series captures Sunny’s simple, systematic yet strong techniques in understanding and applying Mathematical Heuristics. Edited by a strategic marketing communications professional cum parent who understands readers’ psyche and the time crunch parents face, the Mastering Heuristics Series is designed to be highly comprehensive.

Most Mathematics guidebooks provide only answers or, at most, brief workings. Without illustrating each step involved in the workings, readers end up having to figure out for themselves how the author got from one step to another. The Mastering Heuristics Series offers two perspectives:

1. Concepts in action
– to show how easy and efficient Mathematical Heuristics are in solving challenging mathematical questions.

2. Concepts being applied
– to systematically show every step involved in applying each Mathematical Heuristics concept. Easy-to-follow step-by-step instructions make the Mastering Heuristics Series the ultimate practical guide for parents.

The Mastering Heuristics Series consists of four books. The first one, now available, covers six concepts – Before and After, Excess and Shortage, Repeated Identity, Equal, Two Variables, and Ratio and Proportion – under the Unit Transfer Method.

Since its release in the market in January 2009, the book has already garnered coverage by renowned parenting media – ParentsWorld (January 2009) and Wawa Magazine (March 2009) – as well as raving reviews by academia and parents.

Impetus for the School and the Series

While a teacher with Singapore’s Ministry of Education, Sunny observed how the current primary school Mathematics syllabus – different from what today’s parents and teachers were raised on – left many stumped. Mathematical Heuristics has been directly incorporated into the Mathematics syllabus. Teachers are not specifically trained to teach Mathematical Heuristics. Worse still, not neatly self-contained makes Mathematical Heuristics difficult to single out, learn and teach.

Consequently, many parents depend on tuition agencies or private tutors for their children’s Mathematics performance, not realising that most tutors were also raised on the same Mathematics syllabus as themselves, that is sans Mathematical Heuristics.

The more hands-on parents rely on Mathematics syllabus guidebooks to equip themselves to personally guide their children. However, there are no books on the market that specifically teaches Mathematical Heuristics. Where a guidebook comes close to it, its title merely allude to Mathematical strategies (not Mathematical Heuristics), making such books difficult to identify. Once acquired, parents often find themselves second guessing the author’s explanations, and how the author got from one step to another.

With the aim of closing this gap, Sunny emerged with techniques that simplified the application of Mathematical Heuristics. With that as a spring board, Sunny established the mathsHeuristics Programme, and now the Mastering Heuristics Series in 2009. Both Programme and Series are available through Maths Heuristics.

1. mathsHeuristics Programme
– Directly teaches primary students.
– Since its establishment, the Programme has transformed the Mathematics confidence level and performance of numerous students, including a CHIJ P6 student to went from scoring 52% in SA1 to 99% in the Preliminary exam, to A* in the 2008 PSLE – all within just 20 weeks.

2. Mastering Heuristics Series
– Indirectly teaches primary students via parents.
– Backed by mathsHeuristics Programme’s proven track record, Sunny has authored this series of guidebooks based on the Programme’s techniques.

While the Mastering Heuristics Series complements the mathsHeuristics Programme – by keeping parents informed of what their children are learning in the Programme, allowing parents to further support their children in the latter’s Mathematics homework – the Series is also comprehensive enough to be a standalone guide for parents who desire a bigger role in their children’s Mathematics education.

Distribution

Mastering Heuristics Series is available in the US and locally through Maths Heuristics (S) Private Limited. Orders may be placed online (at www.mathsheuristics.com) for home delivery, or in person (at 157A Goldhill Centre, Thomson Road, Singapore 307610) for self-collection.

Media Enquiries

Author / Publisher:
Maths Heuristics (S) Private Limited
Sunny Tan
Principle Trainer
Email: sunny@mathsheuristics.com

Editor / PR Agency:
RE: TEAM
Karen Ralls-Tan
Managing Partner
Mobile: (65) 9787 3081
Email: karen@reteamweb.com

Order Enquiries

Publisher:
Maths Heuristics (S) Private Limited
Christine Tham
Manager
Tel: (65) 6893 5593 (10am – 7pm, Tues to Sun)
Email: admin@mathsheuristics.com

ACS - 2008 Prelim Paper Qns

2009-02-27T15:15:00.001+08:00

Hi Sunny,

My son tried but could not solve the problem using the UTM. This question is familiar. Can you help and explain to him and at the same time forward me with the solution, please?

