There are different levels in any educational system.
This goes with the learning of mathematics too.
At various level of learning, you will be presented with different level of complexity.
At the elementary stage, you will be shown maths questions that are real straight forward type.
At intermediate, a bit of mind twisting has to be done to resolve any challenge.
At the highest level, the questions come embedded with hidden clues to be discovered by learners and used to continue with the solving process.
But hidden clues are now becoming the norm among intermediate level due to its benefits to prevent pure memorising of mathematical technique.
A example of this interesting "hidden clue" can be seen in my Math Challenge 23.
There anyone taking up the challenge needs another step in order to "see" through the simple trick of solving the issue.
(Note: The challenge requires only one step to calculate the area of the path).
Multi-discipline is thus needed for merit of helping get the answer.
Knowledge in utilising maths tools and technique are not sufficient these days.
Maths students have to know some basic theory of motional replacement to understand Math Challenge 23.
Hence, to master mathematics, it will be good to read more, especially, topics outside maths.
This enlarge your understanding of real-life cases roped into maths questions.
Maths is interesting in this manner since it involves not only one learning discipline but encompasses more.
Enjoy maths. It widens your perspective of the world.
:-)
Wednesday, 17 March 2010
Sunday, 14 March 2010
Math Challenge 23
*
Albert needed to create a path through a garden of his.
The garden has a size of a rectangle with length of 20m and width of 15m.
He intend to have a path of 3m wide.
His design is shown below.
But he has a problem.
He wanted to know what is the area of this path he is going to lay across the garden.
Can anyone help him calculate that area?
Basic geometry knowledge may helps.
Albert needed to create a path through a garden of his.
The garden has a size of a rectangle with length of 20m and width of 15m.
He intend to have a path of 3m wide.
His design is shown below.
But he has a problem.
He wanted to know what is the area of this path he is going to lay across the garden.
Can anyone help him calculate that area?
Basic geometry knowledge may helps.
Wednesday, 24 February 2010
Math Challenge 22
*
Given the diagram of boxes below, determine, in the fastest possible way, the area of the dark blue region.
Assume the individual boxes to be 1 unit square in area.
Given the diagram of boxes below, determine, in the fastest possible way, the area of the dark blue region.
Assume the individual boxes to be 1 unit square in area.
Give your answer in the comment space, please.
Maths does not involve plain counting.
It involves some form of intelligence to get things going.
:-)
.
Wednesday, 3 February 2010
Artistic Mathematical Lantern
'
Have you wondered what can maths do to art?
Below is a lantern made by a mathematical expression.
With maths, you can be assured of producing wonderful images when you have the appropriate expression.
Do create some for enjoyment.
Maths is interesting.
:-)
Have you wondered what can maths do to art?
Below is a lantern made by a mathematical expression.
With maths, you can be assured of producing wonderful images when you have the appropriate expression.
Do create some for enjoyment.
Maths is interesting.
:-)
Friday, 29 January 2010
Maths Solution Presentation
'
To get good marks for a maths test requires understanding of how teacher marks the paper.
"Why do I not get full marks when I have the correct numerical answers?".
This is a common question at the back of any maths students when they see marks deducted "illogically".
Explanation:
When maths teacher give a maths question, she will like to know how is the answer obtained.
She wants to know whether the "thinking" part of solving the problem existed.
With the objectives in mind, the marking schemes are sometimes created to have marks for every steps involved in getting the answer.
Thus getting the answer without the required steps, even though it is mental, is a no-no.
Let me give an example.
Solve (x + 1)(x - 4) = 0
Solution A:
x = -1
x = 4
Solution B:
x + 1 = 0 ===> x = 1
x - 4 = 0 ===> x = 4
Comparing the two solutions presented above, you will notice clearly that Solution B is a better presented solution with proper steps reflecting the "thinking" process of the students.
Though the student of Solution A has the answer correct, he did not reveal the steps and demonstrate his understanding.
With that lack of presentation, he lost precious marks.
However, do note that not every time, we need to write down every steps.
It depends on which educational level you are in.
For the above example of presentation, the level is that of elementary, where foundational understanding is a necessity.
Upon graduating to high school, less detailed steps are needed. This is because it is assumed that the students had obtained a certain level of mathematical computing skill to that level of studies.
As such, reflection of the internal thinking to show minor details can be ignored and "by-passed" to shorten solution time.
However, the marks will still be given for steps needed at high-school level.
This goes for university level too.
By then the marking scheme will access advance thinking steps rather the minor calculations.
When errors do occurs in the calculations, it will normally be taken as "human" error as opposed to conceptual error.
In summary, do know the necessary solution steps to present during test or important assignment. Do understand the requirement and objectives of the test.
Do know what is being tested.
Writing too little can be detrimental at a lower educational level.
And writing too much can be disastrous at higher level, since you will be left with little time to complete the paper.
Hence doing maths is not simply completing the paper and getting correct answers.
