[431/441] Addition by subtraction

Or vice-versa.

TRIGGER WARNING FOR MOM: There is a picture of a snake on this post.

There are several different ways that this phrase can be taken. One way that it is commonly used: when people talk about jettisoning some extra weight in their life. This could be a toxic relationship, clutter, or other problems which add to their selves.

However, I’d like to talk about the mathematical thing. Don’t worry, it will not be heavily mathematical.

When I was in kindergarten or first grade, one way that my teacher described subtraction (definitely not in these words, but follow along): “Consider that you are on the 11th floor of a building, and want to go to the seventh floor.  How many floors must you go down?  This is a way to visualize 11-7=4.)

I’m probably badly misremembering this, and it’s not exactly what I had in mind.  I just wanted to mention it.

There are two contexts where I regularly use addition by subtraction, or vice-versa. The G-word and book-keeping.

On the G-word, there tend to be good problems and bad problems.  I have rubrics for math problems which are sometimes additive (i.e. each component is worth a certain amount of points), and sometimes they are subtractive (i.e. I list a number of errors and a number of penalty points for each).

I find that for people who apparently did well, I start from the max points and subtract according to the errors.  Whereas if someone has mostly an answer full of dreck, I try to add points from zero.

At the end of the G-word for exams, I turn into a specific type of snake, as shown below.

Badger badger badger badger badger...

Snaky symbols and letters. (Oops,  wrong photo.) From my blackboard in 2013.

An adder! (Downloaded from Wikipedia, credit Józef Kazimierz Sokołowski)

An adder! (Downloaded from Wikipedia, credit Józef Kazimierz Sokołowski)

The exams have five problems, with their scores to add. If all of the numbers are fairly close to the  maximum, in order to add them I instead do what is similar to the Common Core method of subtraction: consider the max score (usually 100), and then add the LOST points and subtract that from 100.  For example, 17+19+18+20+13 = 100-(3+1+2+0+7) = 87.

On the other hand, if someone doesn’t do so well, I add the points from zero by normal addition.

In book-keeping, I find that instead of carrying when the Cents of the larger number are smaller than the Cents of the smaller number, I add a number of cents to both numbers before subtracting.  For example, $402.33 – $98.69 = $(402.33+1.31)-(98.69+1.31) = $303.64. It’s useful to add zero in some cases–this was a tenet of “Hands-On Equations” that we did in fifth grade.

I’ve touched mostly on the mathematical idea of addition by subtraction. I welcome comments on non-mathematical addition by subtraction (or vice-versa)!


Today is the four-hundred and thirty-first day of Mission 441. Ten days remain.


2 thoughts on “[431/441] Addition by subtraction

  1. Addition by subtraction in the literary sense came to mind as I read your fascinating post, Noah: You subtract superfluous words, and so forth, in order to add effectiveness by making the whole a tighter read!
    Sent your copy of the book on Monday – I hope it will be with you by early next week, but who knows with the vagaries of the post!


    • That is an excellent way to think about it, Ali. Indeed, that reminds me of my senior-level English course in high school, when we were urged to streamline our writing. It was called the “Nike” wordwatch.

      Liked by 1 person

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