Q5: Adeline's monthly salary is $350 more than Bernice. Their monthly spending is the same and each of them spends $800 per month. After some time, Adeline has saved $1950 but Bernice has saved only $900.

(a) How long does each of them take to save the given amount of money?
(b) What is Adeline's monthly salary?

Thanks

Mrs Tan

From the Desk of Sunny Tan........

Catch Us in WaWa Magazine March 2009

2009-02-27T03:59:00.003+08:00

The mathsHeuristics will be featured in this coming WaWa magazine March 2009 issue. We have been invited to contribute questions for the WaWa mathematics contest in this issue. There will also be sneak preview on comparasion of using model approach, guess & check and Unit Transfer Method to solve challenging problems. Do encourage your child to participate in this contest and stand a chance to win attractive prizes including a complimentary copy of UTM book. Good luck.

Any Comments?

2009-02-27T03:55:00.002+08:00

Dear Mr Sunny Tan,

1/5 of the children at the playground were girls and the rest were boys. When 8 girls left the playground, the fraction of girls decreased to 1/7 of the total number of children at the playground. How many children were at the playground at first? (Ans 120)

For the above Question in the UTM book (Pg 20),

We get the answer is 140 children.

Following is the detail

1/5 are girls and 4/5 are boys = 7/35 are girls and 28/35 are boys

8 girls left , so left 1/7 are girls and 6/7 are boys

1/7 will be equal to 5/35 are girls left.

so 7/35 minus 5/35 = 8 girls left

2 units = 8 girls

1 unit = 4

4 x 35 = 140

Check back the answer as follow

and 28-8 = 20 girls left in the playground.

20/140 = 1/7.

Please check.

Question Posted by Mdm Chong - UTM reader

Questions for UTM readers to attempt?

2009-02-26T23:35:00.002+08:00

Posted to all UTM publication readers,

Any UTM readers keen to to attempt the following?
Do post your answers in this blog for discussion.

Clue:
Q1) Chapter 6: Proportion Concept
Q2) Chapter 5: Two Variable Concept
Q3) Chapter 3: Repeated Identity
Q4) Chapter 1.4: Before & After (All changing quantities)

Hi Mr Sunny

Could UTM be used for the following problems?

1) A group of 24 children sold some tickets for a charity show. Each ticket was sold at $5. Each boy sold 5 tickets and each girl sold 3 tickets. The boys collected $40 more than the girls.(a) How many girls were there in the group?(b) How many tickets were sold altogether?

2) There are 85 plates of fried rice for 80 people. Each adult eats 2 plates of fried rice and every three children share 1 plate of fried rice. How many adults and children are there?

3) Four girls, A, B, C and D, each have some stamps. The number of stamps A has is 1/2 of the total number of stamps B, C and D have. The number of B has is 1/3 of the total number of A, C and D have. The number of stamps C has is 1/4 of the total number of stamps A, B and D have. If D has 78 stamps, find the total number of stamps A & B have altogether.

4) At first, Jane had 2/3 as many stamps as Kelly. After Jane bought another 20 stamps and Kelly lost 29 stamps, Jane now has 4/5 as many stamps as Kelly. Find the number of stamps Kelly had at first.

Best Wishes

PSLE Parents

Parents' Concern

2009-02-26T04:50:00.004+08:00

Hi Sunny

Please elaborate more on UTM.
Is it a more effective method as compared to other Heuristics?
Is model drawing or Guess and Check a waste of time?
Will the child be confused if he/she is taught a different method from schools?

Concerned parents

Hi Sunny,

Good Afternoon Sir,
As the name of your blog suggests, there is no better way to learn more about UTM than from the guru himself.

As compared to Model Drawing, UTM lacks the visual impact which enables a student to see Maths,so to speak.
In what way is UTM a more effective method than MD?
Could you help to illustrate with some examples?
Is UTM within MOE Maths syllabus?

