Trying to help someone with Integers

[Hero-0952]

[Sorry, that should be *Integers* up there ^]

Here is an example of what I am trying to explain to someone:
10 - (-3) + (-2) - 6 = 5

And of course the answer is 5...but how to explain the process to someone -who is just not understanding the movement across the number line - is beyond me. I am "Epic Fail" in explaining this.

Any pre-Alg instructors that could give me a few tips on getting this across to someone in layman?

Thank you for your time!! Peace!

 

[sulakvea]

Re: Trying to help someone with Intergers

use a visual effect... numbers are like a never-ending line (in each direction). each time you take a negative version of a given number - you end up at the opposite side of the pole (pole = 0). so start at 6. negative 6 is the opposite side of the pole (-6). twice negative 6 is like bouncing back and forth, you end up where you started...

 

[Sandeep Warrier]

Re: Trying to help someone with Intergers

Hi,

Using the visual number line...

Excel Workbook
	A	B	C	D	E	F	G	H	I	J	K	L
3	-5	-4	-3	-2	-1	0	1	2	3	4	5
4
Sheet1

Excel 2003

1. Positive numbers to the right of 0, negative to the left of 0.
2. In addition move towards right and in subtraction move to the left.
3. Negative numbers follow opposite of positive numbers
3. No sign before a number means "+" (i.e. addition)

Take example 2+(-2) => (2) + (-2)
Since there is no sign before the first 2 we assume it to be "+"
So, go 2 steps from 0 (reaching 2 on the number line). Now since we are adding we need to go to the right. But negative numbers follow opposite of positive numbers, so we move in the opposite direction. Moving 2 steps in the opposite direction (i.e. to the left) we reach back to 0.

So 2+(-2) = 0 (as expected)

Take example 2-(-2) => (2) - (-2)
Since there is no sign before the first 2 we assume it to be "+"
So, go 2 steps from 0 (reaching 2 on the number line). Now since we are subtracting we need to go to the left. But negative numbers follow opposite of positive numbers, so we move in the opposite direction. Moving 2 steps in the opposite direction (i.e. to the right) we reach 4.

So 2-(-2) = 4 (as expected)

Taking your example:
10 - (-3) + (-2) - 6 = 5 => (10) - (-3) + (-2) - (6)

Since there is no sign before 10 & 6 we assume it to be "+"
So, go 10 steps from 0 (reaching 10 on the number line).
Now, since we are subtracting we need to move left. But since negative numbers follow opposite direction to positive numbers we move in the opposite direction (to right). Moving 3 steps to the right we land on 13.
Now addition moves to the right but we move in the opposite direction since we are adding a negative number we move left. Moving 2 steps to the left we land on 11.
Now we subtract 6. Here we move in the normal direction (left) since we are subtracting a positive number. Moving 6 steps left from 11 we land on 5.

Thus 10-(-3)+(-2)-6 = 5 (as expected).

I hope this is not complicated . This was my own way of understanding numbers when I was in school.<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">

 

[Expiry]

Re: Trying to help someone with Intergers

I tried to help someone with integers, once. But, there was nothing I could do. It had taken hold of him and he was riddled.

Sadly, he's no longer with us. Still, I got to keep his computer.

 

[KThatcher]

I teach math... try getting them to understand the concept of "adding the opposite" to understand integers. Alternatively, combining signs to make +- = - --=+ .
Good luck. There are lots of good resources on line. Just Google Integers!

 

[Hero-0952]

Re: Trying to help someone with Intergers

I tried to help someone with integers, once...

Want to laugh, but can't justify it.

 

[Hero-0952]

Thank you all for your assistance. I did end up spending a lot of time with Sandeep's post and we were able to make some great progress using everyone's suggestions.

Again, thank you to everyone - I am sure that I will be back soon. We are passing variables and solving for 'x' already...the fun lies ahead.