As a parent of a kid who thinks you know nothing, please tell me the answer to this problem:

14-27= ?

I say it's -13

He says it's 13.

Help!!!

You are right, but that does not mean that I know anything. May you ask him why the boy has so low opinion about somebody he never met. You may also ask why he thinks the answer is 13.

Has your kid been introduced to negative integers? You should compare positive integers to money in your wallet et negative ones to debt when the wallet becomes empty.

After that, you should explain him that when you add the same integer to the 2 sides of an equality you still have an equality.

So, if 14 - 27 = 13 then 14 - 27 + 27 = 13 + 27 and 14 = 40 is wrong.

But, if 14 - 27 = -13 then 14 - 27 + 27 = -13 + 27 and 14 = 14 is correct.

Good luck!

JeanMarie

It's definately -13

>As a parent of a kid
>who thinks you know nothing,
>please tell me the answer
>to this problem:
>
> 14-27=
> ?
>
>I say it's -13
>
>He says it's 13.
>
>Help!!!

Your right! The answer is -13. Give him 14 dollars and tell him that your gonna take 27 dolalrs away. In the end, he'll see that he actually owes you 13 bucks. (The 13 bucks you can't collect because he doesn't have)

14-27= -13 so you are correct

He is thinking that subraction and addition are the same thing.

He thinks that cos 14+27 and 27+14 is the same answer so
27-14 and 14-27 is also the same.

the difference here is that you are thinking mathematically and your child isn't. He is obvioulsy interested in the difference between 14 and 27 , which is the asme as the differenc between 27 and 14.

He needs to undertstand the subraction oprerator in terms of something else e.g. taking away from

so 14-7 is the same as taking 7 away from 14 but is diiferent from taking 14 away from 7. Use money as an example.

The answer is -13.
Because the larger number has to be in front for the answer to be

positive.

Back in school our first lessons in calculus were with (imagined) oranges. You know, the kind of "If you have 7 oranges, and you get 5 more, how many do you have?"

Maybe you should try to use those with your kid when you stimulate him to find it out. People learn best when they actually have to do things. Letting your kid gain insight in this way would be better than just saying "Well, I'm right and you're wrong!"

So buy a bag of oranges (or whatever currency you want to use), give him fourteen and then ask him to give you 27 oranges back. Try the opposite situation (27 -14), and try a few other combinations. I think that that would be the best way to make him understand. Or maybe you find out that he is right - that's the beauty of experimenting :-)

Whymme

it could be his mind is picturing the equation as 27-14 instead of 14-27.
cos we have been introduced to this maths world through the method of "counting fingers" and all elementry calculations involve +ive result. (ie. "folding down" the fingers to denote minus).
Therefor its time for him to learn new concept (-ive result).it might be quite difficult at first cos there will not be any tangible visual aid for -ive number. just be patient. :)

It is a -13.

I am smart, but.... I have struggled with a good metaphor for subtracting integers. When it is equated to money, the metaphor doesn't make sense. For example, if I say that I have 7 cents and I owe Johnny 4 cents, I could express this as:

+7 + (-4)

Resulting in a net of 3 cents.

However, let's assume that I take away that four cent debt:

+7 - (-4) = ?

In the real world, I should have 7 cents. But if the subtraction algorithm is applied to the problem (turn it into an addition problem and add the opposite) I get:

+7 - (-4) = ? becomes +7 + (+4) = 11

This is the part that confuses me, because I don't have eleven cents, only seven. I'm sure that there an English language explanation of this, but I don't get it.

Instead, I have used a different metaphor passed along to me by another teacher. It involves an island where the cooks cook using special cubes: Hot cubes (+1) and Cold cubes (-1). Each cube raises or lowers the temperature of the stew by one degree. The mathematical notation in the expressions given (as an arithmetic problem) are the recipes the cooks use.

So, adding a hot cube and a cold cube changes the temperature of the stew by zero: (+1) + (-1) equals zero change in temperature. This "zero pair" of cubes is a significnt notion.

Say the recipe says: +2 + (-3)

This indicates that two hot cubes are added and three cold cubes, for a net fall in temperature of -1.

+2 + (-3) = -1

This is clear.

But what happens in subtraction?

+2 - (-3)

Consider:

If I start the pot with two hot cubes:

+
+

How can I remove three cold cubes that don't exist?

The solution is in the notion of zero pairs.

