The four basic operations of integers are addition, subtraction, multiplication, and division. Mastery of integer operations is essential for success in Algebra 1. An understanding of integer values placed on a number line and distance from zero (absolute value) is very important for understanding integer operations.

For the operation of addition, it is helpful to use the number line model while introducing the topic. Students should understand how to place the initial value on the number line and then add either a positive or negative integer. The idea of addition means to increase, or move to the right. When adding a positive integer, this means to move to the right. When adding a negative integer, this means to increase by the opposite of the number. When the student thinks of adding to the right, the “opposite” of the number means to change the direction.

A number line model emphasizing direction is useful for introductions. Another useful model to demonstrate the operation of addition is integer chips. Blue for positive and red for negative. Students can actually manipulate colored objects instead of using direction on a number line.

     
 


Having students memorize rules will not promote deep understanding of the operations on integers.

For the operation of subtraction, it is helpful to use the number line model while introducing the topic. Students should understand how to place the initial value on the number line and then subtract either a positive or negative integer. The idea of subtraction means to decrease, or move to the left. When subtracting a positive integer, this means to move to the left. When subtracting a negative integer this means to decrease by the opposite of the number. When the student thinks of subtracting, to the left the “opposite” of the number means to change the direction.

A number line model emphasizing direction is useful for introductions. Another useful model is integer chips. Blue for positive and red for negative. Students can actually manipulate colored objects instead of using direction on a number line.




For the operation of integer multiplication, the operation should be understood as repeated additions. For example, 5 x 3 should be adding 5 groups of 3 or 3+3+3+3+3.

Therefore, 5 x -3 should be adding 5 groups of negative 3 or
-3+-3+-3+-3+-3.

-5 x 3 means the opposite of adding 5 groups of 3 or –(3 + 3 + 3 + 3 + 3).

-5 x -3 means the opposite of adding 5 groups of negative 3, or –(-3 + -3 + -3 + -3 + -3).

For the operation of integer division, the operation should be understood as repeated subtraction. For example, 15 ÷ 3 means how many times can you subtract 3 from 15. 15 -3 -3 -3 -3 -3 = 0. 3 can be subtracted from 15, 5 times and there is no remainder.