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## Let’s Learn Mathematics (Primary Level) — Model Method 4

03/12/2014 17:53 / Leave a comment

Continuation from Let’s Learn Mathematics (Primary Level) — Model Method 3

Here is another example on comparison model to compare two or more items.

Question: 8 similar dictionaries and 12 similar assessment books cost S$196. Each assessment book costs S$2 less than each dictionary. How much does each dictionary cost?

First, draw the model based on the question.

Each assessment book costs S$2 less than each dictionary, thus 8 similar dictionaries cost S$16 more than 12 similar assessment books.

S$2 x 8 = S$16

From the model, we can see that the total cost is 8 units of dictionaries, 12 units of assessment books and S$16. To find the cost of a single unit, we subtract S$16 from the total cost.

S$196 − S$ 16 = S$180

Total units = 8 + 12

= 20 units

S$180 ÷ 20 = S$9

The cost of a single unit is S$9. The question asks for the cost of each dictionary, thus we need to add S$2 to get the final answer.

S$9 + S$2 = S$11

Each dictionary costs S$11.

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Disclaimer: The Mathematics questions are purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

## When Good Memory Doesn’t Help

18/09/2014 10:05 / 2 Comments on When Good Memory Doesn’t Help

I have been emphasizing on the understanding of Mathematics questions umpteenth time. Most of the time, a student is unable to solve the problem because he or she does not understand the Mathematics question.

There is this student who has very good memory but the good memory does not help him in solving Mathematics questions.

Background of the student: When he was in Primary One (7 years old), his Mathematics teacher at school has scolded him a lot of times and almost given up on him. He has developed a phobia for Mathematics since then. Thus far, in Primary Two, he is surviving in Mathematics by “memorizing” Mathematics questions.

Let’s look at the example 1,

Jane had S$ 5. Her father gave her S$ 10 as pocket-money. How much money does she have now?

5 + 10 = 15

Now she has S$ 15.

Example 1 is a common question for lower Primary Mathematics. The keyword is “Her father gave her”, so the operation used is addition. The question is straightforward and can be solved easily.

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Let’s look at example 2,

Jenny had S$ 5. Her mother gave her some amount of money. Now she has S$ 15. How much money did her mother give her?

Both examples look similar, but they are different. After reading the question to the aforementioned student, he insists to use the operation addition to solve the problem because of the phrase “her mother **gave** her”. He told me, his school Mathematics teacher taught him, gave = addition.

Therefore, I spent time explaining the question to him and finally we solved the problem using the operation subtraction.

I can understand the frustration of the school Mathematics teacher when he or she needs to spend time to explain one question to only one student who does not seem to understand. He or she has the whole class to take care of; giving attention to only one student is not an option.

Nonetheless, I hope that school Mathematics teachers do not teach the students, especially younger students, to memorize questions. THIS DOES NOT HELP!

I have upper primary students who face the same problem because of the understanding issue. With the phobia and the memorization, the same problem is repeated in a cycle until they meet a teacher who can patiently explain the questions to them. By then, whether they are willing to accept the “understanding of the question” method is another problem to solve.

For parents, if you find out that your children face problem at school, please communicate with the school teachers in a tactful way. Extra lessons or remedial lessons for your children are meant to help your children. Also, listen to the advice with an open heart. It may be difficult to accept that your children are slow in learning (Who would want his or her child to be labelled as stupid?), but cooperation with the school teachers will help the children more.

Furthermore, parents can also help the children at home by doing revision together with the children. No matter how busy is your schedule, I believe there is nothing more important than the children. When the children grow old, it is more difficult to mend the problem.

Even if there is no feedback from the school teachers, parents may take the initiative to ask the school teachers on the progress of the children and how they are coping at school. Some children might be too shy to ask questions even though they do not understand. This will create bigger problem in future.

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Disclaimer:

1. The Mathematics questions are purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

2. The student is a case study for parents, teachers and tutors alike to understand why your children or students have phobia in Mathematics. Hopefully we can create a joyful environment for children to learn Mathematics.

## Let’s Learn Mathematics (Primary Level) — Model Method 3

02/05/2014 11:29 / Leave a comment

Continuation from Let’s Learn Mathematics (Primary Level) — Model Method 2

2. Comparison model

Comparison model is used to compare two or more items.

Example (a): Jenny has 6 dresses and 2 pairs of pants. How many more dresses than pants does she have?

6 – 2 = 4

She has 4 more dresses than pants.

Example (b): A pair of pants costs S$35. A dress costs S$ 10 more than a pair of pants. If Jenny buys 3 dresses and 2 pair of pants, how much does she need to pay?

The cost of a dress = 35 + 10

= 45

Total cost = (3 x 45) + (2 x 35)

= 135 + 70

= 205

She needs to pay S$ 205.

To be continued in Let’s Learn Mathematics (Primary Level) — Model Method 4.

Notes:

1. If you cannot draw nicely, cannot draw to scale, etc, no need to worry, this is Mathematics, not arts. Remember, it is the understanding of the questions that is the most important.

2. There are different types of Mathematics questions but there is only one model method. Do more Mathematics questions to practise on the model method.

3. Be flexible about the models, you draw the model according to the question, not to what you remember from previous question(s).