Interested parents

From the desk of Sunny Tan ... ...

UTM RESEARCH BACKGROUD
The Unit Transfer Method is a fundamentally sound approach with research based on Teacher Work Series publication. Unit Transfer Method uses ratio with tabulation to help child to effectively analyze and solve challenging mathematical problems. This simple, logical yet powerful problem-solving technique is an alternative to the model approach and the algebraic framework approach.

MOE SYLLABUS
Reference to MOE forum replies “Different Approaches taught for Mathematical Techniques” dated 12th Feb 2007, Ms Ho Peng, Director, Curriculum Planning and Development.

“Other than the model drawing approach, pupils are also taught different problem solving methods. They are encouraged to try different approaches and have the flexibility to choose the method that works best for them in solving the problems’

“In the marking of PSLE mathematics, pupils are not restricted to the use of any one particular method. All mathematically correct solutions are acceptable”

In the replies above, the Ministry of Education will accept any mathematically correct method in the PSLE. In fact, the reply mentioned that pupils need a wider repertoire of approaches to work with more challenging problems.

The UTM is very effective in solving problems involving the Before and After Concept, which is one of the heuristics stipulated in the MOE curriculum.

PROBLEM SOLVING HEURISTICS
MOE has recommended 11 problem solving heuristics in primary level. Every heuristics plays a role in problem solving. The common misconception in many parents is that many are trying to search for the “holy Grail” or the most “superior” problem solving methods for their child.

Many parents have always raised these concerns during my seminar, “Is guess and check or model drawing a waste of time?” To answer these concerns, we have to ask ourselves "What is heuristics?"

Heuristics are methods that helps in problem solving. Heuristics does not guarantee a solution.
When approaching the problem, the child first understands the problem, chooses the method and carry out the plan. If it doesn’t work, the method should be discarded and a new method should be choose to solve the problem. However, many pupils or even us will “stubbornly” continue to usie the initial method even it doesn’t work!

UTM VERSUS MODEL APPROACH
As mentioned, many parents are guilty of searching for the “Holy Grail” or the most “Superior” problem solving method. We all know in fact, they never or will never exist.

Different children have different learning style - right and left brain dominant learners.
The left brain learners are strong in logical and analytical thinking while the right brain learner seeks to determine the spatial/visual relationships of all the parts.
The question of which is more superior method is therefore very subjective. Therefore, we cannot answer on behalf of our child. What is important as parents, we should equip the child with different approaches so that they have the flexibility to choose the method that works best for them in solving the problems.

The fundamental concept of the model approach and UTM utilizes ratio. Model drawing is visual or UTM uses tabulation. The combination of Model Approach and Unit Transfer Method utilize the left and the right brain- an integrated "whole" brain approach to maximize the untapped potential of the child.

VISUAL PROCESSING TECHNIQUE
“Do you know Guess and Check can be solved just by using 3 steps?”
“Do you know there are other ways to draw model other than horizontal bar?
By changing the orientation of the model, the answers is staring in front of them!

These are some of the topics that will be covered in the Parents’ Seminar.

Using UTM for this question?

2009-02-26T00:22:00.001+08:00

Hi Sunny

Using UTM for this question?

Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.

February 24, 2009 1:53 PM

From the desk of Sunny Tan ... ...

The concept used for this question is propotion concept. The solution is as follows:

Can these problems be solved by UTM? - Mrs Sui

2009-02-24T12:00:00.002+08:00

Q1) In Hall A, 30% of the 800 people were men. In Hall B 40% of the 400 people were women and children. After some of the people in both hall had switched hall, 25% of the people in Hall A and 75% of those in hall B were men. How many people were there in Hall B after the change?

Q2)During a warehouse book sale, Sally spent 62.5% of her money on 24 books and 18 pens. She also spent 25% of her remaining money on 18 files. Each pen costs 8/9 as much as the price of one book. The file costs $7.80 less than a book. Find the total cost of one book and one pen.

Question posted by Mrs Sui, UTM book reader
Tues, 24th Feb 2009

From the desk of Sunny Tan ... ...