It is a total strategic plan involving a lot of soft skills besides the computational abilities.
Cheers to maths, and
Cheers to it being interesting!
.
To get good marks for a maths test requires understanding of how teacher marks the paper.
"Why do I not get full marks when I have the correct numerical answers?".
This is a common question at the back of any maths students when they see marks deducted "illogically".
Explanation:
When maths teacher give a maths question, she will like to know how is the answer obtained.
She wants to know whether the "thinking" part of solving the problem existed.
With the objectives in mind, the marking schemes are sometimes created to have marks for every steps involved in getting the answer.
Thus getting the answer without the required steps, even though it is mental, is a no-no.
Let me give an example.
Solve (x + 1)(x - 4) = 0
Solution A:
x = -1
x = 4
Solution B:
x + 1 = 0 ===> x = 1
x - 4 = 0 ===> x = 4
Comparing the two solutions presented above, you will notice clearly that Solution B is a better presented solution with proper steps reflecting the "thinking" process of the students.
Though the student of Solution A has the answer correct, he did not reveal the steps and demonstrate his understanding.
With that lack of presentation, he lost precious marks.
However, do note that not every time, we need to write down every steps.
It depends on which educational level you are in.
For the above example of presentation, the level is that of elementary, where foundational understanding is a necessity.
Upon graduating to high school, less detailed steps are needed. This is because it is assumed that the students had obtained a certain level of mathematical computing skill to that level of studies.
As such, reflection of the internal thinking to show minor details can be ignored and "by-passed" to shorten solution time.
However, the marks will still be given for steps needed at high-school level.
This goes for university level too.
By then the marking scheme will access advance thinking steps rather the minor calculations.
When errors do occurs in the calculations, it will normally be taken as "human" error as opposed to conceptual error.
In summary, do know the necessary solution steps to present during test or important assignment. Do understand the requirement and objectives of the test.
Do know what is being tested.
Writing too little can be detrimental at a lower educational level.
And writing too much can be disastrous at higher level, since you will be left with little time to complete the paper.
Hence doing maths is not simply completing the paper and getting correct answers.
It is a total strategic plan involving a lot of soft skills besides the computational abilities.
Cheers to maths, and
Cheers to it being interesting!
.
Friday, 8 January 2010
Proper Way Of Writing Maths Expression
*
Maths expression tells certain message. When it is not written properly, or written in such a way that it causes wrong interpretation, then you will expect marks to be deducted.
Examples:
1) y = cos (A + B)
2) g = x + log K
3) y / x + 2
Let's look at the above examples one by one.
Example 1:
If the brackets are taken out, y = cos A + B.
Does it also mean B + cos A?
Example 2:
If the sequence is swapped, y = log K + x
Does it mean y = log (K + x)?
Example 3:
Is the denominator just x or (x + 2)?
Or is the correct expression 2 + (y /x) ?
From the above 3 maths expressions, you will observe and sense that something will go wrong when you did not write "properly".
This need practice and does need some "maths" sense to go along with the practice.
You need to know the different form of expression and its implications.
Questions like:
- one term or two terms in the desired expression?
- which is the actual denominator?
- will anyone mis-interpret the logging of term?
- If the words or symbols are too small, will they be able to see clearly?
To save time and marks, write with the reader or marker at heart.
Write as though they are reading them.
Think and write like they will be.
Maths is afterall, a language that has to be shared and used to solve certain objectives.
Do write clearly and appropriately.
The practice and skill mastered will do you and everyone one good.
Strive to make less unnecessary mistakes and reduce the chance of your marks being subtracted off through improper writing.
Cheers! ^.^
.
Maths expression tells certain message. When it is not written properly, or written in such a way that it causes wrong interpretation, then you will expect marks to be deducted.
Examples:
1) y = cos (A + B)
2) g = x + log K
3) y / x + 2
Let's look at the above examples one by one.
Example 1:
If the brackets are taken out, y = cos A + B.
Does it also mean B + cos A?
Example 2:
If the sequence is swapped, y = log K + x
Does it mean y = log (K + x)?
Example 3:
Is the denominator just x or (x + 2)?
Or is the correct expression 2 + (y /x) ?
From the above 3 maths expressions, you will observe and sense that something will go wrong when you did not write "properly".
This need practice and does need some "maths" sense to go along with the practice.
You need to know the different form of expression and its implications.
Questions like:
- one term or two terms in the desired expression?
- which is the actual denominator?
- will anyone mis-interpret the logging of term?
- If the words or symbols are too small, will they be able to see clearly?
To save time and marks, write with the reader or marker at heart.
Write as though they are reading them.
Think and write like they will be.
Maths is afterall, a language that has to be shared and used to solve certain objectives.
Do write clearly and appropriately.
The practice and skill mastered will do you and everyone one good.
Strive to make less unnecessary mistakes and reduce the chance of your marks being subtracted off through improper writing.
Cheers! ^.^
.
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