Disclaimer: The Mathematics questions are purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

## Let’s Learn Mathematics (Primary Level) — Model Method 2

29/04/2014 11:35 / Leave a comment

Now we know that understanding of Mathematics questions is more important than the tools or methods, let’s look at different models that we can draw to help us in solving Mathematics questions.

1. Taking the example from Let’s Learn Mathematics (Primary Level) — Model Method 1, the model is simple yet powerful. It can be used to find the total (addition) or the difference (subtraction) of the same item.

Example (a): Jane had S$ 5. Her father gave her S$ 10 as pocket-money. How much money does she have now?

5 + 10 = 15

Now she has S$ 15.

Example (b): Jenny has 10 stamps, Kenny has 8 stamps and Lenny has 15 stamps. How many stamps do they have altogether?

10 + 8 + 15 = 33

They have 33 stamps altogether.

Example (c): Jenny had 12 erasers. She gave 2 erasers to Lenny. How many erasers does she have now?

12 – 2 = 10

She has 10 erasers now.

To be continued in Let’s Learn Mathematics (Primary Level) — Model Method 3.

Disclaimer: The Mathematics questions are purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

## Let’s Learn Mathematics (Primary Level) — Model Method 1

11/04/2014 11:49 / 1 Comment on Let’s Learn Mathematics (Primary Level) — Model Method 1

Do you have a model ruler?

This is the question that my students ask me when they are solving Mathematics questions that need to draw model.

When the model method was first introduced, many students and parents face problems on how to use the method to answer the questions. Along the years, students and parents are more acceptive to the method. Somebody even came out with a model ruler and gave names to different models drawn for different types of questions. For example, you draw a comparison model to solve questions that ask you to compare.

For me, this is bizarre. As long as you understand the question, you do not need a model ruler or a name for your model to solve the question. There are two similar questions in this post. I would like to show how the students may confuse themselves if they do not understand the questions.

Q1: There are a total of 110 participants in a seminar and 60 of them are women. How many of the participants are men?

The model for Q1 is as below:

To find the number of male participants, the operation used is subtraction.

110 – 60 = 50

There are 50 men.

Q2: There are 50 men and 60 women in a seminar. How many participants are there altogether?

The model of Q2 is as below:

To find the number of total participants, the operation used is addition.

60 + 50 = 110

There are 110 participants altogether.

From the above two questions, the same model is used, but with a slight difference. We need to understand the question in order to put the numbers correctly and subsequently solve the question. As you can see, the operation used in Q1 and Q2 is different too.

If we do not understand the question, we do not even know which operation to use. Teachers must always remind the students to understand the question rather than memorize a certain type of model. If you can draw a model, but do not understand the question, it is pointless. The main aim in Mathematics is to find the answer, if you do not understand the question, how are you going to solve the question correctly?

I hope students, teachers and parents put the focus at the right place. The focus is the understanding of the question, not the tools or method used.

To be continued in Let’s Learn Mathematics (Primary Level) — Model Method 2.

## Primary Mathematics Notes

15/07/2013 11:56 / Leave a comment

Some parents have been complaining about Primary Mathematics. They say nowadays Primary Mathematics is not “pure” Mathematics anymore. They say that the Mathematics questions are more like playing with word games, if you do not understand the questions, you cannot solve the questions. Nonetheless, we can still solve the “word games” and score high in Mathematics! In addition, the terms are universal, you can keep this note for Secondary Mathematics too.

Caution: Though the wordings used in this post are commonly found in the Mathematics questions, each question is unique and may vary. The most important thing is to read and understand the questions. Treat each question on a case-by-case basis. If you face any problem on Mathematics questions, please feel free to contact me at wendy@joyfulyue.com

Below are some of the common words used in Primary Mathematics questions:

1. as … as = same

Jenny is as tall as Kenny. That means both Jenny and Kenny have the same height.

Variation version:

(a) Jenny has twice as many candies as Kenny. That means if Jenny has 6 candies, Kenny has only 3 candies. In algebra, Jenny’s candies = 2 x Kenny’s candies.

(b) When x is doubled, find y. That means when x = 2x.

2. -er than, the difference of => use subtraction (-)

Kenny has $50 more than Jenny. That means the difference of the amount of money between Kenny and Jenny is $50, most questions can be solved using subtraction.

Kenny is taller than Jenny by 2 cm. That means the difference of the height between Kenny and Jenny is 2 cm and Kenny is taller.

3. altogether, the sum of => use addition (+)

How many flowers are there altogether? The question is asking you to add all the flowers mentioned in the question.

What is the sum of money? The question is asking you to add all the money value mentioned in the question.

4. Mathematics language

(a) Subtract 5 from 9 => 9 – 5

(b) A bag cost $5.00, how much does it cost if Jenny buys 3 bags? => $5 x 3

Below are the concepts that must be understood by Primary students so that they can tackle more difficult questions:

1. Percentage

2. Ratio

3. Average

5. Algebra (This concept will be taught in more details in Secondary school, thus the understanding of the concept is of utmost importance)

In a nutshell, **understanding **the concepts is the most important thing to learn in Mathematics. Once you have understood, solving more questions will reinforce the understanding and A* is on the way!