A manipulative for integer operations

"Thesis". The word still haunts me. It took me a while to come up with a topic to study, but then it hit me: negative numbers.


integer operations tool


They're so weird
"Negative numbers?" people would ask. Absolutely! When I taught Algebra 1, adding -12 + 7 would get in the way of my students solving 10x - 7 = -12. When I was moved up to Algebra 2, the same thing was true. Kids were solving advanced equations wrong, not because they didn't know the algebra but because they couldn't combine integers in the very last steps. My students had a hard time conceptualizing negative numbers. Would the answer be negative? Would it be positive? There isn't a clean set of rules for adding with negative numbers like there is for multiplying them. 



Manipulatives
It took endless trial and error. I'd print, cut, hole punch, grommet and straighten over and over again until I finally had a numberline when the tool was straightened and opposite numbers aligned when the tool was folded in half. After getting human subjects approval, I gave each of my students a ruler and taught them how to use it. To make a long story short, my Algebra 2 students improved their ability to add and subtract integers by 62%. 

negative number adding tool

The data even amazed me. Even though I knew my students would benefit from a simple, easy to use manipulative that made negative numbers concrete, I didn't really think it would work as well as it did. My students felt more confident with integer operations and were getting more practice problems correct. 

negative number adding tool

If your students have trouble with integer operations, you can check out the Integer Operations Manipulative on Teachers pay Teachers. The download comes with simple instructions for printing, constructing and using the tool.

Moving past manipulatives
In class when an integer operation comes up, here is my line of questioning (with student responses). Let's use -12 + 7 as an example.

"Which number is farther from zero?" 
"-12"
"Ok, so the answer will be negative. How much farther away is it?"
"5"
"Ok, so your answer is -5."

More times than not I don't need to go into my absolute value speech, but I do keep it in my back pocket just in case.



Summative Activity
This integers pennant activity is a fun way to sum up an integers unit and add to class decor! Students solve the 3 problems on each pennant, cut out and color their pennants however they want, and hang them on a string in your classroom. There is also one for integer multiplication and division


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