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### Integer Rules Visual References for Addition and Subtraction

We learn how to add and subtract in kindergarten. And this is about the last time addition and subtraction are easier!

When we get to the integers, there are some pretty concrete rules to follow for multiplication and division. But this isn’t so true for addition and subtraction.

This trips kids when working on integer operation problems, solving equations, finding inverses and any other time numbers on either side of zero need to be combined. Kids get to thinking they “can’t do Algebra/Algebra 2/Geometry, etc” when really it’s all integers.

So when I came across this pin leading to Don Steward’s blog post Directed Number Arithmetic Sped Up, it was exactly it. This was the visual I had been searching for to show students the relationship between positive and negative integers when combining.

I reached out to Don to see if he’d allow me to make pdf printables of his visuals, and to my happiness and excitement, he was open to it. What I love most about Don’s visuals is that the integers’ relative sizes are shown with the sizes of the circles, generalizing the “rules” for kids who need it.

There are 8 pages (4 in red/yellow and 4 black/white if you'd like to choose your own color scheme). They cover all of the +/- combination situations when adding and subtracting integers.

Not too long ago a teacher emailed to ask if I could recreate a poster from her classroom that showed the rules for multiplying and dividing integers. What I like about the tic-tac-toe chart is that it can be read in any direction. You can find this multiplying and dividing integers poster free here.

I finished updating all of my math word walls to include digital math word walls in Google Slides (they can also be downloaded as PowerPoints and still be interactive). This makes them easy to send to students working online or used as a digital vocabulary reference, even when back in the classroom. When I updated this vertical number line with its digital version, I added the integers graphics from this post so that students have more to reference.

I've been making (or maybe I should say "catching up on making") digital math activities after finally coming to terms with them being needed. I had willingly buried my head in the sand about digital and, to my total surprise, I have been absolutely loving making digital math resources! Whereas I have always been cognizant of the unavailability of color printers in schools, with digital there are no color limitations. It's been a lot of fun making digital math activities, like this integers digital math escape room

1. I have been looking all over the web for these rules without success. I will be using this site in the future; thank you.

2. These posters are awesome! My students refer to them all the time. I wish there were similar ones for multiplication!

1. Thank you! I can probably make that happen. I will put this on my to-do list for this summer and will update the file when they are done. Than you for the suggestion!

2. thank you for posting this

3. I'll try integers image today in class ans tell you how it goes

4. For integers, I like to teach the 'rules' for mult/div very differently from add/subtract. I find this helps students compartmentalize & keep them separate. Otherwise the new teaching can bleed back & interfere with sound prior learning. So where I'd use your poster ideas for add/subtract, for mult/div (once students understand the connection between these operations), I like the verbal analogy that follows for mult/div: In the movies (pos = GOOD; neg = BAD)
(1) pos; pos -- when a good thing happens to a good person, that's GOOD
(2) neg; pos -- when a bad thing happens to a good person, that's BAD
(3) pos; neg -- when a good thing happens to a bad person, that's BAD
(4) neg; neg -- when a bad thing happens to a bad person, that's GOOD
This can give rise to an interesting debate about ethics & morals, but that just helps anchor the idea. Sometimes I even have the class watch an old serial or western to lead into the lesson.

5. thank you for posting