`
Every thing falls back to basic.
If the fundamentals are weak, any maths learners will have a hard time moving forward in their maths learning journey.
Let me quote an example.
How do we change 4.75 to fraction.
We can use 475 / 100 and reduce it through long division. This will give 4 and 3/4.
However, if we know that 4.75 is actually consisting of 4 add to 0.75, the conversion will be simpler.
4 and 0.75 means 4 + (3/4) which leads directly to 4 whole and 3/4. Same as answer of above.
(NOTE: 0.75 is a quarter which equates to 3/4).
Simple isn't it?
Maths is interesting.
:-)
Monday, 22 November 2010
Sunday, 3 October 2010
Pointers in Teaching, Learning Speed
.
At elementary level in maths education, speed is always a challenging topic for learners.
It caught my attention and I started wondering why?
Many mistakes can be made when dealing with these types of questions.
After studying the various mistakes made by learners, I came to a few conclusion that I like to share here.
How to avoid confusion in doing Speed questions in maths:-
1) Speed involves two parameters, namely, distance and time.
This is the key issue. Dealing with one parameter is already a challenge, and dealng with two is always a "headache".
The concept, has thus to be clearly addressed upon, before the ratio of distance and time leading to speed can be fully understood.
What is distance?
What is time?
These 2 items are variable in nature. They change in value.
They causes confusion when lumped together!
Examples of daily activities will help in this case.
Quote cases like running in a race, where the champion came back in the shortest time covering the same distance as all others.
Get the concept of distance versus time into them.
Also FAST and SLOW relation to speed.
2) Error in units:-
Break up the tasks of calculating km, m or cm and sec, hours, minutes separately.
In other words,deal with one item at a time.
Use basic unit if possible to reduce chances of making costly errors.
The learners have to handle the logical part of the question, and also the mechanical part of unit manipulation in speed problems.
Tell them to find one thing at a time, and the need for doing that. Be patience is the message.
3) Draw out a pictorial image of the question.
This method will help some kids to visualise the real issue.
By having drawn the length for distance to be covered (or covered), they will have a better idea of what distance is about in the maths question. They will not have to "keep" this disatnce in their mind together with the problematic "time" condition.
Use the seeing method helps them clear any doubts and can also reduce mistakes in interpreting the question.
There will definitely be more pointers to be added to my three above.
But with these 3 basic issues settled, most of the queries about speed and its maths problems should be clearer.
If you have any other pointers, you may share in the comment space.
Cheers :-)
Maths is interesting, I suppose you cannot agree more.
.
At elementary level in maths education, speed is always a challenging topic for learners.
It caught my attention and I started wondering why?
Many mistakes can be made when dealing with these types of questions.
After studying the various mistakes made by learners, I came to a few conclusion that I like to share here.
How to avoid confusion in doing Speed questions in maths:-
1) Speed involves two parameters, namely, distance and time.
This is the key issue. Dealing with one parameter is already a challenge, and dealng with two is always a "headache".
The concept, has thus to be clearly addressed upon, before the ratio of distance and time leading to speed can be fully understood.
What is distance?
What is time?
These 2 items are variable in nature. They change in value.
They causes confusion when lumped together!
Examples of daily activities will help in this case.
Quote cases like running in a race, where the champion came back in the shortest time covering the same distance as all others.
Get the concept of distance versus time into them.
Also FAST and SLOW relation to speed.
2) Error in units:-
Break up the tasks of calculating km, m or cm and sec, hours, minutes separately.
In other words,deal with one item at a time.
Use basic unit if possible to reduce chances of making costly errors.
The learners have to handle the logical part of the question, and also the mechanical part of unit manipulation in speed problems.
Tell them to find one thing at a time, and the need for doing that. Be patience is the message.
3) Draw out a pictorial image of the question.
This method will help some kids to visualise the real issue.
By having drawn the length for distance to be covered (or covered), they will have a better idea of what distance is about in the maths question. They will not have to "keep" this disatnce in their mind together with the problematic "time" condition.
Use the seeing method helps them clear any doubts and can also reduce mistakes in interpreting the question.
There will definitely be more pointers to be added to my three above.
But with these 3 basic issues settled, most of the queries about speed and its maths problems should be clearer.
If you have any other pointers, you may share in the comment space.
Cheers :-)
Maths is interesting, I suppose you cannot agree more.
.
Sunday, 13 June 2010
Simple Logarithm Tip
.
Maths expression may at times look challenging, but a bit of a thought may make it otherwise.
Logarithm is always an exciting topics to new learners.
With the "log" coming into the maths expression, one will be confused.
Definitely!
But do rest assure, as the tip below shows.
Maths Tip
eln y = y
Proving this:
"Natural log" both sides will give ln eln y = ln y
Applying the law that ln an = n ln a, and that ln e = 1, you will notice that the above mathematical expressions are true and equal.
NOTE:
This tip applies to "log" too.
10log y = y
Hope this helps.
:-)
Maths expression may at times look challenging, but a bit of a thought may make it otherwise.