Q1)This concept is covered in UTM book, Chapter 1.2 –Before and After (Total unchanged)
with Chapter 5 – Two variables concept.

i) The total number of men in Hall A and Hall B remain unchanged before and after the transfer.
ii) The total number of women and children in Hall A and Hall B remain unchanged before and after the transfer.
iii) The total number of people in Hall A and Hall B remain unchanged before and after the transfer.

2) The UTM concept to solve this question is covered in Chapter 6 - Proportion Concept.

Club A and Club B - Mrs Tan

2009-02-20T12:00:00.002+08:00

Hi Sunny,

My son has school worksheet today and he faces difficulty in solving the question below using the Unit Transfer Method.

Club A and Club B had a total of 270 members. Club A had 80% as many members as Club B. During a recruitment exercise, more people joined both Clubs and for every 3 members who joined Club A, one member joined Club B. Given that the ratio of the number of members in Club A to Club B in the end was 2:1, find the number of members in each club in the end.

Question posted by Mrs Tan, Parent
Thurs, 19th Feb 2009

From the desk of Sunny Tan ... ...

UTM book, chapter 1.1, question 7 - Mdm Chong

2009-02-07T12:00:00.004+08:00

With reference to the UTM book, chapter 1.1, question 7:

A concert hall has 600 seats. 10% of the seats are VIP seats while the rest are normal seats. How many VIP seats must be added so that the number of VIP seats will increase to 20%?

Please advise what is wrong with the following reasoning:

Question posted by Mdm Chong M.K, UTM Book reader
Fri, 6th Feb 2009

From the desk of Sunny Tan ... ...

Confusion Alert:

The 540 normal seats in the Before and After scenario remains unchanged. However, the percentage of the normal seats changes from 90% in the Before to 80% in the After scenario.
It is important to highlight to the students that percentage is relative to the total sum.
The number of the quantity being unchanged does not imply that the percentage of quantity being unchanged.

Therefore, in the Unit Transfer Method, students are encouraged to convert fraction, decimal, ratio, whole number, and percentage into units as follow:

About Unit Transfer Method

2009-02-06T23:57:00.004+08:00

Heuristics in Primary Maths Syllabus

Heuristics is a specialised mathematical problem-solving concept. Mastering it facilitates efficiency in solving regular as well as challenging mathematical problems. The Ministry of Education in Singapore has incorporated 11 Problem-Solving Heuristics into all primary-level mathematical syllabus.

Challenges in Learning Heuristics

Instead of containing the 11 Problem-Solving Heuristics neatly into specific chapters though, they have been integrated into the regular curriculum. This not only makes it difficult for students to pick up Heuristics skills, but can also make mathematics confusing for some students. For us parents, it is difficult for us to put aside the regular-syllabus mathematical concepts we were brought up on to re-learn Heuristics, much less teach our own children this new concept.

Take Algebraic Equations, for instance. Primary-level Mathematics Papers these days include questions from the topic even though the topic has never been, and is still not, taught at primary level. Parents, being familiar with the topic, will attempt to teach their children to solve the question using Algebraic Equations, which will only further confuse their children. According to current primary-level mathematical syllabus, Heuristics should be used instead.

Overcoming the Challenges

These and other challenges were what I observed first hand during my years as a mathematics teacher, and what provided me the impetus for my post-graduate studies, mathsHeuristics™ programmes and now this series of books. Indicative of the effectiveness of my methodology, it helped a P6 girl from CHIJ to improve her Mathematics grade from 52% in the First Semestral Assessment to 99% in the Preliminary Examination, to achieve A* in the 2008 PSLE – all within just 20 weeks!

About this Series

This series of books is a culmination of my systematic thinking, supported by professional instructional writing and editing, to facilitate understanding and mastery of Heuristics. Through it, I have neatly packaged Heuristics into logical topics (Series of books) and sub-topics (Chapters within each book). For each sub-topic, I offer many examples, showing how the sub-topic may be applied, and then explaining the application in easy-to-follow steps and visualisations without skipping a beat.

