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# Tag Archives: Mathematics

## Counting Speed 2

Q: Jeff drives at the speed of 50 km/h from destination A to B. Jackson, who departs 30 minutes after Jeff, drives at the speed of 70 km/h from destination A to B. Both Jeff and Jackson reach destination B at the same time. What is the distance between destination A and destination B?

A: At first glance, the students may question whether there is an answer. Although the speed and the time are given, the time is not the time taken to travel from destination A to destination B.

No worry. The distance travelled is the same for Jeff and Jackson and we can use this information to solve the question. Please note that the unit for time is minute, converting to hour, it is 0.5 hour.

Let’s take t = time take for Jeff to reach destination B.

The distance travelled for Jeff = speed x time

= 50 x t

The distance travelled for Jackson = speed x time

= 70 x (t – 0.5)

The distance travelled is the same,

50t = 70 (t – 0.5)

Solving the above equation,

50t = 70t – 35

t = 35 ÷ 20

= 1.75 h

From the speed triangle, distance (travelled by Jeff) = speed x time

Distance = 50 x 1.75

= 87.5 km

Checking the answer

The distance from destination A to destination B is the same. Thus, the distance travelled by Jeff and Jackson should be the same.

Distance (travelled by Jackson) = speed x time,

Distance = 70 x 1.25

= 87.5 km

Note:

1. Look for all the necessary information in the question and use all of them.

2. Speed is a simple concept. Thus, questions about speed are normally combined with other concepts, for example, circles. Other than the speed formula and the unit conversion, the students must be prepared to use other concepts to solve speed questions.

## Counting Speed 1

After the students learn time and length, the next concept they learn in Higher Primary school is speed. The length is equivalent to the distance travelled.

The formula is

Speed = Distance ÷ Time

To help the students to remember the formula, a speed triangle is taught, as below.

Taking the example from Counting Length, if I cycle to school at the speed of 15 km/h, how much time do I need to reach school?

From the speed triangle, time = distance ÷ speed

From the figure below, the distance between my house and the school is 180 m.

Please take note that the unit for speed is km/h and the unit for distance is m. Thus, the first step is to convert the two different units to the same unit.

1 km = 1000 m

15 km = 15 000 m

With speed = 15000 m/h and distance = 180 m,

Time = (180 ÷ 15000) h

= 0.012 h

= 0.72 min

= 43.2 sec

Speed is a simple concept, once the students remember the speed triangle (and the speed formula) and familiar with unit conversion, the answer is somewhere near 🙂

In our daily lives, we travel by cars and public transport. Use the speed concept in daily life and maybe the student can manage time better too. Enjoy your learning experience!

Note:

1. In Secondary school, the students will learn the term “velocity” in Physics, which is speed with a direction.

2. (a) Take note of the unit used. For distance, common units are km and m. For time, common units are hour, minute and second. The units used for distance and time determine the unit for speed.

(b) Be fluent with unit conversion for distance and time.

## Creativity for Sales

Singapore is well-known for its education system, especially for Mathematics and Science. Nonetheless, you may have read about critics on lack of creativity at the same time.

During schooling, I memorized English words, Mathematics formula, etc. I thought that was normal. As a student, you do whatever the teacher tells you to do. The teachers nowadays have more tools to help them in teaching, but there is a troubling issue behind. Let’s look at three different aspects below:

1. Composition （作文）

In English language, we have a term called “creative writing”. But for Chinese language, my students have feedback to me that their teachers (from different schools) have a favour towards “happy ending”. If you have a sad ending for your composition, too bad, no matter how well you write, you will not score high.

I always encourage my students to let their imagination runs wild. The students nowadays are exposed to worldwide news and information, why limit their imagination to only “good things”? Writing a composition with a happy ending may help to cultivate an optimistic environment. Nonetheless, when the students grow up, they will find out that this world is realistic, not everything will end happily.

2. Oral （口试）

For Primary school oral, the student is given a picture and he / she needs to say what is in the picture, where is the place and describe the people inside the picture. There is a template, it is good to help the weaker students to memorize and excel in oral. But the whole Singapore is using the same template! Okay, saying the whole Singapore is exaggerating, but different students from different schools have shown me the same template.

If the limitation in composition writing is to cultivate an optimistic environment, what about oral? What type of adults are you looking for? A batch of like-minded students?

3. Mathematics （数学）

I love Mathematics because it is fun. But many students face a problem: The school Mathematics teacher teaches you method A and all other methods are not allowed. This may confuse the students when other methods are introduced to them. Because of limitation on the use of certain method, the “stubborn” student may face problem when they see a different type of question.

To solve a Mathematics problem, the most important part is to understand the question, not to draw a beautiful model. Maybe the emphasis on the model method has been misunderstood by students. Two of my students from different schools, again, can draw beautiful model according to what the teachers have taught. The problem is, they do not understand the question and ask me how to solve. What is the point of drawing a model when you cannot solve the problem?

Furthermore, a different method is helpful in checking the answer. I believe the method introduced at the school is suitable for most students from proven record of the best Mathematics teaching. The question to ask is, how about the minor group who cannot grasp the idea? Shouldn’t the teacher allow some flexibility?

The post is written based on my experience with my students, not from a single student, but from different students from different schools. I am not sure how many people out there realize the underlying problem. I will follow the school template, while at the same time, encourage my students to have some creativity whenever it is possible.