The easiest way to do activities on the number line is with a series of jumps. To illustrate 8 + 5 = 13, draw one curve on the number line that goes from zero to 8, and another curve that goes from 8 to 13. All the addition examples will have two curves -- one after the other. For subtraction problems one curve will be inside the other. For example, 8 – 5 = 3 would be illustrated by two curves. One curve goes from zero to 8, and the other curve goes from 8 to 3. If you are adding and subtracting both positive and negative numbers, you can see either pattern. You can do this on the board, but it is less messy to assign as homework with multiple number lines.
You can do a sequence of operations like 3 – (+4) + (+1) – (-2) a little neater with a stack of arrows. The first arrow is drawn just above the number line from zero to +3 with the arrowhead at +3 points to the right. The second arrow starts at +3 and goes to -1 because subtracting 4 from 3 gives -1. The second arrowhead is at –1 and points left. The next arrow in the stack goes from -1 to zero. The arrowhead is at zero and points right. The next arrow goes from zero to +2, because subtracting -2 is the same as adding +2. The arrowhead is at +2 and points right. This can be done in class or as homework.
When dealing with fractions, it is necessary to draw the number lines with more distance between the integers. This activity is much more suited for in the classroom. The simplest activity is to have students come to the board and draw an arrow that points to fractions and mixed numbers. Adding and subtracting fractions on the number line is not really a good idea. You can also do decimals on a number line. Be sure to stress that pointing an arrow to the number line is only an approximation, but that number lines can be divided up into fractions. Demonstrate this by having the students look at a ruler.
A fun variation on number lines is the life-size number line. Place tape on the classroom floor, and have a student stand on the number line while students take turns shouting out instructions like “subtract minus 2”, and the student standing on the life sized number line moves to the correct answer.