This particular book in the series deals specifically with Unit Transfer Method, the use of ratio to effectively analyse and solve challenging mathematical problems. This simple, logical yet powerful problem-solving technique is an alternative to the model approach and the algebraic framework approach.

The entire series of four books provides a complete and comprehensive guide to Heuristics.
While each book introduces parents to a few Heuristics topics, it gives students the opportunity to see how the specific Heuristics work as well as get in some practice. For students enrolled in mathsHeuristics programmes, each book serves as a great companion, while keeping parents well-informed of what their children are learning.

Sunny Tan,
Author

Glen and Ryan - Mrs Tan

2008-12-13T12:00:00.002+08:00

Hi Sunny,

Need your help to solve the following.

Glen and Ryan had $403 altogether. After Glen used 1/4 of his money and Ryan used 1/3 of his money, Glen has twice as much money as Ryan. How much money did Ryan have at first?

Question posted by Mrs Tan, Parent
Fri, 12th Dec 2008

From the desk of Sunny Tan ... ...

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3 questions - Mr Shew

2008-10-10T11:00:00.003+08:00

Dear Sunny,

Thanks for the extra mile for the consultation session.
Alden has the following questions to ask:

(a) A bill of $72 was paid with $10, $5 and $1 notes. If 13 notes were used for payments, how many notes of each kind were used?

(b) Vanessa and Bobby had some telephone cards. AfterBobby gave 4/9 of his cards to Vanessa, the ratio of the number of Bobby’s cards to the number of Vanessa’s cards became 10 : 17. What was the ratio of the number of Vanessa’s cards to the number of Bobby’s cards at first?

(c) 12 workers took 10 days to make 800 bowls. How many days 3 workers need to make 40 bowls?

Question posted by Mr Shew, Parent
Thurs, 9th Oct 2008

From the desk of Sunny Tan ... ...

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Ning and Zongwei - Dr Lua

2008-09-24T11:00:00.004+08:00

Hi Sunny,

Please find attached the P6 PSLE Maths question which contains an answer using alegbraic method. How to solve using Heuristic Model?

Ning and Zongwei jogged to and fro repeatedly along a straight path in a park between 2 points, A and B. Ning jogged at a uniform speed of 4m/s and Zongwei jogged at a uniform speed of 6 m/s. They started jogging from opposite directions at the same time as shown below.

They first met on another at point X. The second time they met was at point Y.
a) Given that the distance between X and Y is 160 m, find the distance between A and B.
b) If they started jogging at 8 am, how long did they take to meet again for the third time? (Express your answers in min and seconds)

Question posted by Dr E.K. Lua, Parent
Tues, 23rd Sept 2008

From the desk of Sunny Tan ... ...

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2 questions - Mrs Tan

2008-08-06T11:00:00.002+08:00

Hi Sunny,

Please advise how to solve the following using UTM:

1. Ryan and Jude have some pencils each. If Ryan give Jude 28 pencils, he will have as many pencils as Jude. If Ryan gives Jude 12 pencils, he will have many pencils as Jude. How many pencils does each of them have?

2. At a party, Mrs. Lim serves either lemonade in glasses or cups. She has exactly 100 glasses or 150 cups of lemonade. If she has already served her guests 40 glasses and 28 cups of lemonade, what is the maximum number of glasses of lemonade she had left?

Question posted by Mrs Tan, Parent
Fri, 5th Dec 2008

From the desk of Sunny Tan ... ...

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Factory Qn - Mr Shew

2008-07-15T11:00:00.004+08:00

Dear Sunny,

I came across an interesting problem sum while revising Maths with Alden:

There are 500 male and 200 female employees in factory A. There are 400 male and 600 female employees in factory B. Some employees are transferred from factory A to factory B. After the transfer, the number of male employees is the same as the number of female employees in factory B and the number of male employees is twice the number of female employees in factory A. How many female employees were transferred from factory A to factory B? (Answer: 100)

Could you advise other method besides Model Drawing to solve this question? The question is taken from math456.com P5 Maths CAs and Sas for Top Primary Schools.

Question posted by Mr Shew, Parent
Mon, 14th Jul 2008

From the desk of Sunny Tan ... ...

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