Logarithm is always an exciting topics to new learners.
With the "log" coming into the maths expression, one will be confused.
Definitely!
But do rest assure, as the tip below shows.
Maths Tip
eln y = y
Proving this:
"Natural log" both sides will give ln eln y = ln y
Applying the law that ln an = n ln a, and that ln e = 1, you will notice that the above mathematical expressions are true and equal.
NOTE:
This tip applies to "log" too.
10log y = y
Hope this helps.
:-)
Wednesday, 2 June 2010
Model versus Variable Technique
'
In using Model method of solving maths question, we are using visual blocks to scope our thinking. This is followed by analysis through the models.
Models become a link to our thinking process.
The demerit is when we did not create the Model properly, or miss out some details that cause the model to be represented wrongly.
The merit is that it can be simple and straight forward when drawn properly. It reflects outright the relationship between many unknowns.
Less workings is thus needed, as visual que sets in.
For algebraic variable technique, the unknowns are pre-defined and booked as "letters". A space, mentally, has been reserved for the answer.
The working is just simply to accept that the answer is already there but only not numerical. Following through the working steps will ultimately reveal the letter of its numerical data which is what we want.
Variable as letter is good in the sense that we need less analysis, but just mechanically following the rules and steps leading to the final step, of course with some logic and mathematical strategy.
Each has its own advantages and weakness. It is up to us to make use of them in the correct way.
Experience is the only way to overcome the proper selection of which technique.
Thus practice to gain experience in maths is one good way to master maths.
Skiving is a no-no.
Through practice, you will sooner or later find that maths is interesting.
:-)
In using Model method of solving maths question, we are using visual blocks to scope our thinking. This is followed by analysis through the models.
Models become a link to our thinking process.
The demerit is when we did not create the Model properly, or miss out some details that cause the model to be represented wrongly.
The merit is that it can be simple and straight forward when drawn properly. It reflects outright the relationship between many unknowns.
Less workings is thus needed, as visual que sets in.
For algebraic variable technique, the unknowns are pre-defined and booked as "letters". A space, mentally, has been reserved for the answer.
The working is just simply to accept that the answer is already there but only not numerical. Following through the working steps will ultimately reveal the letter of its numerical data which is what we want.
Variable as letter is good in the sense that we need less analysis, but just mechanically following the rules and steps leading to the final step, of course with some logic and mathematical strategy.
Each has its own advantages and weakness. It is up to us to make use of them in the correct way.
Experience is the only way to overcome the proper selection of which technique.
Thus practice to gain experience in maths is one good way to master maths.
Skiving is a no-no.
Through practice, you will sooner or later find that maths is interesting.
:-)
Thursday, 27 May 2010
Purpose of Variables in Algebra
'
Unknowns are literally unknowns.
In maths, these unknowns are a cuause formaths anxiety.
When you are in unfamiliar territory, you will naturally be uncomfortable and unease.
This is the same feelingwhen dealing with unknowns in maths.
Algebra came to the rescue for this problems.
Here, you will find unknowns named as "variables".
They served as "parking lots" for the final answers or unknowns.
In this algebra, you replace the variables for final numbers and work with them as though you already know them.
You simply go through the motion of solving the question with any given condition and numbers / data.
Upon finally reaching the last step, the numerical answers for the problem will be revealed.
This is the power of the variables in algebra.
Just simply work along, and not be fearful of the unknowns.
The steps will align you to the final answers.
Cheers!
Maths is interesting!
.
Unknowns are literally unknowns.
In maths, these unknowns are a cuause formaths anxiety.
When you are in unfamiliar territory, you will naturally be uncomfortable and unease.
This is the same feelingwhen dealing with unknowns in maths.
Algebra came to the rescue for this problems.
Here, you will find unknowns named as "variables".
They served as "parking lots" for the final answers or unknowns.
In this algebra, you replace the variables for final numbers and work with them as though you already know them.
You simply go through the motion of solving the question with any given condition and numbers / data.
Upon finally reaching the last step, the numerical answers for the problem will be revealed.
This is the power of the variables in algebra.
Just simply work along, and not be fearful of the unknowns.
The steps will align you to the final answers.
Cheers!
Maths is interesting!
.
Saturday, 24 April 2010
A Mathematical Waterfall
'
Mathematics equation can be fun.
It is not only used as a problem-solving tool, it can be used to create visual image simulating scene.
By trying a few equations, anyone with patience and basic maths knowledge can do it.
Simply create an expression or equation in a graph and tweet it to form any image.
Here you will see an image formed up to look like a waterfall.
Enjoy yourself.
This was done with both logarithm and trigonometry functions.
:-)
Mathematics equation can be fun.
It is not only used as a problem-solving tool, it can be used to create visual image simulating scene.
By trying a few equations, anyone with patience and basic maths knowledge can do it.
Simply create an expression or equation in a graph and tweet it to form any image.
Here you will see an image formed up to look like a waterfall.
Enjoy yourself.
This was done with both logarithm and trigonometry functions.
:-)
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