Fun Ways to Teach Integers
The natural and artificial worlds work by mathematical rules. The growth of plants, the temperature on a sunny day, the amount of a paycheck  all are describable by mathematical rules. The more a child understands of the world of numbers, the more likely the child will grow into an adult who is comfortable with the mathematical side of the world. A good start is developing the understanding of whole numbers, integers.

The Real World

Integers are not something made up to torture math students and teachers; they represent useful measurements of tangible quantities. The sooner that understanding can be introduced and made clear, the easier it will be to apply operations with integers. For example, if it’s necessary to take a school lunch count every day, have the entire class count and record the number on a number line in front of the class. Your class can count the number of people who brought umbrellas, and those who didn’t; or the number of students wearing something red or blue; or the number of pencils in the classroom and the number of pens.
Comparisons

Identifying numbers and connecting them with a real quantity is the first step. The second is making some use of those numbers. For example, the concept of relative size is an important one: it establishes the connection between numbers and the real world. When you measure two quantities, have the class decide which is larger or which is smaller. You can even introduce the greater than,” “less than,” and “equals” signs.

Addition

If you structure your questions correctly, you can make sure that each day’s numbers will total the number of students in the classroom. Then add the numbers together. To make this concrete  and fun  for your students, have them do it with you. If 12 students are wearing blue and 16 students wearing red, have the number of students wearing blue stand up, and start at 16. Have each child add one number to the total, then sit down. When all the students are seated, there are no more to be added. You may find that your students are disappointed if they don’t have the opportunity to count, so you may have to do it the other way as well, have the redwearing students stand and start the count at 12.
Extracurricular

You can use similar methods to introduce subtraction, multiplication, and division, incorporating integers into everyday situations. Outside of the classroom, there are dozens, if not hundreds, of online or offline software packages designed to introduce the concepts of integers and operations with integers. For a start, you can investigate some at the Jefferson County Integers page, in References.

References
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