The last time I effectively taught adding & subtracting with negative numbers I was on to a good idea, but there were a couple of faults – only the kids actually walking the number line were engaged, and they lost their positional cues as soon as they went back to their desk.

So this time, every kid gets a go:

Get a bucket of Lakeshore kid counters, and print out a bunch of number lines^{1}. Have a talk about the difference between positive/negative and adding/subtracting. (i.e one thing is a property of a number, the other is something you do between two numbers). Once they kind of get it (it doesn’t need to be perfect, they just kind of need to know that there *is* a difference), go through a couple of example expressions just having them identify whether the expression involves addition or subtraction, and whether each term is positive or negative. Once they get pretty good, have them them fill in the hint blanks with walking forward/backward^{2} for positive/negative, and facing right/left for adding/subtracting.

Now comes the easy part. They find the first number on the number line, decide which way their kid should face, and whether he should go forwards or backwards. By carefully choosing mirroring problems, they can see both the difference and the similarity between swapping both operation and sign. Eventually sneak in problems that drift off of the number line, and let them start proposing rules for how to solve those problems.

^{1} Numberline pdf

^{2} A couple of kids in my third period were fixated on forward=right, backward=left, regardless of which way their kid was facing. With them I had better luck using walk/moonwalk. Feel free to demonstrate as your ability allows.

## { 5 } Comments

I love this, and am planning to copy the idea. Had my kids walk on a number line two weeks ago, but many did tune out as soon as they weren’t walking themselves.

Would you mind sharing the number line document? Generating those takes time…

I added a footnote with a pdf file. And I want video if you do the moonwalk.

This is a great trick! When teaching negative and positive integers, I model using the number line and red and chips first. I want sttudents to try to discover the rules before I teach them. I then teach them using a song. It sung to Row, Row, Your Boat.

It goes:

Same sign add and keep,

Different sign subtract.

Take the sign of the highest absolute value,

Then you’ll be exact.

I really like this idea for integers. We are starting integers next week and I have been looking for something to help my students be less confused about subtraction. Thanks!

This is a great teaching tool. Thanks for sharing.