I can add three zero pairs to get

+
+
+ -
+ -
+ -

(Imagine the plusses and minuses as cubes.)

This does not change the temperature of the stew. Now I can remove three cold cubes from the stew. The result is:

+
+
+
+
+

Written as a recipe, it looks like this:

+2 - (-3) = +5

It is difficult with number lines to develop a reasonable method for subtractive movement by operation. But this metaphor holds for addition and subtraction of integers (there is an extension for multiplication that involves bunches of cubes).

Is it useful? Well, some children learn the algorithms rotely: "Turn subtraction problems into addition problems and add the opposite...."

The same children often generalize the rule and turn addition problems into subtraction problems with the opposite and the whole thing gets very messy.

I think the value could be in establishing a simple way of constructing the algorithm. If a child is presented with a problem and they are not sure of the correct algorithm, they could, with the metaphor, complete a simple problem to verify the procedure, estimate the sign and magnitude of the number, and pull the whole problem solving process into the realm of common sense and mental math.

As for the money metaphor, maybe it has something to do with double entry bookkeeping....I don't know. It just hasn't worked for me.

I welcome any further comments on this: jmeyer@cusd.net

>I am smart, but.... I have struggled with a good metaphor
>for subtracting integers. When it is equated to money, the
>metaphor doesn't make sense. For example, if I say that I
>have 7 cents and I owe Johnny 4 cents, I could express this
>as:
>
>+7 + (-4)
>
>Resulting in a net of 3 cents.

Just do not forget about that.

>However, let's assume that I take away that four cent debt:
>
>+7 - (-4) = ?

If you take away the four cent debt, you get

3 - (-4) = 7,

which is OK.

>In the real world, I should have 7 cents. But if the
>subtraction algorithm is applied to the problem (turn it
>into an addition problem and add the opposite) I get:
>
>+7 - (-4) = ? becomes +7 + (+4) = 11

No. I think the right way to describe the action is

7 + (-4) - (-4) = 7

This is what truly describes the real world situation.

>This is the part that confuses me, because I don't have
>eleven cents, only seven. I'm sure that there an English
>language explanation of this, but I don't get it.
>
>Instead, I have used a different metaphor passed along to me
>by another teacher. It involves an island where the cooks
>cook using special cubes: Hot cubes (+1) and Cold cubes
>(-1). Each cube raises or lowers the temperature of the
>stew by one degree. The mathematical notation in the
>expressions given (as an arithmetic problem) are the recipes
>the cooks use.

This is an excellent metaphor. But of course all brains work differently. It's always a good idea to have several approaches up your sleeve. No one will work with all children.

Where did you first encounter this metaphor?

Thank you.

It is -13

Your parent is correct. 14-27 is -13 because of the subtraction rule . The subtraction rule states that you must change the minus sign to addition and change the sign of the number behind it. In short terms, add it's opposite.
14-27
14 + (-27)
-13

Consider doing your addition or subtraction on a number line. To save space, I'll use the example of 3 - 5, rather than the original. On a number line, addition is done by moving to the right and subtraction is done bymoving to the left. So, if you wanted to add 1 + 2, you'd start at 1 and move 2 spaces right. Similarly, to subtract 3 - 5, you start at three and move 5 spaces left:

-4...-3...-2...-1....0....1....2....3....4....5
....................................X (start here)
...............................X (move 1 space left ...)
..........................X (move 2 spaces left ...)
.....................X (move 3 spaces left ...)
................X (move 4 spaces left ...)
...........X (move 5 spaces left ... and you're done!)

As you can see, you're now at -2, not 2. Try this with the original operation of 14 - 27, and you'll find yourself ending up at -13, not 13.

And I've just noticed that I'm typing this in a monospace font, but it will be posted in a proportional font. If you have trouble reading my diagram above, copy it into a word processor and format it into a monospace font such as Courier.

>-4...-3...-2...-1....0....1....2....3....4....5
>....................................X (start here)
>...............................X (move 1 space left ...)
>..........................X (move 2 spaces left ...)
>.....................X (move 3 spaces left ...)
>................X (move 4 spaces left ...)
>...........X (move 5 spaces left ... and you're done!)

>And I've just noticed that I'm typing this in a monospace
>font, but it will be posted in a proportional font. If you
>have trouble reading my diagram above, copy it into a word
>processor and format it into a monospace font such as
>Courier.

You can use <pre> tags (with square brackets instead of angled) if you like.

Rich