## Sunday, August 2, 2015

### Subtracting Negative Integers: "Why do you get a Positive Answer?"

Inquiring Minds: "Why do you get a Positive Answer?"

My students had a hard time understanding why you get a positive answer when you subtract a negative in some situations.... for example 2 - -5 = 7.

"Keep - Change - Change", just did not make sense to them (of course they used the K-C-C method and memorized it - but it just didn't make sense to them).

I always remembered the rules and never questioned why this happens.  I loved that some of my students (especially one) really wanted to know "why" and wanted eagerly to understand this situation.

Therefore, I explained the hot air balloon method of where the balloon rises as you throw out (minus) a negative load.  Then recently thinking about it some more... I came up with the 'Ladder Method' which I do believe they would understand.  This integrates vertical graphing!  (YEAH, integrating positives, negatives, graphing, understanding).  I know the students would really understand this method of subtracting negative integers.  Below is a pictorial representation I drew explaining the method.

As seen in the visual representation above that I drew, the figure is on 2 with 5 negative bags and 2 + bags.... it can only go up 2 and the -5 bags are keeping you there.... if you subtract the 5 - bags then you can go up to rung 7 on the ladder.

For example -9 - -5 = -4, the Ladder Method still works....  You would be standing on -9 rung of the ladder and release -5 bags, therefore, you can go up to -4.

I'm sure I'm not the first person to think of this idea or utilize this method with their class...yet enjoy that I came up with it too, great teaching minds think to engage and teach our students!  I hope this method assists you with teaching Positive & Negative Integers.

## Best Wishes, M Moore

Certified K-6, 6-9 math, and 6-9 science

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