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#1 2005-10-12 23:31:32

austin81
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Basic Algebra for Form1 students in secondary schl

How can Basic  Algebra be  introduced successful to year one students in secondary schools?
Can one start with
3bannanas+4bannanas=7bannanas
3pears+4pears=7pears
In general,3a+4a=7a?

 

#2 2005-10-13 07:46:57

MathsIsFun
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Re: Basic Algebra for Form1 students in secondary schl

Hey, Members, how did you learn Algebra? What worked best?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#3 2005-10-13 08:34:21

Zach
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Re: Basic Algebra for Form1 students in secondary schl

By going to my maths lessons.

Plus, I have a very useful ability to understand things quickly.

Last edited by Zach (2005-10-13 08:34:43)


Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.
 

#4 2005-10-14 04:08:58

kylekatarn
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Re: Basic Algebra for Form1 students in secondary schl

I started working with x and y directly and wasn't hard.

start with obvious things
x=x
x+x=x+x
2x=x+x

2x+x=x+x+x
3x+x=x+x+x+x

now
a(z+z')=az+az'
b(a(z+z')=(ab)(z+z')=abz+abz'

I'm not a teacher, but if I were, I would shurelly avoid fruit-algebra in my classes.

 

#5 2005-10-14 07:46:10

MathsIsFun
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Re: Basic Algebra for Form1 students in secondary schl

I actually have a page "in production" that starts something like:

2 + ? = 6
What does the "?" equal?

Then I go on to say that it is better to put an "x" instead:

2 + x = 6
What does the "x" equal?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#6 2005-10-14 14:29:16

ganesh
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Re: Basic Algebra for Form1 students in secondary schl

I was first taught the difference between variables and constants.
Thereafter, the lessons were on simple operations of addition, division, multpilication, subtraction, extracting roots, exponentiation etc.
The next step was solving linear equations in one variable, simultaneous equations of two, three variables. A little later I learnt solving quadratic equations and their properties. I forgot to mention, I was also taught plotting graphs and solving equations with graphs.
The Binomial theorem was the last I was taught, and Pascal's triangle too.


Character is who you are when no one is looking.
 

#7 2005-10-27 23:43:09

austin81
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Re: Basic Algebra for Form1 students in secondary schl

Thanks for  the clues.

 

#8 2006-03-18 08:52:04

kafkan
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Re: Basic Algebra for Form1 students in secondary schl

this is my first time to use this forum, and i hope i will be ok for me

 

#9 2006-03-18 08:55:29

kafkan
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Re: Basic Algebra for Form1 students in secondary schl

math is hard not because it requires lots of figuring but because we take it to be something hard!

 

#10 2006-03-18 10:00:27

mathsyperson
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Re: Basic Algebra for Form1 students in secondary schl

When I first came across algebra, I tried to solve the equations with trial and error.
Later on, I drew a set of scales to visualise the fact that I needed to do the same to each side.
Then I did the same method, but without the drawing, just lots of lines of working.

And now I'm able to do all kinds of crazy algebra in my head. big_smile
Just take small steps at a time.


Why did the vector cross the road?
It wanted to be normal.
 

#11 2006-03-18 15:48:52

MathsIsFun
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Re: Basic Algebra for Form1 students in secondary schl

Hi kafkan, and welcome to the forum.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#12 2012-10-16 23:11:54

austin81
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Re: Basic Algebra for Form1 students in secondary schl

Thanks for all the assistance you give students and teachers of Mathematics in this forum. We greatly appreciate that
big_smile

 

#13 2012-10-16 23:18:49

austin81
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Re: Basic Algebra for Form1 students in secondary schl

A number of books say we can use the substitution ysadm+1/m) to solve quartic equations that are symmetric i.e equations of the form ax^4 +bx^3+cx^2+bx+a=0, but do not talk much on quartic equations that are not symmetrical and are not easily factorised. The question is, are there other general methods of solving non-factorisable polynomial equations of degree greater than 3?

 

#14 2012-10-16 23:25:42

bobbym
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Re: Basic Algebra for Form1 students in secondary schl

Hi;

Welcome to the forum.

There are Descartes' and Ferrari's solutions for the general quartic but they are both difficult. There are no algebraic solutions for the general quintic or higher.

Download "First Course in the the Theory of Equations." It is free!

http://www.gutenberg.org/ebooks/29785

Down the page are the links.

Starting at page 56 of that book you will find everything you need.

If you need help with the examples he provides just post here.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#15 2012-10-17 08:23:53

ShivamS
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Re: Basic Algebra for Form1 students in secondary schl

I was taught adding variables in grade 4 and it seemed fairly easy. I was told that as long as the literal coefficients are the same, I can simply add and/or multiply the numerical coefficients depending on the operator.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann
 

#16 2012-10-18 23:21:52

austin81
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Re: Basic Algebra for Form1 students in secondary schl

Thanks

 

#17 2012-10-18 23:23:45

bobbym
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Re: Basic Algebra for Form1 students in secondary schl

Hi austin81;

You are welcome. You will find several methods in that book,


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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