Re: [Math4u] maths problem

The recommended equations give at least two options for problem solving 1) substitution or 2) a system of linear equations (two equations with two variables). If for example there were 20 animals with a total of 66 legs, the equations would be written:

Cows are represented by x and chickens by y.

  x +  y = 20
4x + 2y = 66.

If the problem solving method to be used is the second as 2) a system of linear equations, Gaussian elimination is often employed. Multiply the first equation by (-2) then add it to the second equation in order to eliminate the y variables.

-2x - 2y = -40
 4x + 2y =  66 
 2x        =  26

Solve for x: x = 13.
If x = 13, then there are 13 cows. Substitute 13 into the first equation: 13 + y = 20. Solve for y:
y = 7. There are 7 chickens. Use substitution into the second equation about the number of legs to check the solution: Does 4(13) + 2(7) = 66?  Yes, 52 + 14 = 66.  Thus, 13 cows (with 4 legs) and 7 chickens (with 2 legs) have 66 legs total.

The experience of having observed cows and chickens is helpful, but not necessary. That which is necessary to solve the problem is the knowledge that cows have 4 legs and chickens have two.

The point about inner city kids not having seen cows and chickens in a farmyard is very relevant, but either a picture or a description of the essential information makes the problem manageable. 

The point is especially relevant because if the students are expected to solve the problem from past experience and without assistance, then the absence of experience with cows and chickens makes it very difficult (nearly impossible) to solve.

Teachers need to meet students at their level of understanding in order to help them develop greater understanding.

sbk

 

Rick <rcastrap@yahoo.com> wrote:

There are x cows and y chickens.

x + y = 30 animals
4x + 2y = 98 legs

-- Rick

-----Original Message-----
From: Buck Dick <kcubar34@yahoo.com>
To: Math4u@yahoogroups.com
Sent: Fri, 7 Dec 2007 9:13 am
Subject: Re: [Math4u] maths problem

Isn't it amazing how many unstated assumptions persons who write math problems expect us to make?  Are there any crippled cows or chickens in this group, any having fewer than four or two legs?  If not, state it.  Don't expect the problem solver to have that knowledge independently of the situation.  Also, don't expect every problem solver to have the knowledge that healthy, fully formed cows have four legs and the same types of chickens have two legs.  Many inner city people have never seen a cow or a chicken.

 

I once asked a group of students to estimate the distance from point A to point B in the local locale.  I did not indicate any units.  The best answer I got was US$5.00.  That was the taxi fare to go from point A to point B.  That student really thought "out of the box."

 

And while I have time to type, Vinaire, I don't like the word "opposite" in your writing, I would prefer "inverse" then it has additional applicability later.  Also the word "cancel" is being used with two different meanings.  In my language usage "cancel" means to make worthless, as in cancel a stamp.  What you are really doing is carrying out one of the operations, perhaps getting zero or perhaps the unity of the system.  Also, I again agree with Brian that left to right with operations of the same valence is the only way to go, not subtraction before addition and division before multiplication.

 

Buck Dick

Rick <rcastrap@yahoo.com> wrote:

There are x cows and y chickens.

x + y = 30 animals
4x + 2y = 98 legs

-- Rick

--- khybermaarij2000 <khybermaarij2000@yahoo.fr> wrote:

> Dear all,
> I have recently joined this group and i have a little bit english
> problems as well, bus any way now i want to write a question that
> involves math, and i have been asked this question when i wanted to
> do
> AS math in a college:
>
> In a big room we have a number of cows and chickens, a person get
> inside the room and count all the cows and chickens together and the
> total number of them is 30,
> then he counts all the legs in the floor of that room, and he notice
> that there are 98 legs together, now the question is how many cows
> and
> chicken are there in the room;
>
>
>
>
>
> Yahoo! Groups Links
>
>
>
>

---

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