'
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!
.
Showing posts with label maths symbols. Show all posts
Showing posts with label maths symbols. Show all posts
Thursday, 27 May 2010
Saturday, 18 July 2009
Maths Is Just Another Language
'
"I don't understand maths!"
Does this sound familiar?
This statement is not only from young learners, but from adults too.
What actually happened?
Maths is interestingly unique. This is so because it represents a different way of presenting messages.
Maths is a "short form" of written langauge.
It is like the short-hand symbols that many people use to note down minutes of meeting.
What is 1 + 3 = 4?
In the common English language, it simply means "one added to three equals four".
Nothing different.
However, visually, the maths equation is encoded with symbols.
What is this "+" and "="?
If you do not understand the meaning and usage of these two symbols, then you are lost.
Thetefore, learning and understanding maths is knowing the unique symbols presenting the "message".
How about 3y = 24. What is "y"?
The question is finding "y" given the relationship above.
The equation in English means "When we multiply "y" by 3, it gives 24".
The solution, thus, it English, is: If I divide this 24 by 3, I will get the answer that is 24/3 = 8.
In maths concept: 3y = 24 ===> y = 24/3 = 8.
It is the interpretation of the maths symbol and its communication with the learners that is key to doing maths.
It is not difficult if you understand the language of maths.
Maths is interesting!
:D
"I don't understand maths!"
Does this sound familiar?
This statement is not only from young learners, but from adults too.
What actually happened?
Maths is interestingly unique. This is so because it represents a different way of presenting messages.
Maths is a "short form" of written langauge.
It is like the short-hand symbols that many people use to note down minutes of meeting.
What is 1 + 3 = 4?
In the common English language, it simply means "one added to three equals four".
Nothing different.
However, visually, the maths equation is encoded with symbols.
What is this "+" and "="?
If you do not understand the meaning and usage of these two symbols, then you are lost.
Thetefore, learning and understanding maths is knowing the unique symbols presenting the "message".
How about 3y = 24. What is "y"?
The question is finding "y" given the relationship above.
The equation in English means "When we multiply "y" by 3, it gives 24".
The solution, thus, it English, is: If I divide this 24 by 3, I will get the answer that is 24/3 = 8.
In maths concept: 3y = 24 ===> y = 24/3 = 8.
It is the interpretation of the maths symbol and its communication with the learners that is key to doing maths.
It is not difficult if you understand the language of maths.
Maths is interesting!
:D
Monday, 8 June 2009
Meaning of Minus
'
To the ignorant, a "-" or minus is a strange symbol.
Is this more so when it is expressed as "-6", "-5 km", "-$3", etc.
What is then the true meaning of this "minus" sign?
Answer: It indicates a reversal of action of intention.
Maths is a useful tool to help explain this concept.
Example:
When a car moves forward by 5 km, it moves +5 km. ( By default, no sign means positive)
When it reverses by 5 km, it moves -5 km. The direction of movement reverses!
When a person gain $3, he has +$3 in his pocket.
When he loses $3, he has -$3.
From the 2 examples above, you can see that the "minus" sign is a reversal to the default.
If you "reverse" and then "reverse" again, you find yourself in the positive direction.
(-1) x (-1) = + 1
If you reverse 5 times, 5 x (-1) = -5 . You are facing the reverse to the default starting direction.
Now take note of this coming information.
If you reverse the car by 5m and another 5m, you reversed in total (-5) + (-5) = -10m.
If you reverse the car by 5m, followed by changing the direction and moving by another 5m, you moved (-5) + (+5) = 0m.
(Reverse direction followed by forward direction).
Does all these "reversing" cause a daze in you?
Do not despair.
Message is "When there is a reversal, put a minus in front of the number". Simply that!
I owe you $5 ==> -$5.
I gained $5 but lost $3 ==> + $5 + (- $3) = $2 (Action followed by another using "+").
Understand?
Hope this post on minus sign reduces your anxiety about this little maths symbol.
Cheers :-)
.
To the ignorant, a "-" or minus is a strange symbol.
Is this more so when it is expressed as "-6", "-5 km", "-$3", etc.
What is then the true meaning of this "minus" sign?
Answer: It indicates a reversal of action of intention.
Maths is a useful tool to help explain this concept.
Example:
When a car moves forward by 5 km, it moves +5 km. ( By default, no sign means positive)
When it reverses by 5 km, it moves -5 km. The direction of movement reverses!
When a person gain $3, he has +$3 in his pocket.
When he loses $3, he has -$3.
From the 2 examples above, you can see that the "minus" sign is a reversal to the default.
If you "reverse" and then "reverse" again, you find yourself in the positive direction.
(-1) x (-1) = + 1
If you reverse 5 times, 5 x (-1) = -5 . You are facing the reverse to the default starting direction.
