I just tested my Pre-algebra class on integers and they are still struggling with negative signs. Based on the answers I checked, the kids see the problems in one of two ways.
A.) They do not recognize the negative sign with a negative number so they treat everything as positive.
B. ) They do not understand what the integer calculations represent.
With this, I am going to reteach it next week before I introduce variables. I am seriously considering having the students create a number line that resembles a slide rule so they can put the window on the first number and then slide it left or right based on the second number.
I found an activity for making a slider using a zip lock bag but I'm afraid it looks too "elementary". I want it to resemble a tool so they won't feel as if they are being treated as elementary students. I did a search for instructions so that on Monday my students can make their own.
I looked at several images and finally found one that looks like it will work.
You can see how it might work in the picture below.
I am going to have students make these on Monday so they can use these with a worksheet of problems. I'll let you know how it goes.
Just in case, I did find a web site with an interactive number line where you input the ends of the number line and it automatically creates a number line which you can then use to solve a problem. You can choose to count by any number be it one or 20. Unfortunately, it requires flash so it cannot be used on an iPad. You could use computers.