Tips on Estimation

In maths, we do come across topics on estimation.

This topics relate to our daily living very closely and is truly practical. 
Example is when we go shopping and starts to count the expenses to be paid. 

But mathematical estimation has one key concern.
To what extent or how accurate does one wish to?

There is no right or wrong to an answer when dealing with estimation. After all it is an ESTIMATED answer.

The basic requirement is thus to get as close to the true answer as possible.

Let's start with one simple example to demonstrate the concept.

Example:
y = 0.501 + square root(3.89)
What is y without using calculator ?

Answer 1:
y = 1 + square root (4)
y = 1 + 2 = 3

Answer 2:
y = 0.5 + square root (4)
y = 0.5 + 2 = 2.5

You can now see that both answers is close to the actual answer of 2.4733.
However, it is the gap or extent of the difference you wish for.

If possible, LOOK carefully at the numbers and give a best estimation closest to ability to compute the answer.

Here, from the above, you will notice the first term of 0.501 decides the outcome.
Estimate this 0.501 to what numeric value?

Think further and you will find that 0.501 to 1 will give you a bigger difference compared to 0.501 to 0.5.

If you can mentally handle 0.5 as the estimated value for computation, go for it since this should be closer to the final outcome.

Thus in conclusion, do look a bit closer to the numbers presented in your problem and simply do a brief calculation of the differences between estimated and raw data. Then you are one step closer to getting a good estimation.

Estimation, finally, boils down to how far you are to the actual answer. Nothing difficult.

Interesting? Any more suggestions?

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Building Up Presentation Skills With Maths

Maths is not about just doing and computing mathematical challenges. It is also not just about planning strategies to solve a problem. It involves more than mentioned.

It includes skill seemingly not related to maths.

What is it then?
It is about presenting the solution and steps in approaching the maths problems.
And presenting them well and in an understandable way.

Example :

3x - 6 = x. Find x.

Solution A:
x = 6 / 2 = 3

Solution B:
3x - x = 6
2x = 6
x = 6 / 2 =3

In your view, which solution has a better presentation?
Which shows the approach better?

My view is Solution B is better. Why?
It showed the thinking that goes on in the learner's mind.

In real life, we need to make clear our thoughts in getting and convincing partners and team-mates to work with us. It is an important skill  to present our ideas to others.

By doing and presenting our maths solution, we are actually aligning ourselves to real working life.
Thus performing good presentation in our maths solving helps.

Agree?

Maths is interesting.

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Fear Over Maths

Maths is one of the crucial and necessary subject we have to learn in school. Everyone has to go through it.

Some like it, while some fear it. Have you wonder why?

Actually this fear is not only towards maths. The underlying reasons applies to anything we do.
It could be literature, Chinese language, dancing, or even driving and riding a bicycle.

What we have to do to reduce maths anxiety is to know why the fear occurs.

One of the issue links to the confidence level. This affects the comfort level. With things we are not comfortable, we tend to avoid. Avoiding make us do less of the subject.

We thus lack practices.

Learning maths involves 2 parts, namely:-
1) Procedural skills, and
2) Conceptual understanding.

Different stages / levels in the learning journey entails different focus of these 2 stages.

To have a better understanding, you may go to this maths site to read more.
It is rather enlightening.

Learning anything needs a plan. (Procedure ==> Conceptual ==> Application)
If fear is the barrier, and causes obtrusion to learning, seek out why.
We grow as a result of this process.

Maths is one target in life that we can use to challenge yourself, besides the tools and techniques picked up to solve mathematical problems.
It involves character development as well, if you border to analyse the learning process.

Finally, to motive any maths learners,

just know that "Maths Is Interesting!".

You will then like maths, and anything you set forth to master.

Cheers!   :-D.

Caution on Mixed Number

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Fractions are a necessary part of maths.
They come in many forms; improper, proper and mixed number.


Though improper and proper forms are direct in its presentation and interpretation, mixed number form may pose a potential mistake for young learners.

Example:
   
Is this 2 + (3/4) or 2 x (3/4) ?

Caution has to be taken to stress it as 2 + (3/4).

Some students have taken it to mean 2 pieces of (3/4) !
Dangerous isn't it.

But rest assure.
If you understand the language of maths and its "grammar", all will be well and interesting.

:-)

Tips On Using Substitution

Maths entails the usage of our brain juice in solving problems. It is a good platform for stretching our imagination and creativity by using simple concepts learned to handle seemingly complex maths questions.

Let's look at a "complex" simultaneous equations maths problem, and its way of solving (suggested).

Question:

  ---- (A)

--- (B)

Solve for y and x.

How do you go about it?

Look scary, right?

But like what I said, looks can be deceiving. Use the brain to go around the issue!

Tips: The structure of the simultaneous equations looks similar to the conventional type.
(Conventional type:-
Ax + By = nn
Cx + Dy = kk      )

So what we have to do can be to simply substitute  by m, and  by h (or any variable name).

What we thus convert to is:
  ---- (A)

 --- (B)

Will this simultaneous equations be more comfortable to solve?

Hence, a simple twist to the former mathematical questions can result in a totally familiar situations where we have solve many a times.

Thus, the technique and usefulness of substitution cannot be under-estimated.

It can be powerful at times to reveal a beautiful mathematical expression for user to resolve.

Maths Is Interesting!

Treasure our brain and our thinking. 

:-)

Zippy Graphical Maths

Trigonometry is a fun topic in maths.

It generates curves more than many other topics.

By combining various trigonometrical functions, you can get interesting patterns on a graph.

Putting these functions on an algebraic expression produces even exciting diagram.

Below is one I created and an array of zips appears.

Enjoy maths.
maths is interesting!

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