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**austin81****Member**- Registered: 2005-03-21
- Posts: 39

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?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

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

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

By going to my maths lessons.

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

*Last edited by Zach (2005-10-12 10:34:43)*

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.

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

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.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 25,606

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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**austin81****Member**- Registered: 2005-03-21
- Posts: 39

Thanks for the clues.

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**kafkan****Member**- Registered: 2005-09-25
- Posts: 2

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

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**kafkan****Member**- Registered: 2005-09-25
- Posts: 2

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

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

Just take small steps at a time.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

Hi kafkan, and welcome to the forum.

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

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**austin81****Member**- Registered: 2005-03-21
- Posts: 39

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

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**austin81****Member**- Registered: 2005-03-21
- Posts: 39

A number of books say we can use the substitution y=(m+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?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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.

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**austin81****Member**- Registered: 2005-03-21
- Posts: 39

Thanks

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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