Hands on Equations - the -x is actually X with a - thru it

dncflint

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Jan 16, 2006
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I have to solve the following type of problem and I am not sure how to do this please help.

2X + -X + 2X = 10 + X

x = ?
-X = ?
 
Re: Hands on Equations - the -x is actually X with a - thru

Hello, dncflint!

Sorry, but I don't understand the notation . . .Can you explain it?

It sounds like the equation looks like this:

\(\displaystyle \;\;\;2X\,+\,\sout{X}\,+\,2X\;=\;10\,+\,X\)


I have no idea what \(\displaystyle \sout{X}\) means.
 
The -x symbol you listed is correct. The integer for both will be the same but one will be + and the other -.
 
dncflint said:
The integer for both will be the same but one will be + and the other -.
Maybe I'm missing something, but if you mean "the absolute value for the integers will be the same, but they will have opposite signs", then how does "x with a slash through it" differ from "-x"?

Eliz.
 
This is the confusion I have with my son's worksheet. He seems to be clueless and the worksheet packet does not give explanatons at all, and there is no book to reference. Can you solve it assuming it is absolute value? It has been 35 years for me and things apparewntly changed in notations.
 
Is it possible for you to post a copy of the worksheet?
At the top of this page is ‘Forum help’. It tells you how to post an image.
 
dncflint said:
...the worksheet packet does not give explanatons at all, and there is no book to reference....It has been 35 years for me and things apparewntly changed in notations.
Well, the fact that none of us tutors has any idea what his worksheet means should indicate to you that it's not a notational problem, per se. More likely, the book and/or class is using some invented notation, specific to this book or educator. This seems, unfortunately, to be a common practice any more. :roll:

In other words: Don't feel bad; the problem ain't you. :wink:

Eliz.
 
Thanks for all your collected efforts. I think I will take this up with the administration. How can parents become involved when materials are like this.
 
Re: Hands on Equations - the -x is actually X with a - thru

dncflint said:
I have to solve the following type of problem and I am not sure how to do this please help.
2X + -X + 2X = 10 + X
x = ?
-X = ?
I have a feeling what is meant is "+(-X)", which equals -X

If that's the case, your equation is:
2X - X + 2X = 10 + X
2X = 10
X = 5
 
Denis said:
I have a feeling what is meant is....
But wouldn't it have been nice if the school could have used the regular notation then, (1) so everybody would have known what they meant and (2) so the kids wouldn't have to re-learn the topic later the "normal" way...?

...very frustrating.... :?

Eliz.
 
While I agree with what the previous responders have said, I've had some experience with this type of problem.

You'll notice that the topic was "Hands On Equations." This type of exercise is usually done using manipulatives, such as plastic chips. There is one type of chip (maybe a white square) used to represent each x. Another type of chip (perhaps a black square) is used to represent -x (or the "x with the line through it"). A white chip and a black chip, taken together, represent 0. A white chip and black chip can be removed together from one side of the equation without changing anything (not surprising, that.) Another type of chip, maybe a red circle, would be used to represent 1 unit.

The given problem,

2x + (-x) + 2x = 10 + x

could be represented with manipulatives this way (often the left and right sides of the equation are shown as the pans of a balance scale, and the equals sign is the balance point for the two pans):

2 white squares + 1 black square + 2 white squares = 10 red circles + 1 white square

The "goal" is to get 1 white chip by itself on one side of the balance scale, and some number of red chips on the other side.

On the left side, 1 of the white squares and the black square can be removed since they "cancel each other out." Now we will have

1 white square + 2 white squares = 10 red circles + 1 white square

We can now take 1 white square off each side without disturbing the balance:

2 white squares = 10 red circles

Now, if we divide what is on each side of the equals sign by 2, things should still balance:

1 white square = 5 red circles
x = 5

And since a black square "cancels out" a white square, 1 black square, or -x, is -5.

I did this in my pre-algebra classes because it was required, not because I thought it was of any great value. The smarter kids caught on right away, and easily moved using symbols like x and -x.....perhaps it has a benefit for students who learn best using a more "physical" technique. Seems to me this all came about at the same time that there was a lot of emphasis on different learning styles.

I hope this explains a bit what was going on.....
 
Mrspi said:
You'll notice that the topic was "Hands On Equations." This type of exercise is usually done using manipulatives, such as plastic chips....
So the educator was supposed to have sent blocks or "chips" home with the worksheet...?

Eliz.
 
stapel said:
So the educator was supposed to have sent blocks or "chips" home with the worksheet...?

Eliz.

In an ideal world, yes.....if the student was supposed to do these as "hands on" exercises, then manipulatives should have been provided. Alternatively, the worksheet should have been completed in the classroom where the manipulatives are available.
 
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