Integers are the foundation of basic mathematics. Researchers at Northwestern University believe that children think of integers as sets, e.g., they connect the number "three" to a set of three objects. They distinguish between larger and smaller numbers by connecting the numbers to a larger or smaller number of objects. This connection helps them to relate to positive integers. However, they do not perceive negative integers in the same way. There are a number of techniques that can be used to teach children about integers and integer operations.
Motivating Children to Add and Subtract

Teach integer addition and subtraction by using store transactions as examples. Give each child 10 fake dollar bills. Have them pair up and roleplay selling each other small objects. Have them add money to their total when they sell an object and subtract money from their total when they purchase an object. Explain the concept of negative numbers by talking about the concept of "owing" someone money or having a "negative" amount of money.
Teaching With the Number Line

A number line is a visual method that can be used to teach children about integers. Create a number line with positive and negative integers on a large piece of poster board. Ask your students to move forward on the number line when they add and backward when they subtract. Divide the class into teams and give each team a different colored marker. Provide integer arithmetic problems and ask the students to mark their answers on the correct location of the poster board. Award a small prize to the team that wins.
Teaching Integer Multiplication With Cards

Use decks of cards to help children learn multiplication. Divide your students into teams and give each team a deck of cards. Have each team leader pass out three cards to each member of her team, and then say, "go." The first student to correctly multiply the three numbers on her cards gets to keep everyone's cards. The student with the most cards at the end of the game is the winner. Remove the jack, king and queen from the deck before playing.
Using Integer Multiplication to Teach Integer Division

You can teach integer division once your students have a firm grasp on integer multiplication. Set up worksheets with multiplication tables. Remove one integer on the left hand side of each equation. For example, in the problem: "3 times __ = 18," ask your students to determine what goes in the blank. Connect this to dividing the answer with the number on the lefthand side to get the answer.