Now take note of this coming information.
If you reverse the car by 5m and another 5m, you reversed in total (-5) + (-5) = -10m.
If you reverse the car by 5m, followed by changing the direction and moving by another 5m, you moved (-5) + (+5) = 0m.
(Reverse direction followed by forward direction).
Does all these "reversing" cause a daze in you?
Do not despair.
Message is "When there is a reversal, put a minus in front of the number". Simply that!
I owe you $5 ==> -$5.
I gained $5 but lost $3 ==> + $5 + (- $3) = $2 (Action followed by another using "+").
Understand?
Hope this post on minus sign reduces your anxiety about this little maths symbol.
Cheers :-)
.
Thursday, 2 April 2009
Algebra | Moving Forward in Usage
'
In the study of algebra, symbolic representation of number or unknown is key concept to solving mathematical equations.
The letter "x" or "y" are examples.
Other symbols can also be used as long as the usages are understood.
In the expression, x + 0.5 = 3.
This meant that the unknown "x" added to 0.5 will give a total of 3.
"x" here is nothing other than an unknown item to be solved.
It should be a number that relates to that maths equation. Nothing more, nothing less.
Another example:
x2 + 2x - 1 = 0
This "x" again is an unknown number to be found out.
Thus this algebraic expression and its "x" are just mathematical item representing a relationship.
Many students learning maths, when faced with this "x" always look puzzled.
With this post, the queries of this "x" (or "y", etc) should be cleared.
With this knowledge of the symbolic representation of unknowns, other areas of maths can be explained easily.
Topics like the trigonometry and logarithm will be expanded from this symbolic concept.
Cos A and log B will thus be finalised to a number, with this "A" and "B" yet to be solved.
Equation like
cos A + 2 = 2.4
will then be nothing more than to relate this unknown "A" to the expression.
It is also an easier way to explain and express this relationship between the unknown (A) and the other number (2 and 2.4).
Similarly,
log x + log 2 = 3
means that "x" is related to the 2 and 3 according to the given equation.
From the above few examples, the question now of what really is this "letter" doing forms meaning, right?
Maths starts off easy when this concept is clear.
Alot of the maths study involves this simple "trick" of presenting unknowns.
You notice how clever past mathematicians were now?
The use of simple symbol to pass off as number to carry on with maths solving.
Without this algebraic presentation, maths will not be as interesting as now.
Alot of guessing will have to be done and .... guess what? Maths will be HELL then.
Enjoy this symbolic concept in maths.
Enjoy your maths.
:-) (-:
In the study of algebra, symbolic representation of number or unknown is key concept to solving mathematical equations.
The letter "x" or "y" are examples.
Other symbols can also be used as long as the usages are understood.
In the expression, x + 0.5 = 3.
This meant that the unknown "x" added to 0.5 will give a total of 3.
"x" here is nothing other than an unknown item to be solved.
It should be a number that relates to that maths equation. Nothing more, nothing less.
Another example:
x2 + 2x - 1 = 0
This "x" again is an unknown number to be found out.
Thus this algebraic expression and its "x" are just mathematical item representing a relationship.
Many students learning maths, when faced with this "x" always look puzzled.
With this post, the queries of this "x" (or "y", etc) should be cleared.
With this knowledge of the symbolic representation of unknowns, other areas of maths can be explained easily.
Topics like the trigonometry and logarithm will be expanded from this symbolic concept.
Cos A and log B will thus be finalised to a number, with this "A" and "B" yet to be solved.
Equation like
cos A + 2 = 2.4
will then be nothing more than to relate this unknown "A" to the expression.
It is also an easier way to explain and express this relationship between the unknown (A) and the other number (2 and 2.4).
Similarly,
log x + log 2 = 3
means that "x" is related to the 2 and 3 according to the given equation.
From the above few examples, the question now of what really is this "letter" doing forms meaning, right?
Maths starts off easy when this concept is clear.
Alot of the maths study involves this simple "trick" of presenting unknowns.
You notice how clever past mathematicians were now?
The use of simple symbol to pass off as number to carry on with maths solving.
Without this algebraic presentation, maths will not be as interesting as now.
Alot of guessing will have to be done and .... guess what? Maths will be HELL then.
Enjoy this symbolic concept in maths.
Enjoy your maths.
:-) (-:
Thursday, 14 August 2008
Math Terms, Math Symbols, Do You Know Them ?
Math has many terms, symbols and signs. They formed up to represent certain meaning. They may be equations, problems, formula, functions, relation between input and output, and many more.
Test your understanding of the below math items, or explanation for their usage.
Ready.... here we go ...
