Maths Solution Presentation

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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!


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Proper Way Of Writing Maths Expression

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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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Math Challenge 21

Some math questions are simple and can be answered easily.

See this math challenge 20 and its answer in the comment.

But a twist of the questioning will and can make it more challenging without changing the math expression.

Below is one:

Base on math challenge 20, if all unknowns CANNOT be repeated, what are they?
Again they are integers and below 10.

Enjoy the math thrill answering this.

Merry Christmas!
^.^

Math Challenge 20

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Can anyone come out the answers for A, B, C and D in the below math expression?

A² + B² + 2C² = D²

The rule is that the unknowns are all integers and below 10.

Happy trying, and
don't forget that maths is interesting!

:-)

Percentage | Common Mistake

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Percentage problems can be tricky at times when you are careless.

Let's us look at one maths word problem related to it.

Question:
There are 3 persons, John, Mary and Jane.
John is richer than Mary by 10%, and Mary is richer than Jane by 20%.
Is John richer than Jane by (10 + 20)% = 30% ?

Most students, upon quick thinking, will acknowledge that 30% is the correct answer.

Is it so?

To verify the answer, let us assume that Jane has $1000.
As such, Mary will have (100+20)% of $1000 = 1.2 x $1000 = $1200.
John is then 1.1 x $1200 = $1320 richer than Jane ==> By 32%.

If 30% is correct, we should get 1.3 X $1000 = $1300.

The latter number (dollar) is not the same as the first worked out solution.
Why?

Mistake in understanding what is percentage:
To assume that John is 10% + 20% richer than Jane is incorrect.
This is due to the fact that percentage has to take a common reference for this to be correct.

In the word problem, the percentages of comparison are not to a common reference.
The first one is to Mary, while the next is to Jane.

These made the denominator of the ratio different.
Thus adding the percentage up is a mistake, and an easy one too!

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Square Root | An Exciting Outcome

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Everyone knows what a square root is for and what it does to a number.

But have you tried multiple square rooting ?

What do I mean?

Let's take an example.

Start with a number, say, 3.

i)  Square root this 3.
ii) You will get a number after step one.
iii) Square root this new number again.
iv) Continue the steps above and look closely at the number.

Findings: 
You will notice that the number after multiple square rootings, will give you closer and closer to or approaching the number "1".


Now let's start with another number. This time, let's choose, 0.4

After doing the same procedures, you will again notice that the answer is getting and approaching the number "1"!

Amazing isn't it?

What other wonders can you find from this Square Root maths operator?
Share with me in the comment section.

Maths is interesting.........

:D