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#1 2005-10-12 01:31:32

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

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?

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#2 2005-10-12 09:46:57

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

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

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#3 2005-10-12 10:34:21

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

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 (2005-10-12 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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#4 2005-10-13 06:08:58

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

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.

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#5 2005-10-13 09:46:10

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

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

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#6 2005-10-13 16:29:16

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,842

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.

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#7 2005-10-27 01:43:09

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

Re: Basic Algebra for Form1 students in secondary schl

Thanks for  the clues.

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#8 2006-03-17 09:52:04

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

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

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#9 2006-03-17 09:55:29

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

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!

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#10 2006-03-17 11:00:27

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

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.

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#11 2006-03-17 16:48:52

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

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

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#12 2012-10-16 00:11:54

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

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

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#13 2012-10-16 00:18:49

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

Re: Basic Algebra for Form1 students in secondary schl

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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#14 2012-10-16 00:25:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,893

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#15 2012-10-16 09:23:53

ShivamS
Member
Registered: 2011-02-07
Posts: 3,610

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.

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#16 2012-10-18 00:21:52

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

Re: Basic Algebra for Form1 students in secondary schl

Thanks

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#17 2012-10-18 00:23:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,893

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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