Improper fractions, Composite numbers, Integers, Whole numbers,
Factors, Divisors, Dividend, Multiplicand, Multiplier,
Power, Base, Indices, Variables, Inequality, Simultaneous equations,
Gradient, Constant, Integration, Permutation, Factorial,
Venn Diagram, Subset, Remainder, Modulus, Argument, Imaginary term,
Limits, %, ( ), Differentiation, Ð , ¥, ¹, Partial fraction,
Test your understanding of the below math items, or explanation for their usage.
Ready.... here we go ...
Improper fractions, Composite numbers, Integers, Whole numbers,
Factors, Divisors, Dividend, Multiplicand, Multiplier,
Power, Base, Indices, Variables, Inequality, Simultaneous equations,
Gradient, Constant, Integration, Permutation, Factorial,
Venn Diagram, Subset, Remainder, Modulus, Argument, Imaginary term,
Limits, %, ( ), Differentiation, Ð , ¥, ¹, Partial fraction,
µ, Conjugate, Polynomial, D, º, Roots, Mode, Standard Deviation,
Median, Proper fraction, Irrational number, Phase,
ò, Derivative, Quadratic Formula, Denominator, !
Well, how's the going?
Are you able to explain all the terms and symbols of the above ?
Do not despair if you are not able to know all the math items.
What is important is to know what you missed out and start from there. This is LEARNING! Nothing abnormal.
For those who are able to tell all the usage and meaning of the math items, WELL DONE! Keep it up!
:)
Sunday, 10 August 2008
Simple Trick To Encourage Maths Practice
In maths teaching, worksheets are a necessary tools to enable students practice and apply their newly found knowledge. It serves to reflect the underlying level of understanding to both the teachers and learners. It shows whether the teaching is effective and whether the topics taught has been learned correctly.
In maths, symbols, variables, equations and expressions are aplenty. They tells many "stories". It is through these that ideas get across.
So what happens when they are not properly written?
What happens when even maths questions are poorly written?
Will the students be motivated to practice on them?
For good maths teaching, questions on the worksheets can preferably be written with a font size suitable for the topics. If there are many superscripts involved, it will be good to have bigger font size.
Example is Indices, where the placement of the "power" number is at a higher level. If this "power" number is too small, what happen when the students have to strain their eyes to encode this number?
Compare 2x with 2x. Which has a better chance to motivate or at least make maths practice pleasant?
If original maths worksheets is already small in font size, we can make a zoom-up copy of it and hand to the students. The students will be delighted!
This is an indirect way of clearing obstacles to the learning journey. A small and simple step mentioned above can set a positive direction to anyone learning maths.
Focus on the basic essential of teaching, and all else can start with a happy footing.
:-)
.
In maths, symbols, variables, equations and expressions are aplenty. They tells many "stories". It is through these that ideas get across.
So what happens when they are not properly written?
What happens when even maths questions are poorly written?
Will the students be motivated to practice on them?
For good maths teaching, questions on the worksheets can preferably be written with a font size suitable for the topics. If there are many superscripts involved, it will be good to have bigger font size.
Example is Indices, where the placement of the "power" number is at a higher level. If this "power" number is too small, what happen when the students have to strain their eyes to encode this number?
Compare 2x with 2x. Which has a better chance to motivate or at least make maths practice pleasant?
If original maths worksheets is already small in font size, we can make a zoom-up copy of it and hand to the students. The students will be delighted!
This is an indirect way of clearing obstacles to the learning journey. A small and simple step mentioned above can set a positive direction to anyone learning maths.
Focus on the basic essential of teaching, and all else can start with a happy footing.
:-)
.
Saturday, 19 July 2008
Maths - How students perceive it
What is it that makes mathematics difficult to understand?
The fact may be due to the many symbols used to represent the maths operations and expression or equations.
An example is the operator "x". This tells the student it represents the operation "multiply". If the student does not understand the function of this symbol or, worst, does not know this symbol, how can the student be expected to do the multiplication?
To the students, the symbols are basically graphical in nature. They may perceive them to be "static", or, for the mathematically-inclined, "alive".
Therefore for students to understand maths, they have first to understand the way maths is being presented.
Symbols like "log X", "tan P" and "2 - i6" are some examples of more complex presentations.
Students must understand the true meaning of this way of presentation before they can reduce the barrier for actual mathematical calculation / operation.
The fact may be due to the many symbols used to represent the maths operations and expression or equations.
An example is the operator "x". This tells the student it represents the operation "multiply". If the student does not understand the function of this symbol or, worst, does not know this symbol, how can the student be expected to do the multiplication?
To the students, the symbols are basically graphical in nature. They may perceive them to be "static", or, for the mathematically-inclined, "alive".
Therefore for students to understand maths, they have first to understand the way maths is being presented.
Symbols like "log X", "tan P" and "2 - i6" are some examples of more complex presentations.
Students must understand the true meaning of this way of presentation before they can reduce the barrier for actual mathematical calculation / operation.
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