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.


Anonymous said...

Is it easier to use unit method or model?


Anonymous said...


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.

Anonymous said...

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

Anonymous said...

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

Anonymous said...

Hi Mr Sunny

Speed is one of the most demanding topics in PSLE Maths. Many students and parents are often overwhelmed by the wordings of the problems. How can UTM helps in solving the following problems.

1) Jolin is meeting Amanda at a certain time. If she drives at 80km/h, she will be 1/3 hr late. If she drives at 60km/h, she will be 3/4 hr late. How long will the journey take if she drives at 90km/h?

2) At 7 am, Car A left Town X for Town Y while Car B left Town Y for Town X.
At 3 pm. the two cars passed each other.
5 hour later, Car A reached Town Y but Car B was still 150 km away from Town X.
Find the distance between Town X and Town Y?

3) Tracy took 15 minutes to jog from her home to a swimming pool. After swimming, she took 20 minutes to walk the same way home. Her walking speed was 3 km/h slower than his jogging speed. Find Tracy's walking speed in km/h.

PSLE Parents

Anonymous said...

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

Anonymous said...

Hi Mr Sunny

With the introduction of calculators for PSLE Maths 2009, Maths will definitely be more exciting and perhaps even more challenging.

Are there any types of new trend questions?Please help to show some examples if there are any?

As Model Drawing is also taught in your school, will you also be starting another blog showcasing MD as the strategy for solving problems.You may want to share the steps for effective MD.

Best Wishes
PSLE Parents

Sunny Tan said...

Hi PSLE Parents,

The Unit Transfer Method In Solving Speed problems will be our in upcoming publication in Mastering Heuristics Series 2. In the publcation, we will introduced UTM to solve challenging problems that even baffled parents and educators.The current blog discuss the first publication which focus on five main topics: Whole number, fraction, decimal, ratio and percentage. We will update in our website once the publication is out.

Thank you for your interest.


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