Operations with Negative Numbers

• Like many ideas in mathematics that are abstract or symbolic, it often helps students to have a visual model to help them conceptualize the idea. A number line is a great choice for this topic.
• Students should investigate whether the properties for addition of whole numbers hold for the addition of negative numbers.
• Make use of ideas students already know, such as multiplication being repeated addition. This can help them realize that 3 (3) = 9, since 3 + (3) + (3) = 9
• Connect the fact that multiplication is commutative to help you justify 3 4 = 12, since they already know that 4 (3) = 12.
• Give students a positive or negative number and ask them to give you two numbers whose sum, difference, product, or quotient is the given number. For example, given the number 8, it could be the product of 4 and 2.
• Don't let students say things like, "Two negatives gives a positive." They need to state, "The product of two negative numbers is positive." Otherwise, they may misuse the above when doing addition of two negative numbers.

• Introducing the Concept
• Developing the Concept

• Introducing the Concept
• Developing the Concept