Friday, February 27

ACS - 2008 Prelim Paper Qns

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?


Mrs Tan

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

Catch Us in WaWa Magazine March 2009

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?

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

Thursday, February 26

Questions for UTM readers to attempt?

Posted to all UTM publication readers,

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

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

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 ... ...

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.

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.

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!

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.

“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?

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:

Tuesday, February 24

Can these problems be solved by UTM? - Mrs Sui

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.

Friday, February 20

Club A and Club B - Mrs Tan

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 ... ...

Saturday, February 7

UTM book, chapter 1.1, question 7 - Mdm Chong

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:

Friday, February 6

About Unit Transfer Method

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,